From b7fc7fd81567c4b0db84dcb1b4ea541fc103f7d3 Mon Sep 17 00:00:00 2001 From: ab-jiteshlalwani Date: Tue, 26 Jul 2022 14:33:11 +0530 Subject: [PATCH 01/39] Added bussiness application file --- team 8/Business_Application.md | 0 team 8/__init__.py | 0 2 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 team 8/Business_Application.md create mode 100644 team 8/__init__.py diff --git a/team 8/Business_Application.md b/team 8/Business_Application.md new file mode 100644 index 0000000..e69de29 diff --git a/team 8/__init__.py b/team 8/__init__.py new file mode 100644 index 0000000..e69de29 From c97541ac24cec5373e7fb55e5636b05f8723751c Mon Sep 17 00:00:00 2001 From: ab-jiteshlalwani Date: Tue, 26 Jul 2022 18:40:27 +0530 Subject: [PATCH 02/39] Business application v0.1 --- team 8/Business_Application.md | 23 +++++++++++++++++++++++ team 8/images/space_debris.jpg | Bin 0 -> 127299 bytes 2 files changed, 23 insertions(+) create mode 100644 team 8/images/space_debris.jpg diff --git a/team 8/Business_Application.md b/team 8/Business_Application.md index e69de29..dd24330 100644 --- a/team 8/Business_Application.md +++ b/team 8/Business_Application.md @@ -0,0 +1,23 @@ +# Space Debris Removal Optimization + +### What is Space Debris? +Space debris (also known as space junk, space pollution, space waste, space trash, or space garbage) refers to objects that were created by humans but are no longer functional in space. +The debris includes rocket thrusters, abandoned satellites, and most importantly, fragments from collisions and explosions. It is estimated that 95% of all manmade satellites in low Earth orbit (LEO) are space junk. + +![Space Debris](https://github.com/ab-jiteshlalwani/Hackathon2022/tree/main/team%208/images/space_debris.jpg?raw=true) + +### Problems created by Space Debris +There were approximately 128 million pieces of debris under 1 cm (0.4 in), about 900,000 pieces between 1 and 10 cm, and approximately 34,000 pieces larger than 10 cm (3.9 in) in orbit around the Earth as of January 2019. + +There is a possibility that active satellites and spacecraft could be damaged by space debris traveling at tens of thousands of miles per hour. Space travel is also at risk due to all this debris. + +### Recent Events + +### Space Debris Removal Optimization + +### Potential Customers +* Space agencies such as NASA, ESA, etc. +* Space companies such as SpaceX, OneWeb, etc. +* Space debris removal startups such as CleanSpace, Astroscale, etc. + + diff --git a/team 8/images/space_debris.jpg b/team 8/images/space_debris.jpg new file mode 100644 index 0000000000000000000000000000000000000000..892f2c0b6e67b04822d4a44825871068c702fdeb GIT binary patch literal 127299 zcmb4qcRX9~`*&iMphlC{-mM7Q+MCddS&~R>rKnldrdDVvsohf4oddH#FC!O1x}?sMJOeO>SO`?}8A$Fol$Ms1W93Iqm&Kw#htbT$Wi z0-_|RfIw)eX=tb+G&C1zfIonrz#a_*c!Qc6_@;(1(o<72K&YuN!Y(o}FI>As8T8Eb^z_XC->PB;M=!i=^D$+Xjz~Y@QTM zuBqGQwU15UZ0`gAhXV|}KxE|qYaIVG4B)6V6NroqL_q~61FT36A_s;FCSxL};1vVL zp^CXjWF@AHzism0Of$MMrzYJaCg(dD4e@L#sJZ#UA*e{?D`)q&7 z3}GMWK=f(q&Gi3LpLA~*Lsdh&R&Qux8N>E4EI!e7>H7NY2hr@9_TpZSlD-s4k{JY* z0i}lL5*gt|M0yY@mk7!wS`%;v&`s)zV(S#8V16nBsPr_r&FV$ROD1!Y@kgBpop}nA zmafJOj0=xSRIP~=Z??_<7|F)Ed$=jL-$N8Zl<}A%dQTuib}3MDr~$2kUk}9C#;@l$u?FIWA0(m%a*h1P>62q*n$kHl>0)LS zG%TIUcD2cJGvS?Z2+=POnvD=zj>bk=7sG#@98Eak)UWcGXXGahi$rq-I!R)1z({WK zs*`2HDb=A6P$3Pc(#Je#B@$}T$x;Bu=tD_lnR=i-*6uIZLO3PLF#!d?a6W!i0VZ3J zKY4vX>piQ$^Kf>fspHy9+M)k^E*mC>5*ne@n=jNm{XP5fb3BW(B4vGmLem67lAJFs z_T86)G)mC)vcz!8kc8$0G1KHimY&81H;Z@L$#Ck?|FO_63QlPdei;9rOtt5tjL@HZ zTcXGjnlq4|1C7d`M>utSLuy9q{95{2EU4G5lZ3vg#Zr=Eji*60Ud7eF#s$cg;Kkvc zUZjl`EDogWPOLym?sA`%A-Fkw-y@80|7>3>2dVA$p~l-@5l7=fG*vtH(M*gbm4|7^6!wO#&YBjL)gW>P2L4)kdBo2=#?< zz9cXf-MEt;y(eImu&R0JlmRtNAS1#H=(Vt&@^G?b2T5y!7_vy8yFC=clw-g>9v5z5 zZu;8k8^8Fxh9F%B&IOXaEpqhpu?tHn23O#?JeM@jPKUIjrW2cRJ#>nKHQ$

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zFjKcQpb7ck78zF(G)WxjCu4zrc^uLx?w=E%4p3FavXd7(QO-gpfa~ zeA$>`8BB+;F0D5~ofyLM!~u;-buKD(s|Mf>ErEs8l~t5^Hu4`05mV44#oSaUEiHuY zSbAZM(1>$)vav9Ev|>W0akXGmhtkXQ(v|H z48`GhHor1fORXM;{QMS3=gTn#08o=eZz!DGg!dx8B1sBBj%obx)EY~uRO+mj9iAzV zD=I%}xU%=4v~SN>9c-%1?d&sJ$)w45bIC9)+d>qz;(%a6lg{D`zAh8+?h2s);95t0eNIVQVEpH_u^g950R|lEGVRQN&u?}g<~OPPG0#f=8P)yU*%G-3dK|R z?U3A1f(%|`#G)jQZd0dbMMADoiVTnA%uwrdEfNbSP=hBac3aP5j~=|_LLkZzF+1$kFlnW=M4 kk{kh;mT#<3%>wAtLwnHPL|L5}w3$lGSC)6#h5t Date: Tue, 26 Jul 2022 18:53:30 +0530 Subject: [PATCH 03/39] Added gitignore file --- .gitignore | 213 +++++++++++++++++++++++++++++++++ team 8/Business_Application.md | 12 +- 2 files changed, 222 insertions(+), 3 deletions(-) create mode 100644 .gitignore diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..93d2055 --- /dev/null +++ b/.gitignore @@ -0,0 +1,213 @@ +### Python template +# Byte-compiled / optimized / DLL files +__pycache__/ +*.py[cod] +*$py.class + +# C extensions +*.so + +# Distribution / packaging +.Python +build/ +develop-eggs/ +dist/ +downloads/ +eggs/ +.eggs/ +lib/ +lib64/ +parts/ +sdist/ +var/ +wheels/ +share/python-wheels/ +*.egg-info/ +.installed.cfg +*.egg +MANIFEST + +# PyInstaller +# Usually these files are written by a python script from a template +# before PyInstaller builds the exe, so as to inject date/other infos into it. +*.manifest +*.spec + +# Installer logs +pip-log.txt +pip-delete-this-directory.txt + +# Unit test / coverage reports +htmlcov/ +.tox/ +.nox/ +.coverage +.coverage.* +.cache +nosetests.xml +coverage.xml +*.cover +*.py,cover +.hypothesis/ +.pytest_cache/ +cover/ + +# Translations +*.mo +*.pot + +# Django stuff: +*.log +local_settings.py +db.sqlite3 +db.sqlite3-journal + +# Flask stuff: +instance/ +.webassets-cache + +# Scrapy stuff: +.scrapy + +# Sphinx documentation +docs/_build/ + +# PyBuilder +.pybuilder/ +target/ + +# Jupyter Notebook +.ipynb_checkpoints + +# IPython +profile_default/ +ipython_config.py + +# pyenv +# For a library or package, you might want to ignore these files since the code is +# intended to run in multiple environments; otherwise, check them in: +# .python-version + +# pipenv +# According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. +# However, in case of collaboration, if having platform-specific dependencies or dependencies +# having no cross-platform support, pipenv may install dependencies that don't work, or not +# install all needed dependencies. +#Pipfile.lock + +# PEP 582; used by e.g. github.com/David-OConnor/pyflow +__pypackages__/ + +# Celery stuff +celerybeat-schedule +celerybeat.pid + +# SageMath parsed files +*.sage.py + +# Environments +.env +.venv +env/ +venv/ +ENV/ +env.bak/ +venv.bak/ + +# Spyder project settings +.spyderproject +.spyproject + +# Rope project settings +.ropeproject + +# mkdocs documentation +/site + +# mypy +.mypy_cache/ +.dmypy.json +dmypy.json + +# Pyre type checker +.pyre/ + +# pytype static type analyzer +.pytype/ + +# Cython debug symbols +cython_debug/ + +### JetBrains template +# Covers JetBrains IDEs: IntelliJ, RubyMine, PhpStorm, AppCode, PyCharm, CLion, Android Studio, WebStorm and Rider +# Reference: https://intellij-support.jetbrains.com/hc/en-us/articles/206544839 + +# User-specific stuff +.idea/**/workspace.xml +.idea/**/tasks.xml +.idea/**/usage.statistics.xml +.idea/**/dictionaries +.idea/**/shelf + +# Generated files +.idea/**/contentModel.xml + +# Sensitive or high-churn files +.idea/**/dataSources/ +.idea/**/dataSources.ids +.idea/**/dataSources.local.xml +.idea/**/sqlDataSources.xml +.idea/**/dynamic.xml +.idea/**/uiDesigner.xml +.idea/**/dbnavigator.xml + +# Gradle +.idea/**/gradle.xml +.idea/**/libraries + +# Gradle and Maven with auto-import +# When using Gradle or Maven with auto-import, you should exclude module files, +# since they will be recreated, and may cause churn. Uncomment if using +# auto-import. +# .idea/artifacts +# .idea/compiler.xml +# .idea/jarRepositories.xml +# .idea/modules.xml +# .idea/*.iml +# .idea/modules +# *.iml +# *.ipr + +# CMake +cmake-build-*/ + +# Mongo Explorer plugin +.idea/**/mongoSettings.xml + +# File-based project format +*.iws + +# IntelliJ +out/ + +# mpeltonen/sbt-idea plugin +.idea_modules/ + +# JIRA plugin +atlassian-ide-plugin.xml + +# Cursive Clojure plugin +.idea/replstate.xml + +# Crashlytics plugin (for Android Studio and IntelliJ) +com_crashlytics_export_strings.xml +crashlytics.properties +crashlytics-build.properties +fabric.properties + +# Editor-based Rest Client +.idea/httpRequests + +# Android studio 3.1+ serialized cache file +.idea/caches/build_file_checksums.ser + diff --git a/team 8/Business_Application.md b/team 8/Business_Application.md index dd24330..779956d 100644 --- a/team 8/Business_Application.md +++ b/team 8/Business_Application.md @@ -4,20 +4,26 @@ Space debris (also known as space junk, space pollution, space waste, space trash, or space garbage) refers to objects that were created by humans but are no longer functional in space. The debris includes rocket thrusters, abandoned satellites, and most importantly, fragments from collisions and explosions. It is estimated that 95% of all manmade satellites in low Earth orbit (LEO) are space junk. -![Space Debris](https://github.com/ab-jiteshlalwani/Hackathon2022/tree/main/team%208/images/space_debris.jpg?raw=true) +![Space Debris](./images/space_debris.jpg) -### Problems created by Space Debris +### Problems Created by Space Debris There were approximately 128 million pieces of debris under 1 cm (0.4 in), about 900,000 pieces between 1 and 10 cm, and approximately 34,000 pieces larger than 10 cm (3.9 in) in orbit around the Earth as of January 2019. -There is a possibility that active satellites and spacecraft could be damaged by space debris traveling at tens of thousands of miles per hour. Space travel is also at risk due to all this debris. +Space debris orbits around the earth at tremendous speeds - about 15,700 miles per hour (25,265 kph) in low Earth orbit which is 10 times the speed of a bullet. So there is a possibility that active satellites and spacecraft could be damaged by space debris. Space travel is also at risk due to all this debris. ### Recent Events ### Space Debris Removal Optimization +* SpaceX starlink satellites ### Potential Customers * Space agencies such as NASA, ESA, etc. * Space companies such as SpaceX, OneWeb, etc. * Space debris removal startups such as CleanSpace, Astroscale, etc. +### Business Value + +### References: +* https://en.wikipedia.org/wiki/Space_debris +* https://www.youtube.com/watch?v=Ctvzf_p0qUA From 9077e33e5d1f3c8db6cfd623b504ed48d88c3a7f Mon Sep 17 00:00:00 2001 From: ab-jiteshlalwani Date: Tue, 26 Jul 2022 21:49:50 +0530 Subject: [PATCH 04/39] Updated business application --- team 8/Business_Application.md | 30 ++++++++++++++++++++++++++++-- team 8/images/knapsack.png | Bin 0 -> 277635 bytes 2 files changed, 28 insertions(+), 2 deletions(-) create mode 100644 team 8/images/knapsack.png diff --git a/team 8/Business_Application.md b/team 8/Business_Application.md index 779956d..03b1be4 100644 --- a/team 8/Business_Application.md +++ b/team 8/Business_Application.md @@ -11,19 +11,45 @@ There were approximately 128 million pieces of debris under 1 cm (0.4 in), about Space debris orbits around the earth at tremendous speeds - about 15,700 miles per hour (25,265 kph) in low Earth orbit which is 10 times the speed of a bullet. So there is a possibility that active satellites and spacecraft could be damaged by space debris. Space travel is also at risk due to all this debris. +A large amount of space debris in orbit could hinder satellite activities for many generations to come. + +Kessler syndrome (also called Kessler effect) was proposed by NASA scientist Donald J. Kessler in 1978 as a scenario where collisions between objects in low Earth orbit (LEO) may result in a cascade creating space debris and increasing collision likelihood. According to Kessler, modeling results concluded in 2009 that the debris environment was already unstable, "such that attempts to eliminate past debris sources will likely fail since fragments from future collisions will be generated faster than atmospheric drag can remove them." + ### Recent Events +* Space junk slams into International Space Station, leaving hole in robotic arm: Space junk hurtling towards the station smashed into one of its robotic arms, leaving a hole. +NASA and the Canadian Space Agency first noticed the damage on Canadarm2 on May 12, according to a recent statement. The debris left a gaping hole in a section of the arm boom and thermal blanket. +* International Space Station swerves to dodge space junk: +The ISS had been forced to move due to space junk from a U.S. launch vehicle sent into orbit in 1994. + A close encounter was avoided by dropping by 310 metres (339 yards) as part of an unscheduled maneuver carried out by mission control. + ### Space Debris Removal Optimization -* SpaceX starlink satellites +In space debris removal optimization, the goal is to create an optimal path for satellite vessels to collect as much debris as possible in one pass, while saving fuel. As a result, space debris collection will take fewer days overall. + +A space debris removal optimization could also be described as combinatorial optimization, which is searching for maxima (or minima) of an objective function F whose domain is a discrete but large configuration space (in contrast to an N-dimensional continuous space). + +![Space Debris](./images/knapsack.png) + +This can be also considered as a Knapsack problem where the goal is to determine the number of items each with a weight and value to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. According to its name, it refers to the problem of filling a fixed-size knapsack with valuable items when constrained by a fixed size. A similar problem occurs when decision-makers have to select from a set of non-divisible projects or tasks within a fixed budget or timeframe. ### Potential Customers * Space agencies such as NASA, ESA, etc. +* Governments across the world. * Space companies such as SpaceX, OneWeb, etc. * Space debris removal startups such as CleanSpace, Astroscale, etc. -### Business Value +### Architecture + +We gather open source space debris data and encode it for Pennylane from Xanadu. As a pre-processing step, we also use AI to clean and rank debris according to size, collection cost, etc. + +### Business Model +Yearly Subscription: Our solution is scalable and can be used by several space companies or agencies with no or minimal changes. Our model returns the optimal path for satellite vessels to collect as much debris as possible in one pass. +We offer both on-premises and cloud deployment options for our model on yearly subscription basis. ### References: * https://en.wikipedia.org/wiki/Space_debris * https://www.youtube.com/watch?v=Ctvzf_p0qUA +* https://www.cbsnews.com/news/space-junk-damage-international-space-station +* https://www.reuters.com/lifestyle/science/international-space-station-swerves-dodge-space-junk-2021-12-03 +* https://en.wikipedia.org/wiki/Knapsack_problem \ No newline at end of file diff --git a/team 8/images/knapsack.png b/team 8/images/knapsack.png new file mode 100644 index 0000000000000000000000000000000000000000..9143970739e941df9ca3714ce71c3b1d55bca38f GIT binary patch literal 277635 zcmeFYcOcdM`#*jVvR8Ig9Arhv9)+^^PDUizJA0L#kz-{?HrZP^C4|V9eIzU6oQ!O~ z&qH_J@6YG+{eJ%Z{qu7>_ucIr&*$~LuE+Jb9@q7J6|Sx-M}$v@4}n046y#+!ArRaE 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z^8o+#=MX^vTKeH9l+)(V+;`PxoSP;$C!BHOn|}ZL1~~hvEdo8S0!A|^`c-sH?_Kpt z=t`!4>#@+!;?+<8`Cg3;Pz}+lKg0xCFf9TnPGy}hk^Sel%6{dlmNEX7VqeEgwN!{9 zvmgKY9V9MnXnyh%=iR^`H~;Nl|M}6Ej!}@l!1(*oH9AU)DZl;m+y9^Zw7p+)vb5TP S)xUu;pu4JCD!Dfwzy3dDr7Rl& literal 0 HcmV?d00001 From 99a7a84488d0d623017d1920a20d9e3372bb665e Mon Sep 17 00:00:00 2001 From: ab-jiteshlalwani Date: Wed, 27 Jul 2022 11:53:16 +0530 Subject: [PATCH 05/39] Updated potential customers and archiecture text --- .gitignore | 2 ++ team 8/Business_Application.md | 21 +++++++++++---------- 2 files changed, 13 insertions(+), 10 deletions(-) diff --git a/.gitignore b/.gitignore index 93d2055..d62621e 100644 --- a/.gitignore +++ b/.gitignore @@ -142,6 +142,8 @@ cython_debug/ # Covers JetBrains IDEs: IntelliJ, RubyMine, PhpStorm, AppCode, PyCharm, CLion, Android Studio, WebStorm and Rider # Reference: https://intellij-support.jetbrains.com/hc/en-us/articles/206544839 +# Entire idea folder +.idea/* # User-specific stuff .idea/**/workspace.xml .idea/**/tasks.xml diff --git a/team 8/Business_Application.md b/team 8/Business_Application.md index 03b1be4..755887f 100644 --- a/team 8/Business_Application.md +++ b/team 8/Business_Application.md @@ -13,13 +13,12 @@ Space debris orbits around the earth at tremendous speeds - about 15,700 miles p A large amount of space debris in orbit could hinder satellite activities for many generations to come. -Kessler syndrome (also called Kessler effect) was proposed by NASA scientist Donald J. Kessler in 1978 as a scenario where collisions between objects in low Earth orbit (LEO) may result in a cascade creating space debris and increasing collision likelihood. According to Kessler, modeling results concluded in 2009 that the debris environment was already unstable, "such that attempts to eliminate past debris sources will likely fail since fragments from future collisions will be generated faster than atmospheric drag can remove them." +**Kessler syndrome** (also called Kessler effect) was proposed by NASA scientist Donald J. Kessler in 1978 as a scenario where collisions between objects in low Earth orbit (LEO) may result in a cascade creating space debris and increasing collision likelihood. According to Kessler, modeling results concluded in 2009 that the debris environment was already unstable, "such that attempts to eliminate past debris sources will likely fail since fragments from future collisions will be generated faster than atmospheric drag can remove them." ### Recent Events -* Space junk slams into International Space Station, leaving hole in robotic arm: Space junk hurtling towards the station smashed into one of its robotic arms, leaving a hole. +* **Space junk slams into International Space Station, leaving hole in robotic arm:** Space junk hurtling towards the station smashed into one of its robotic arms, leaving a hole. NASA and the Canadian Space Agency first noticed the damage on Canadarm2 on May 12, according to a recent statement. The debris left a gaping hole in a section of the arm boom and thermal blanket. -* International Space Station swerves to dodge space junk: -The ISS had been forced to move due to space junk from a U.S. launch vehicle sent into orbit in 1994. +* **International Space Station swerves to dodge space junk:** The ISS had been forced to move due to space junk from a U.S. launch vehicle sent into orbit in 1994. A close encounter was avoided by dropping by 310 metres (339 yards) as part of an unscheduled maneuver carried out by mission control. @@ -33,19 +32,21 @@ A space debris removal optimization could also be described as combinatorial opt This can be also considered as a Knapsack problem where the goal is to determine the number of items each with a weight and value to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. According to its name, it refers to the problem of filling a fixed-size knapsack with valuable items when constrained by a fixed size. A similar problem occurs when decision-makers have to select from a set of non-divisible projects or tasks within a fixed budget or timeframe. ### Potential Customers -* Space agencies such as NASA, ESA, etc. -* Governments across the world. -* Space companies such as SpaceX, OneWeb, etc. -* Space debris removal startups such as CleanSpace, Astroscale, etc. +* Space agencies, like NASA, ESA, etc, are potential customers because space debris can hinder their missions. +* Governments around the world are also our potential customers since space debris can interfere with satellite operations as this is a matter of national security. In addition, it is related to the sustainability of space. +* Space companies such as SpaceX and OneWeb, which plan to deploy 40,000+ satellites in the near future, will also be interested in our product since they wish to avoid collisions with space debris. +* We believe that startups such as CleanSpace, Astroscale, and others who are interested in space debris removal will be interested in our product since they want to collect more space debris with less cost and mission time. ### Architecture -We gather open source space debris data and encode it for Pennylane from Xanadu. As a pre-processing step, we also use AI to clean and rank debris according to size, collection cost, etc. +We gather open source space debris data and encode it for quantum computers. Our model is platform agnostic and can be run either on IBM hardware or Xanadu hardware. In the near future, it will be also possible to run our model on quantum annealers such as D-Wave hardware. + +As a pre-processing step, we also use AI to clean and rank debris according to size, collection cost, etc. ### Business Model Yearly Subscription: Our solution is scalable and can be used by several space companies or agencies with no or minimal changes. Our model returns the optimal path for satellite vessels to collect as much debris as possible in one pass. -We offer both on-premises and cloud deployment options for our model on yearly subscription basis. +We offer both on-premises and cloud deployment options for our model on a yearly subscription basis. ### References: * https://en.wikipedia.org/wiki/Space_debris From 8740f0bc8bcc12e0a780aaedac5534ddb437f49f Mon Sep 17 00:00:00 2001 From: JPazem <109220752+JPazem@users.noreply.github.com> Date: Wed, 27 Jul 2022 09:56:21 +0200 Subject: [PATCH 06/39] Add files via upload --- team 8/space_debris_collection.ipynb | 771 +++++++++++++++++++++++++++ 1 file changed, 771 insertions(+) create mode 100644 team 8/space_debris_collection.ipynb diff --git a/team 8/space_debris_collection.ipynb b/team 8/space_debris_collection.ipynb new file mode 100644 index 0000000..3ed2a24 --- /dev/null +++ b/team 8/space_debris_collection.ipynb @@ -0,0 +1,771 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "space_debris_collection.ipynb", + "provenance": [] + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "iEYhchm4dvze", + "outputId": "0647ac5d-3647-4be3-e094-0b88c3a6a1bd" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n", + "Collecting pennylane\n", + " Downloading PennyLane-0.24.0-py3-none-any.whl (957 kB)\n", + "\u001b[K |████████████████████████████████| 957 kB 6.7 MB/s \n", + "\u001b[?25hCollecting pennylane-lightning>=0.24\n", + " Downloading PennyLane_Lightning-0.24.0-cp37-cp37m-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (9.3 MB)\n", + "\u001b[K |████████████████████████████████| 9.3 MB 27.1 MB/s \n", + "\u001b[?25hRequirement already satisfied: appdirs in /usr/local/lib/python3.7/dist-packages (from pennylane) (1.4.4)\n", + "Collecting semantic-version==2.6\n", + " Downloading semantic_version-2.6.0-py3-none-any.whl (14 kB)\n", + "Requirement already satisfied: cachetools in /usr/local/lib/python3.7/dist-packages (from pennylane) (4.2.4)\n", + "Collecting retworkx\n", + " Downloading retworkx-0.11.0-cp37-cp37m-manylinux_2_5_x86_64.manylinux1_x86_64.manylinux_2_12_x86_64.manylinux2010_x86_64.whl (1.6 MB)\n", + "\u001b[K |████████████████████████████████| 1.6 MB 47.5 MB/s \n", + "\u001b[?25hRequirement already satisfied: autograd in /usr/local/lib/python3.7/dist-packages (from pennylane) (1.4)\n", + "Requirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from pennylane) (1.21.6)\n", + "Collecting toml\n", + " Downloading toml-0.10.2-py2.py3-none-any.whl (16 kB)\n", + "Collecting autoray>=0.3.1\n", + " Downloading autoray-0.3.2-py3-none-any.whl (36 kB)\n", + "Requirement already satisfied: networkx in /usr/local/lib/python3.7/dist-packages (from pennylane) (2.6.3)\n", + "Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from pennylane) (1.7.3)\n", + "Collecting ninja\n", + " Downloading ninja-1.10.2.3-py2.py3-none-manylinux_2_5_x86_64.manylinux1_x86_64.whl (108 kB)\n", + "\u001b[K |████████████████████████████████| 108 kB 48.6 MB/s \n", + "\u001b[?25hRequirement already satisfied: future>=0.15.2 in /usr/local/lib/python3.7/dist-packages (from autograd->pennylane) (0.16.0)\n", + "Installing collected packages: ninja, toml, semantic-version, retworkx, pennylane-lightning, autoray, pennylane\n", + "Successfully installed autoray-0.3.2 ninja-1.10.2.3 pennylane-0.24.0 pennylane-lightning-0.24.0 retworkx-0.11.0 semantic-version-2.6.0 toml-0.10.2\n", + "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n", + "Requirement already satisfied: networkx in /usr/local/lib/python3.7/dist-packages (2.6.3)\n" + ] + } + ], + "source": [ + "import sys\n", + "!{sys.executable} -m pip install pennylane\n", + "!{sys.executable} -m pip install networkx" + ] + }, + { + "cell_type": "code", + "source": [ + "import networkx as nx\n", + "import pennylane as qml\n", + "from pennylane import numpy as np \n", + "import matplotlib.pyplot as plt" + ], + "metadata": { + "id": "vTd6PsprHhIm" + }, + "execution_count": 5, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "# Space debris optimization" + ], + "metadata": { + "id": "wr3gMLPUepdb" + } + }, + { + "cell_type": "markdown", + "source": [ + "In this work, we solve the combinatorial optimization problem of space debris collection. A challenge for space agencies, satellite producers and any actor involved in space travel is to avoid space debris. In spite of possibly small sizes, their speeds on orbits make any collision with satellite or spacecraft threaten the success of space expeditions with major damage. Therefore, a major concern is to collect these debris and destroy them at the entrance of the atmosphere." + ], + "metadata": { + "id": "FdAx9nEVeytw" + } + }, + { + "cell_type": "markdown", + "source": [ + "The problem is the following. Debris collection journeys are expensive, since the quantity of fuels used to propel the engins is massive, and the capacity of each space craft limits the amount of space garbage that can be collected. To optimize each trip to space, we must therefore seek debris located at particular locations, such that they minimize the distance and hence the fuel consumption, and they maximize the quantity of trash collected. We solve the latter problem first, and add further constraints to the problem progressively." + ], + "metadata": { + "id": "sMUPN0CCfzsU" + } + }, + { + "cell_type": "markdown", + "source": [ + "### Formulation of the cost function " + ], + "metadata": { + "id": "wKXwHlEhP2_-" + } + }, + { + "cell_type": "markdown", + "source": [ + "Let us first consider the problem of maximization of the volume of trash that is collected. This task is related to the knapsack problem. \n", + "\n", + "We start with a set of N debris. We encode the information about the debris to collect in a bitstring:\n", + "\\begin{equation}\n", + "z = z_1 z_2 \\cdots z_N, \\text{where } z_i = \\begin{cases}\n", + "1, & \\text{if debris i is collected} \\\\\n", + "0, & \\text{if otherwise.}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "To solve the problem with brute force method, we must inspect all possible bitstrings $z$ and pick the one that maximizes the volume of the debris collected. Therefore, it is a combinatorial optimization problem. To formulate it, we pair each debris $i$ with its weight/size $w_i$. The debris locations can be reported on a graph with edge set $E$ and vertex set $V$ such that $G = \\{E,V\\}$. Each vertex is associated with a weight, and each edge $i -j$ with a distance $d_{ij}$. With these notations, we encode the problem into the cost function:\n", + "\\begin{equation}\n", + "C(z) = (V-\\sum_{i=1}^{N} w_i z_i)^2 + \\sum_{i, j=1}^{N} d_{ij} z_i z_j\n", + "\\end{equation}\n", + "where the first term corresponds to the knapsack problem and the second aims at minimizing the travelled distance. To simplify the implementation, the constant term can be removed:\n", + "\\begin{align}\n", + "C(z) &= (-2V\\sum_{i=1}^{N} w_i z_i + 2\\sum_{ii} g_{ij} -\\sum_{j 1]\n", + "light_edges = [(u, v) for (u, v, d) in G.edges(data=True) if d[\"weight\"] <= 1]\n", + "pos = nx.spring_layout(G, seed=11) \n", + "nx.draw_networkx_nodes(G, pos, node_size=700, node_color=\"r\")\n", + "nx.draw_networkx_edges(G, pos, edgelist=heavy_edges, width=6)\n", + "nx.draw_networkx_edges(G, pos, edgelist=light_edges, width=6, edge_color=\"b\", style=\"dashed\")\n", + "nx.draw_networkx_labels(G, pos, font_size=20, font_family=\"sans-serif\")\n", + "edge_labels = nx.get_edge_attributes(G, \"weight\")\n", + "nx.draw_networkx_edge_labels(G, pos, edge_labels)\n", + " \n", + "#nx.draw(G, with_labels=True, alpha=0.8, node_size=300)\n", + "\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 418 + }, + "id": "987QfIbfgt6D", + "outputId": "329c4481-f867-409f-dc81-467fc2ec0d07" + }, + "execution_count": 6, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "{('0', '1'): Text(-0.31213490044069825, 0.0229285235823255, '1'),\n", + " ('0', '2'): Text(0.18180059090333675, -0.7976561108038269, '2'),\n", + " ('0', '3'): Text(-0.6981592185316541, -0.4262551763130149, '2'),\n", + " ('0', '4'): Text(0.2340158724740534, -0.207744883060842, '1'),\n", + " ('1', '2'): Text(0.26598412752594675, 0.16442417717540436, '1'),\n", + " ('1', '3'): Text(-0.6139756819090442, 0.5358251116662163, '2'),\n", + " ('1', '4'): Text(0.3181994090966634, 0.7543354049183892, '2'),\n", + " ('2', '3'): Text(-0.12004019056500914, -0.28475952271993604, '1'),\n", + " ('2', '4'): Text(0.8121349004406984, -0.06624922946776313, '2'),\n", + " ('3', '4'): Text(-0.0678249089942925, 0.30515170502304884, '1')}" + ] + }, + "metadata": {}, + "execution_count": 6 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "We implement the QAOA algorithm on this data set. We choose:\n", + "- Mixer Hamiltonian: $\\hat{H}_M = \\sum_{i=0}^{N-1} X_i$\n", + "- Problem Hamiltonin as defined above\n", + "\n", + "For an approximate Trotterization with p steps, the evolution yields the following state:\n", + "\\begin{equation}\n", + "|\\overrightarrow{\\gamma}, \\overrightarrow{\\beta}\\rangle = e^{i\\beta_p H_M} e^{i\\gamma_p H_P} \\cdots e^{i\\beta_1 H_M} e^{i\\gamma_1 H_P}|+\\rangle^{\\otimes{N}}\n", + "\\end{equation}\n", + "where $|+\\rangle^{\\otimes{N}} = \\frac{1}{\\sqrt{2^N}} \\sum_{z\\in \\{0,1\\}^N} |z\\rangle $ is an equal superposition of all bitstrings." + ], + "metadata": { + "id": "QiItM9uZKZoU" + } + }, + { + "cell_type": "code", + "source": [ + "dev = qml.device(\"default.qubit\", wires=len(G.nodes()), shots= 1024)\n", + "\n", + "@qml.qnode(dev)\n", + "def QAOA_Circuit(G, weights, V, p, angles):\n", + " N_vertices = len(G.nodes())\n", + " wires = range(N_vertices)\n", + " distances = nx.get_edge_attributes(G, \"weight\")\n", + "\n", + " # Initialize the states\n", + " for i in range(N_vertices):\n", + " qml.Hadamard(wires=wires[i])\n", + "\n", + " # Apply QAOA\n", + " gammas = angles[:p]\n", + " beta = angles[p:]\n", + "\n", + " problem_coef = []\n", + " problem_operators = []\n", + "\n", + " for step in range(0, p):\n", + " \n", + " # Apply the problem Hamiltonian\n", + " \n", + " for i in range(0, N_vertices):\n", + " coef_single = V*weights[i] - sum([v for k,v in distances.items() if str(i) in k])\n", + " qml.RZ(coef_single*gammas[step], wires=wires[i])\n", + " if step == 1:\n", + " problem_coef += [coef_single]\n", + " problem_operators += [qml.PauliZ(wires=wires[i])]\n", + "\n", + " for j in range(i+1, N_vertices):\n", + " coef_double = (1/2*weights[i]*weights[j] + 1/4*nx.get_edge_attributes(G, \"weight\")[(str(i), str(j))])\n", + " qml.MultiRZ(gammas[step]*coef_double, wires=[wires[i]]+[wires[j]])\n", + " if step == 1:\n", + " problem_coef += [coef_double]\n", + " problem_operators += [qml.PauliZ(wires[i]) @ qml.PauliZ(wires[j])]\n", + "\n", + "\n", + " # Apply the mixer Hamiltonian\n", + " for i in range(0, N_vertices):\n", + " qml.RX(beta[step], wires=wires[i])\n", + "\n", + " # Compute the expectation value of the problem Hamiltonian\n", + " # problem_H = qml.Hamiltonian(problem_coef, problem_operators)\n", + "\n", + " return qml.expval(qml.Hamiltonian(problem_coef, problem_operators))\n" + ], + "metadata": { + "id": "zc9MhBK3MJqV" + }, + "execution_count": 7, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "@qml.qnode(dev)\n", + "def QAOA_Circuit_optimized_probas(G, weights, V, p, angles):\n", + " N_vertices = len(G.nodes())\n", + " wires = range(N_vertices)\n", + " distances = nx.get_edge_attributes(G, \"weight\")\n", + "\n", + " # Initialize the states\n", + " for i in range(N_vertices):\n", + " qml.Hadamard(wires=wires[i])\n", + "\n", + " # Apply QAOA\n", + " gammas = angles[:p]\n", + " beta = angles[p:]\n", + "\n", + " for step in range(0, p):\n", + " \n", + " # Apply the problem Hamiltonian\n", + " \n", + " for i in range(0, N_vertices):\n", + " coef_single = V*weights[i] - sum([v for k,v in distances.items() if str(i) in k])\n", + " qml.RZ(coef_single*gammas[step], wires=wires[i])\n", + "\n", + " for j in range(i+1, N_vertices):\n", + " coef_double = (1/2*weights[i]*weights[j] + 1/4*nx.get_edge_attributes(G, \"weight\")[(str(i), str(j))])\n", + " qml.MultiRZ(gammas[step]*coef_double, wires=[wires[i]]+[wires[j]])\n", + "\n", + " # Apply the mixer Hamiltonian\n", + " for i in range(0, N_vertices):\n", + " qml.RX(beta[step], wires=wires[i])\n", + "\n", + " return qml.probs(wires)" + ], + "metadata": { + "id": "ZKp_UBGi23J6" + }, + "execution_count": 151, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Optimize the angles\n", + "def cost_function(G, weights, V, p, angles):\n", + " def optimizable_object(angles):\n", + " cost_exp_val = QAOA_Circuit(G, weights, V, p, angles)\n", + " return cost_exp_val\n", + " return optimizable_object" + ], + "metadata": { + "id": "i3CKY8f0mdV1" + }, + "execution_count": 105, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Parameters\n", + "V = 10\n", + "weights = np.array([1,2,7,4,5], requires_grad=False)\n", + "p=2\n", + "\n", + "angles = np.array(2*p*[np.pi/4], requires_grad=True)\n", + "#angles = np.pi/p*np.array(2*p*[0])\n", + "shots=1024\n", + "\n", + "dev = qml.device(\"default.qubit\", wires=len(G.nodes()), shots=shots)" + ], + "metadata": { + "id": "7hZXeG4dOj1w" + }, + "execution_count": 235, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "circuit = QAOA_Circuit(G, weights, V, p, angles)" + ], + "metadata": { + "id": "c2H1BfBmu6Ma" + }, + "execution_count": 236, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "from scipy.optimize import minimize\n", + "cost = cost_function(G, weights, V, p, angles)\n", + "optimized_params = minimize(cost, angles, method='COBYLA')\n", + "optimized_angles = optimized_params.x\n", + "\n", + "#optimizer = qml.GradientDescentOptimizer(stepsize=0.8)\n", + "#cost = cost_function(G, weights, V, p, angles)\n", + "#for k in range(100):\n", + "# if k % 5 == 0:\n", + "# print(f\"Step {k}, cost: {cost(angles)}\")\n", + "# angles = optimizer.step(cost, angles)\n", + "#optimized_angles = angles" + ], + "metadata": { + "id": "t-XpCGgc1edP" + }, + "execution_count": 237, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "proba_opt = QAOA_Circuit_optimized_probas(G, weights, V, p, optimized_angles)\n", + "exp_val_opt = QAOA_Circuit(G, weights, V, p, optimized_angles)\n", + "#probas_opt = result(0)\n", + "#exp_val = result(1)\n", + "print(exp_val_opt)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "jvZnSGY8BgR8", + "outputId": "51e52b12-59d5-4db2-c805-352f2cab3af7" + }, + "execution_count": 238, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "-34.09912109375\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [ + "xlabels = [str(bin(i)[2:]) for i in range(len(proba_opt))]\n", + "for x in range(len(xlabels)):\n", + " while len(xlabels[x]))" + ] + }, + "metadata": {}, + "execution_count": 239 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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RfClLRMwG/hfwIUnPdluwmZl1JqXRbwJOi4hTImIGsBxY3xCznuLLVoBB4CFJiohjgXuB1ZL+tq6izcwsXdtGL2k/sAp4AHgSuEvStoi4NiLeV4bdApwQETuATwCry+WrgFOBqyPiB+XjzbW/CjMzaynpGL2kDcCGhmVXV6b3ARc1ed51wHVd1mhmZl3wL2PNzDI3IWfdmJnVwb9EHxvv0ZuZZc579FYb722Z9Sfv0ZuZZc6N3swsc270ZmaZc6M3M8ucG72ZWeZ81o1Zh0Y7u8hnFlk/8h69mVnm3OjNzDLnRm9mljkfozczmyC9+vW49+jNzDLnPXpL4jNNzCYv79GbmWXOe/Rmpcl+9c0665/s74Udynv0ZmaZc6M3M8ucG72ZWeZ8jD5j1eOsPsZqNnV5j97MLHPeozcbBz5rxfqJ9+jNzDLnRm9mljk3ejOzzLnRm5llzo3ezCxzU/KsG58RYWZTiffozcwyNyX36M2s//ieB+MnaY8+IpZGxPaI2BERq5usPyoi7izXPxoRcyvrPlUu3x4R59dXupmZpWi7Rx8R04CbgXOBXcCmiFgv6YlK2GXAXkmnRsRyYC3w/oiYBywH3gn8E+CvIuJ0Sa/X/UJsbPx9hVk9+vkvkpQ9+rOAHZKek/QaMAQsa4hZBtxWTt8NnBMRUS4fkvQLST8EdpT5zMxsgoSk0QMiBoGlki4v5y8BFklaVYnZWsbsKuefBRYB1wCPSLqjXH4LcJ+kuxvGWAmsLGffBmzv/qUBcCLw0gTHTYVcvRizX3P1Ysx+zdWLMfs1V91jpnirpF9vukbSqA9gEPhKZf4S4KaGmK3A7Mr8s+ULuAn43cryW4DBdmPW9QAem+i4qZBrstfv98LvxWR7L7p9pBy62Q3MqczPLpc1jYmI6cAs4OXE55qZ2ThKafSbgNMi4pSImEHx5er6hpj1wKXl9CDwkIrN1XpgeXlWzinAacD36indzMxStD3rRtL+iFgFPABMA26VtC0irqX4s2M9xSGZ2yNiB7CHYmNAGXcX8ASwH/i4JvaMm3U9iJsKuXoxZr/m6sWY/ZqrF2P2a666x+xK2y9jzcxscvMlEMzMMudGb2aWOTd6M7PMudGbmWUuq0YfEW+PiKsi4sbycVVEvKOD53+4Mn1+RHw5ItaXjy9HxNIOcl1dd66ImB4RH4mI+yPi8fJxX0R8NCKOTMy1rmF+zLU1vMauaqvWVXOuWRGxJiKeiog9EfFyRDxZLjs28XXelxJnBhARx0fE8b2uoyqbs24i4irgYopr8ewqF8+mONVzSNKahBzPSzo5Ir4InA58vSHXh4BnJP1+j3L9BfBTiusKVXNdChwv6f1lfKsPWQD/IGl2GddVbSN1ldNta+ugrjpzPQA8BNwm6f+Wy95S5jpH0nnlsjNGyXePpN+ovO7zgQuBk8pFu4G/lHR/ixwHk0VcLenacno6xQUBf4fion8HcgG3SPplm1zrJK0ch1yzgE+Vr/HNgIAfl7nWSPppwuu8T9IF3dZVra3mumrLVU6fDHwOOIfisxvAr1F89lZL2tku33jKqdE/Dbyz8YNT/shrm6TTyvnHW6UATpd0VEQ8Len0JmME8HQl1z+OkutoSdMnIlf5/APrIuJ14Eflc0eonD9J0ozG57SqLaWu0XJV13Vb1xhzbZf0tha5Dqwr832nId+IsyUdXcZ549jBxrHOnZOa66p1ByAivgt8Ebh75LdCUVz59yLgDySd3SIPZewWSfNHi+lGTjceeYNij+FHDct/o1w3YgA4H9jbEBfA35XT+yLiTEmbGmLOBPZV5n8KnCnpxcZiIuKFcci1JyIuAv6npDfKdUdQfJiqr+c5ig/r86PkSq0tpa7U2lLrqjPXjyLikxT/oV8s1w8AK4Bq3JPARyQ90ybfv2mxcbwTeBr4/XYbx8r8gia5dgGPlDsuAD+h9QbtzeOUa66ktdVEZTNcGxH/sbJ4E603jiOHxVLqSq2tzrrqzAVwoqQ7G/K9DgxFxGcBIuLfNclBmfstLdbVIqdG/wfAtyPiGQ7+Bz4ZOBVYVYm7B5gp6QeNCSJiYzm5AvhyRPwqB/dC5gCvlOtGfB14K3BYEwS+MQ65Rq71/6WIGGl4xwIPl+tGfBE4DjisCVL8eTkipbaUulJrS62rMVeUuR4aQ673A6uB70TESMN4keLyHP+hEncNrb+z+r3KtDeOB6VsHOvcOamzrrp3ADZHxJco/nIZWT6H4i+Evy/n7wT+nGID1uhNTZbVRxNw5bSJelD8Rz0b+Pfl42xgWhf53gIsKB9v6bK22nKV+U4ATqjpfevn2mrLVVM9ZwCPUlzW48Hy8STwCMXeK8B1wFktnr+2Mj2X4j//Tyj+Gnia4jjxncApZczHgXe1yPV7o+R6ppweS67jKDa0T1Fc0mRP+RrXUhxuGYkbBN7WIt+FqXWl1lZzXdVce8vHmHKV0zOA/wTcD2wpH/cBHwOOKmM2A/+8Ra4XxvNzm80xejhwbPksDv2S7HtqeJGpcS3GeLukpzqJK7/4Wdow3gNq+MInNa7FeOdK+lancSljdlNXam1N6no7xY1rGr/wfKpNzHpJTybW9WFJXx1LXHk898C4Ko/zjlVEnAAg6eVu8tSdq079WtdEiYh3Az9S879aFkp6bNzGzqXRR8R5wJco9hhGLoU8m+LQzcckPdhJ3CjjHPgyLSUuIj4EfIZiz6863rnAn0j6ehmfFFdXXaljdltXam0NdbU9gyolpo66msV549jZxjGlrm5rG2NdSWdPpcaNMuaBM616JadG/yRwgRpOY4ri8sgbJL0jNS4ibmw1DHCppF8rn9M2LiK2U9yRq3Hv/TjgUR08U6ZtXEQ0Xh66Ot57JB1TPic1LmXM1PrbjtlBXW3PoEqJKefbnmXVYZw3jp3t6CSN2W1tY6gr6eyp1LhuaxvvjUFOX8ZO5+A/RNVu4MgO4z4MXAH8okncxZXplLig+Zcvb3DoN/kpce8GfhcYbogZORRFh3EpY6bWnzJmal0pZ1DVeZZVJ3F/RHEsvumGj6IhpMS02ziekBpTuozmG74vANuANYkx7TZ6A5XnpcQljZkSV3Ndbc+e6iQu0s+0auVywI0+wa3ApogY4tBvvZdTXC+/k7hNwFZJ1f/gAETENZXZlLj/Anw/Ih7k0LOBzgU+W3lKStwjwM8lfafJeNX77KbGpYyZWn/KmKl1pZxBVedZVp3EeePYWVzqmClxddaVetpzbadH17AxGLNsDt0ARMQ84H0cfozviU7iovjxxj5JP28zXmrccRQfvMbjtXvHElenlDF7VNcRHP6F+SZVblyTEjMOdV0KXE1xWOawDZ+kr6XElLnuAz4n6eEm4/y1pN9KiSmnl1Lco7nphk/S/SkxZa5bgK9K+psmY35D0gdS4zoYM6X+Ous6A/gy0OzU4o9L2lzGp8ZdR9FDDruDXkSslXRVRDzPKBsDSXMal9clq0Y/omzASNrTbVydufpVFOcPV88gafZBbBtTd64W+WdKaty77TimmzhvHOuvq4e1JZ09lRrXZqy2G4NOcyaPnUujj4PXmngPxda26bUmUuIi8boVqXGj1Jz0s+eUuLHkioh/AfwPipu57yrrn12+lo9J+n5KTJnrX1Ls+czi0C8gq7naxiTU39GXlOMV541jelxEfac915lrlNo7PoW6jrjxlNMx+jspfi35QR1+rYkhih9PpcbVlisSf/acEldnrtLXKH719+ghQRFnA18F3pUYQzndLi4lhoj4xCj1z0yNGae4phu+iGi7cazGlLmabvgacrWNaVF31RMUh0G6jek4LkY5nTkikk57HomrM1eb2h9MfI21xY33xiCnPfpnVJ5SN9q6lLiac/2S1j97HpT0q2V827g6cyXUv0PSqSkx45BrH/DfKW4o3+gPJR2bEpOaq8O4H9B6Y/Vnkt6VEjMOuUbbUP2RpONTYlJzdTBmnac99+Up1J3EtZL61+VY5bRHn3KtidS4OnM9Dnxe0tbGgiPityuzKXF15gK4LyLupTjdr1r/hyh+yp0aU3eu7wPfVPlFV0P9l3cQMx5xxzQ2XQBJj0TEMR3E1J3rv9J6Q3VEBzF1x9V52nO/nkKdFNdmY5B0b4SxymmPfgbFubiH/bKO4rrXv0iNqzlX0s+eU+LqzFWZv6BZ/ZI2dBJTZ66IeBvwsqSXmtQ/IOnFlJjUXB3G3Qj8M5pvrH4oaVVKzDjk+juKa8I021C9IGlOSkxqrg7G/BTFxeOanc58l6T/Vsa3jas510PAp9X81OgfSjqlnK4tLiL+H603BtdLOrHJ8lpk0+jNJkofbxz3SPpJk3qrG8dRY1JzdRj3jhb1N5723DaurlxR/ynUbeNSNxrjIZtGHwfvZHPYNSmo3MkmJW6cco16h52UuDpzJbyfB+441E3MZM/VSZzZaFI3GuMydkaNPvVONil34sk+VxmXclef1LsSTdpcHcaN3IJuGcUvMA+7BV1KzDjmanlrvJSY1FydxLUSlVvxdRvXr7k6iRtPOTX61NvspdymLvtc5XTb2/GlxEz2XB3GtboF3QqKC7OdlxIzgbkO3BovJSY1Vwdjpt6KL+X2f32Zq5O4VsZ9Y6BxvlHDRD0orqNyEXBEZdkRFHcYerSTuKmQq1z2DHByi/fzhdSYyZ6rw7jto3wGt6fGTPZcHYz5OsXG4OEmj1cr8W3j+jVXB2Oe0eKxAPg/rd7LOh7jlniiHxy8k82PaXG3ntS4qZCrjEu5q0/qXYkmba4O4x4EPgkMVJYNAFcBf5UaM9lzdTDmVuC0Fu9rdQPaNq5fc3UwZtJGYzwe2Ry6gZbftP+lGm5ckBI3FXKVcW1v9pASM9lzdTDmcRT3oF3GwZtWj9yDdo2kvSkxkz1XB2MOAlskVa9OOvJeXijpm+V027h+zdXBmFuB31GL+89qHC9q1upmyJNOFDcu+AbFcdVHywfAX0TE6k7ipkKuMu6TFOcaB/C98hENY7aNmey5OomTtFfSVZLeLun48vEOFRekujA1ZrLn6mDMu5s1v9JxlVxt4/o1Vwdx15B2A/r61fFnQT88KA5PHNlk+QyKO8Ekx02FXJO9/l68FwmfwefriJnsuSZ7/T16Lz6ckmusj5wugVDnDQ6mQq7JXn8v3gsi4e5FKTGTPVcvxuzXXJ3EjeJPKC7sNy5yavSpdxyq8+5FkznXZK+/F+8FpN29qM47IfVrrsle/4S/FzVsDMYsm0av4g40p9PmxgUpcVMh12SvvxfvRSnlloN13r6wX3NN9vp78V6kbjRql9VZN2Zm/SoSb4U4LmO70ZuZ5S2b0yvNzKw5N3ozs8y50ZuZZc6N3swsc/8ftRiOY9t4HN4AAAAASUVORK5CYII=\n" + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "source": [ + "print(np.max(proba_opt))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "yYn1_QjXbPaX", + "outputId": "cb8738fa-4e89-458e-9b11-aa1b9ecaa37f" + }, + "execution_count": 240, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "0.1015625\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## Classical algorithm" + ], + "metadata": { + "id": "3biD-ZFOZB5U" + } + }, + { + "cell_type": "code", + "source": [ + "# Brute force\n", + "def classical_cost_calculator(z, G, weights, V):\n", + " weights = np.array(weights)\n", + " z = np.array(list(int(z[i]) for i in range(len(z))), requires_grad=False)\n", + " distances = nx.get_edge_attributes(G, \"weight\")\n", + " cost = (V-np.dot(weights,z))**2\n", + " for i in range(len(G.nodes())):\n", + " for j in range(i+1, len(G.nodes())):\n", + " cost += distances[(str(i), str(j))] * z[i] * z[j]\n", + " return cost\n", + "\n", + "def int_to_binary(G):\n", + " N = len(G.nodes())\n", + " n_list = list(range(2^N))\n", + "\n", + " def binary_filler(z,N):\n", + " while len(z)\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0mz_list\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mint_to_binary\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mG\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0mz_list\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mbin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn_list\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;31mNameError\u001b[0m: name 'n_list' is not defined" + ] + } + ] + }, + { + "cell_type": "code", + "source": [ + "distances = nx.get_edge_attributes(G, \"weight\")\n", + "distances[('0', '1')]\n", + "cost = (V-weights*z)**2\n", + "cost" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "1ISZliobdc2N", + "outputId": "005b97e9-1cde-4895-b276-c1da049d145b" + }, + "execution_count": 212, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "tensor([100, 100, 9, 100, 25], requires_grad=True)" + ] + }, + "metadata": {}, + "execution_count": 212 + } + ] + }, + { + "cell_type": "code", + "source": [ + "len(G.nodes())" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "yl52JAZOeCU1", + "outputId": "e0979ac3-32c2-427e-8043-aeda094ac383" + }, + "execution_count": 225, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "5" + ] + }, + "metadata": {}, + "execution_count": 225 + } + ] + }, + { + "cell_type": "code", + "source": [ + "" + ], + "metadata": { + "id": "Fe2uMEuXhDq3" + }, + "execution_count": null, + "outputs": [] + } + ] +} \ No newline at end of file From 4604be96c6d3d2a9983a853096a5ce12adf75546 Mon Sep 17 00:00:00 2001 From: VasilyBokov <62181457+VasilyBokov@users.noreply.github.com> Date: Wed, 27 Jul 2022 11:35:56 +0300 Subject: [PATCH 07/39] Add files via upload --- team 8/Debris_Removal_Model.ipynb | 856 ++++++++++++++++++++++++++++++ team 8/dummy_graph.png | Bin 0 -> 28867 bytes 2 files changed, 856 insertions(+) create mode 100644 team 8/Debris_Removal_Model.ipynb create mode 100644 team 8/dummy_graph.png diff --git a/team 8/Debris_Removal_Model.ipynb b/team 8/Debris_Removal_Model.ipynb new file mode 100644 index 0000000..a216815 --- /dev/null +++ b/team 8/Debris_Removal_Model.ipynb @@ -0,0 +1,856 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import networkx as nx # tool to handle general Graphs \n", + "import matplotlib.pyplot as plt \n", + "from matplotlib import cm\n", + "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n", + "from typing import Any, Dict, List, Tuple\n", + "from qiskit import Aer, IBMQ\n", + "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit, transpile, assemble\n", + "from qiskit.providers.ibmq import least_busy\n", + "from qiskit.tools.monitor import job_monitor\n", + "from qiskit.visualization import plot_histogram" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Firstly, we define a class we can draw a graph in convinient way\n", + "class GraphModel:\n", + " \n", + " n_nodes: int\n", + " edges: List[Tuple[int, int]]\n", + " graph: nx.Graph\n", + " \n", + " def __init__(self, n_nodes, edges, weights, distancies, qaoa_solve=None):\n", + " \n", + " self.n_nodes = n_nodes\n", + " self.edges = edges\n", + " self.weights = weights\n", + " self.distancies = distancies\n", + " self.graph = nx.Graph()\n", + " self.graph.add_nodes_from(np.arange(0,n_nodes,1))\n", + " self.graph.add_edges_from(edges)\n", + " #self.qaoa_solve = qaoa_solve\n", + " \n", + " def draw_raw_graph(self):\n", + " \n", + " # Generate plot of the Graph\n", + " colors = ['cornflowerblue' for node in self.graph.nodes()]\n", + " default_axes = plt.axes(frameon=False)\n", + " random_pos = nx.random_layout(self.graph, seed=42)\n", + " pos = nx.spring_layout(self.graph, pos=random_pos)\n", + "\n", + " nx.draw_networkx_nodes(self.graph, node_color=colors, node_size=900,pos = pos, \n", + " alpha=1, ax=default_axes) \n", + " nx.draw_networkx_edges(self.graph, pos = pos, width=8,alpha=1,ax=default_axes,\n", + " edge_color=\"tab:gray\")\n", + " nx.draw_networkx_labels(self.graph, pos = pos, font_size=22, font_color=\"white\")\n", + "\n", + "\n", + " def draw_done_graph(self,bitstring):\n", + " \n", + " # Draw a graph in accordance with its bitstring\n", + " color_map = []\n", + " edgelist_different = []\n", + " edgelist_same = []\n", + " default_axes = plt.axes(frameon=False)\n", + " default_axes.axis('off')\n", + " random_pos = nx.random_layout(self.graph, seed=42)\n", + " pos = nx.spring_layout(self.graph, pos=random_pos)\n", + " \n", + " if bitstring == None:\n", + " self.draw_raw_graph()\n", + " else:\n", + " for i in bitstring:\n", + " if i > 0:\n", + " color_map.append('red')\n", + " else: \n", + " color_map.append('cornflowerblue')\n", + "# for edge in self.edges:\n", + "# if bitstring[edge[0]] != bitstring[edge[1]]:\n", + "# edgelist_different.append(edge)\n", + "# else:\n", + "# edgelist_same.append(edge)\n", + " \n", + " nx.draw_networkx_nodes(self.graph, node_color=color_map, node_size=900,pos = pos, \n", + " alpha=1, ax=default_axes) \n", + " nx.draw_networkx_edges(self.graph, pos = pos, edgelist = self.edges, \n", + " width=8,alpha=1,ax=default_axes,edge_color=\"tab:grey\")\n", + "# nx.draw_networkx_edges(self.graph, pos = pos, edgelist = edgelist_different,\n", + "# width=8,alpha=1,ax=default_axes, edge_color=\"tab:red\")\n", + " nx.draw_networkx_labels(self.graph, pos = pos, font_size=22, font_color=\"white\")\n", + " \n", + " def connections(self, node): \n", + " connection_list = []\n", + " for edge in self.edges:\n", + " if (edge[0] == node):\n", + " connection_list.append(edge[1])\n", + " elif (edge[1] == node):\n", + " connection_list.append(edge[0])\n", + " connection_list = list(dict.fromkeys(connection_list))\n", + " return connection_list\n", + " \n", + " # This function returns all edges corresponding to certain node of the graph G \n", + " def find_edges(self, node): \n", + " connection_edges = []\n", + " for edge in self.edges:\n", + " if (edge[0] == node):\n", + " connection_edges.append(edge)\n", + " elif (edge[1] == node):\n", + " connection_edges.append(edge)\n", + " connection_edges = list(dict.fromkeys(connection_edges)) \n", + " return connection_edges" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def graph_drawing(G,regime, *args, **kwargs):\n", + " bitstring = kwargs.get('bitstring', None)\n", + " filename = kwargs.get('filename', None)\n", + " figure, axes = plt.subplots(frameon=False)\n", + " axes.axis('off')\n", + " # Turn off tick labels\n", + " req_dpi = 100 \n", + " figure.set_size_inches(500 / float(req_dpi), \n", + " 500 / float(req_dpi)) \n", + " if regime == 'raw':\n", + " G.draw_raw_graph()\n", + " elif regime == 'done':\n", + " G.draw_done_graph(bitstring)\n", + " else:\n", + " raise ValueError('Regime is wrong')\n", + " \n", + " figure.savefig(filename, format='png',\n", + " transparent=True, dpi=req_dpi) " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Example of drawing method of the class GrapgModel\n", + "n_nodes = 5\n", + "E = [(0,1),(0,2),(0,3), (0,4),(1,2),(1,3), (1,4), (2,3), (2,4),(3,4) ]\n", + "weghts_list = [1,2,7,4,5]\n", + "distancies_list = [1,2,2,1,1,2,2,1,2,1]\n", + "G = GraphModel(n_nodes, E, weghts_list, distancies_list )\n", + "graph_drawing(G,'raw',filename = 'dummy_graph.png')\n", + "\n", + "# n_nodes = 3\n", + "# E = [(0,1),(0,2),(1,2)]\n", + "# weghts_list = [5,5,100]\n", + "# distancies_list = [1,10,10]\n", + "# G = GraphModel(n_nodes, E, weghts_list, distancies_list )\n", + "# graph_drawing(G,'raw',filename = 'dummy_graph.png')" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "graph_drawing(G,'done',bitstring = [1,1,1,0,1],filename = 'dummy_graph_option.png')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[1, 2, 7, 4, 5]" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.weights" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(G.distancies) == len(G.edges)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Circuit construction" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calculation of the hamiltonian coefficients \n", + "\n", + "\\begin{equation}\n", + "H = \\sum_{(i,j) \\in E} q_{ij} \\frac{1}{2} (1 - \\hat{Z_i} \\hat{Z_j}) - \\sum_{i=1}^{N} k_i \\hat{Z_i}\n", + " \\end{equation}\n", + "\n", + " where $k_i = \\frac{1}{2} (p_i - \\sum_{j=1}^{N} q_{ij})$ ;\n", + " $q_{ij} = d_{ij} + w_i w_j $ ;\n", + " $p_i = 2 \\epsilon V w_i$\n", + " \n", + " $\\epsilon$ is a penatly parameter here" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[1, 2, 7, 4, 5]" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.weights" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# Calculation the parameters \n", + "eps = 1 # defining the penalty term \n", + "V = 10 # the total volume of the vessel\n", + "\n", + "p = []\n", + "for weight in G.weights:\n", + " p.append(2*eps*V*weight)\n", + " \n", + "q = [] # 1-1 correspondabce between edge and q_ij\n", + "for edge in G.edges:\n", + " index = G.edges.index(edge)\n", + " q.append(G.distancies[index] + G.weights[G.edges[index][0]]*G.weights[G.edges[index][1]])\n", + "\n", + "\n", + "k = []\n", + "for node in range(0,G.n_nodes):\n", + " q_part = 0\n", + " for edge in G.find_edges(node):\n", + " q_part += q[G.edges.index(edge)]\n", + " k.append(0.5*(p[node] - q_part))" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "q = [3, 9, 6, 6, 15, 10, 12, 29, 37, 21] \n", + " p = [20, 40, 140, 80, 100] \n", + " k = [-2.0, 0.0, 25.0, 7.0, 12.0]\n" + ] + } + ], + "source": [ + "print(\"q = \",q,'\\n',\"p = \",p,'\\n','k = ',k)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit.circuit import QuantumCircuit, Parameter\n", + "\n", + "# create the parameter\n", + "phi = Parameter('phi')\n", + "qc = QuantumCircuit(1)\n", + "\n", + "# parameterize the rotation\n", + "qc.rx(2*phi, 0)\n", + "qc.rz(2*phi,0)\n", + "qc.draw()\n", + "\n", + "# bind the parameters after circuit to create a bound circuit\n", + "bc = qc.bind_parameters({phi: 3.14})\n", + "\n", + "bc.measure_all()\n", + "bc.draw(\"mpl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3\n", + "9\n", + "6\n", + "6\n", + "15\n", + "10\n", + "12\n", + "29\n", + "37\n", + "21\n" + ] + } + ], + "source": [ + "for edge in G.edges:\n", + " print(q[G.edges.index(edge)])" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
    " + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n", + "from qiskit import Aer, execute\n", + "from qiskit.circuit import Parameter\n", + "\n", + "nqubits = n_nodes\n", + "# Drawing the circuit for p=1\n", + "beta = Parameter(\"$\\\\beta$\")\n", + "qc_mix = QuantumCircuit(nqubits)\n", + "for i in range(0, nqubits):\n", + " qc_mix.rx(2 * beta, i)\n", + "\n", + "gamma = Parameter(\"$\\\\gamma$\")\n", + "qc_p_1 = QuantumCircuit(nqubits)\n", + "for edge in G.edges: # pairs of nodes\n", + " qc_p_1.rzz(2 * gamma * q[G.edges.index(edge)], edge[0], edge[1])\n", + " qc_p_1.barrier()\n", + "\n", + "qc_p_2 = QuantumCircuit(nqubits)\n", + "for i in range(0, nqubits):\n", + " qc_p_2.rz((2 * gamma * k[i] * (-1)),i) # we added (-1) as in H we have -k_iZ_i\n", + " qc_p_2.barrier()\n", + " \n", + "qc_0 = QuantumCircuit(nqubits)\n", + "for i in range(0, nqubits):\n", + " qc_0.h(i)\n", + "\n", + "qc_qaoa = QuantumCircuit(nqubits)\n", + "\n", + "qc_qaoa.append(qc_0, [i for i in range(0, nqubits)])\n", + "qc_qaoa.append(qc_p_1, [i for i in range(0, nqubits)])\n", + "qc_qaoa.append(qc_p_2, [i for i in range(0, nqubits)])\n", + "qc_qaoa.append(qc_mix, [i for i in range(0, nqubits)])\n", + "qc_qaoa.measure_all()\n", + "qc_qaoa.decompose().decompose().draw(\"mpl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.optimize import minimize\n", + "from qiskit.visualization import plot_histogram" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we create the QAOA model to **minimize** the function: \n", + "\n", + "\\begin{equation}\n", + "C(\\vec{x}) = - \\sum_{i=1}^{N} p_i x_i + \\sum_{i,j=1}^{N} x_i x_j q_{ij} \n", + " \\end{equation} " + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-20" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = [1,0,0,0,0]\n", + "obj = 0\n", + "q_part = 0\n", + "p_part = 0\n", + "for i in range(0,G.n_nodes):\n", + " p_part += p[i]*x[i]\n", + " for j in range(0,G.n_nodes):\n", + " if (i,j) in G.edges:\n", + " q_part+= x[i]*x[j]*q[G.edges.index((i,j))]\n", + "obj = q_part - p_part \n", + "obj" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[0, 0, 0, 0, 1]" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "list(reversed(x))" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "def problem_obj(x, G):\n", + "\n", + "# Given a bitstring as a solution, this function returns\n", + "# the value of C(x)\n", + "\n", + "# Args:\n", + "# x: str\n", + "# solution bitstring\n", + "\n", + "# G: networkx graph\n", + "\n", + "# Returns:\n", + "# obj: float\n", + "# Objective\n", + "\n", + "# obj = 0\n", + "# for i, j in G.edges():\n", + "# if x[i] != x[j]:\n", + "# obj -= 1\n", + "# return obj\n", + " obj = 0\n", + " q_part = 0\n", + " p_part = 0\n", + " x = list(map(int,list(x)))\n", + " x = list(reversed(x))# we changed the order here\n", + " for i in range(0,G.n_nodes):\n", + "# print(p,x)\n", + " p_part += p[i]*x[i]\n", + " for j in range(0,G.n_nodes):\n", + " if (i,j) in G.edges:\n", + " q_part+= x[i]*x[j]*q[G.edges.index((i,j))]\n", + " obj = q_part - p_part \n", + " return obj\n", + "\n", + "def compute_expectation(counts, G):\n", + "\n", + " \"\"\"\n", + " Computes expectation value based on measurement results\n", + "\n", + " Args:\n", + " counts: dict\n", + " key as bitstring, val as count\n", + "\n", + " G: networkx graph\n", + "\n", + " Returns:\n", + " avg: float\n", + " expectation value\n", + " \"\"\"\n", + "\n", + " avg = 0\n", + " sum_count = 0\n", + " for bitstring, count in counts.items():\n", + "# print(counts.items())\n", + " obj = problem_obj(bitstring, G)\n", + " avg += obj * count\n", + " sum_count += count\n", + "\n", + " return avg/sum_count\n", + "\n", + "\n", + "# We will also bring the different circuit components that\n", + "# build the qaoa circuit under a single function\n", + "def create_qaoa_circ(G, theta):\n", + "\n", + "# \"\"\"\n", + "# Creates a parametrized qaoa circuit\n", + "\n", + "# Args: \n", + "# G: networkx graph\n", + "# theta: list\n", + "# unitary parameters\n", + "\n", + "# Returns:\n", + "# qc: qiskit circuit\n", + "# \"\"\"\n", + "\n", + " nqubits = G.n_nodes\n", + " depth = len(theta)//2 # number of alternating unitaries\n", + " qc = QuantumCircuit(nqubits)\n", + "\n", + " beta = theta[:depth]\n", + " gamma = theta[depth:]\n", + "\n", + " # initial_state\n", + " for i in range(0, nqubits):\n", + " qc.h(i)\n", + "\n", + " for irep in range(0, depth):\n", + "\n", + " # problem unitary\n", + " for edge in G.edges: # pairs of nodes\n", + " qc.rzz(2 * gamma[irep] * q[G.edges.index(edge)], edge[0], edge[1])\n", + " qc.barrier()\n", + " \n", + " for i in range(0, nqubits):\n", + " qc.rz((2 * gamma[irep] * k[i] * (-1)),i) # we added (-1) as in H we have -k_iZ_i\n", + " qc.barrier()\n", + " \n", + " # mixer unitary\n", + " for i in range(0, nqubits):\n", + " qc_mix.rx(2 * beta[irep], i)\n", + "\n", + " qc.measure_all()\n", + "\n", + " return qc\n", + "\n", + "# Finally we write a function that executes the circuit on the chosen backend\n", + "def get_expectation(G, backend):\n", + "\n", + "# \"\"\"\n", + "# Runs parametrized circuit\n", + "\n", + "# Args:\n", + "# G: networkx graph\n", + "# p: int,\n", + "# Number of repetitions of unitaries\n", + "# \"\"\"\n", + "\n", + "# backend = Aer.get_backend('qasm_simulator')\n", + "# backend.shots = shots\n", + "\n", + " def execute_circ(theta):\n", + " qc = create_qaoa_circ(G, theta)\n", + " counts = backend.run(qc,nshots=backend.shots).result().get_counts()\n", + "\n", + " return compute_expectation(counts, G)\n", + "\n", + " return execute_circ\n", + "\n", + "def optimization(G,initial_parameters,backend):\n", + " expectation = get_expectation(G,backend)\n", + "\n", + " res = minimize(expectation, initial_parameters, method='COBYLA')\n", + " return res" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "# class QAOA:\n", + "# # counts: dict\n", + "# def __init__(self, graph, initial_parameters):\n", + "# self.graph = graph\n", + "# self.initial_parameters = initial_parameters\n", + " \n", + "# backend = Aer.get_backend('qasm_simulator')\n", + "# backend.shots = 1024\n", + "# qc_res = create_qaoa_circ(graph, optimization(graph,initial_parameters,backend).x)\n", + "# counts = backend.run(qc_res, seed_simulator=10).result().get_counts()\n", + "# self.counts = counts\n", + " \n", + "# def result(self):\n", + "# pass\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "depth = 20\n", + "initial_parameters = [0.5,0.5]*depth\n", + "\n", + "backend = Aer.get_backend('qasm_simulator')\n", + "backend.shots = 2048\n", + "qc_res = create_qaoa_circ(G, optimization(G,initial_parameters,backend).x)\n", + "\n", + "# model = QAOA(G,initial_parameters)\n", + "# counts = model.counts" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'11011': 61,\n", + " '10111': 58,\n", + " '11000': 67,\n", + " '01010': 60,\n", + " '10001': 61,\n", + " '00100': 59,\n", + " '00011': 52,\n", + " '01110': 76,\n", + " '10000': 60,\n", + " '10101': 75,\n", + " '11001': 67,\n", + " '10100': 67,\n", + " '11101': 49,\n", + " '00110': 68,\n", + " '00111': 74,\n", + " '01100': 68,\n", + " '00010': 73,\n", + " '11100': 62,\n", + " '11110': 70,\n", + " '00001': 51,\n", + " '01101': 56,\n", + " '11010': 61,\n", + " '01000': 61,\n", + " '01111': 63,\n", + " '00101': 58,\n", + " '01001': 68,\n", + " '10011': 62,\n", + " '10110': 56,\n", + " '10010': 71,\n", + " '11111': 58,\n", + " '00000': 79,\n", + " '01011': 77}" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "counts = backend.run(qc_res, shots=2048).result().get_counts()\n", + "counts" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot_histogram(counts, figsize=(16, 10), color=None, number_to_keep=None,\n", + " sort='asc', target_string=None, legend=None,\n", + " bar_labels=True, title=\"Final Distribution\", ax=None)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit import BasicAer\n", + "qc = QuantumCircuit(2)\n", + "# qc.h(0) \n", + "qc.x(0) \n", + "qc.measure_all() \n", + "qasm_sim = BasicAer.get_backend('qasm_simulator') #this time we call the qasm simulator\n", + "result = execute(qc, qasm_sim, shots=100).result() # NOTICE: we can skip some steps by doing .result() directly, we could go further!\n", + "counts = result.get_counts() #this time, we are not getting the state, but the counts!\n", + "qc.draw(\"mpl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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zr>QtmO7ByV=gr9(>#NjDuUf$ca%UfVJyVH)(Ucq{wo&gc<`CEOn)J1W&LwQSRv(SM zKKs%8U`nrPZ$Z{@@VCagU$&?-jztB}t95{RkztXv*QFt%^ zVXzF}a3hEgb0JcmCYG@f=*z`$2aF?r5yKO=?Qj9Z!3;ocd@F;lX@ zpYUSMUne-Qx}vjJgJr!$Ix|jzIhTZq*{pYywgs~S4KE%K{>uJM7tin@X$B;el7nd7 zrW$y%%)!y-_U{O6LDJ9z6e>Z9=e5T~N0?O^tZeW~adIc1)o+9YalDLjK<1zQ?9}DG z%0h34dmq3`f_VseJjpqB=_>iX{t(E9R0ae29qzG!E1Mvsr92qw?9pL8TNE}HdMrXz z#7Bcc_{r^p8_R6KTDb!8lzfOiEci`H7dUZqD?dt?4Gz$F2(h^h$e8EuA@0JDUiwwgT zM#gjBLd7Sa62sp=1(&U*aDatDx`_?g(f+^7*8bm}bpQALd)PC|xTx}c-`h|9z=eWj NFfD^SrMK+D{y(Kxe Date: Wed, 27 Jul 2022 12:38:27 +0300 Subject: [PATCH 08/39] Add files via upload --- team 8/Debris_Removal_Model.ipynb | 218 +++++++++--------------------- 1 file changed, 66 insertions(+), 152 deletions(-) diff --git a/team 8/Debris_Removal_Model.ipynb b/team 8/Debris_Removal_Model.ipynb index a216815..4a684c3 100644 --- a/team 8/Debris_Removal_Model.ipynb +++ b/team 8/Debris_Removal_Model.ipynb @@ -141,7 +141,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 78, "metadata": {}, "outputs": [ { @@ -169,14 +169,14 @@ "# n_nodes = 3\n", "# E = [(0,1),(0,2),(1,2)]\n", "# weghts_list = [5,5,100]\n", - "# distancies_list = [1,10,10]\n", + "# distancies_list = [1,1,10]\n", "# G = GraphModel(n_nodes, E, weghts_list, distancies_list )\n", "# graph_drawing(G,'raw',filename = 'dummy_graph.png')" ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 79, "metadata": {}, "outputs": [ { @@ -193,12 +193,13 @@ } ], "source": [ - "graph_drawing(G,'done',bitstring = [1,1,1,0,1],filename = 'dummy_graph_option.png')" + "graph_drawing(G,'done',bitstring = [1,1,1,0,1],filename = 'dummy_graph_option.png')\n", + "# graph_drawing(G,'done',bitstring = [1,0,1],filename = 'dummy_graph_option.png')" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 80, "metadata": {}, "outputs": [ { @@ -207,7 +208,7 @@ "[1, 2, 7, 4, 5]" ] }, - "execution_count": 7, + "execution_count": 80, "metadata": {}, "output_type": "execute_result" } @@ -218,7 +219,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 81, "metadata": {}, "outputs": [ { @@ -227,7 +228,7 @@ "True" ] }, - "execution_count": 8, + "execution_count": 81, "metadata": {}, "output_type": "execute_result" } @@ -262,7 +263,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 82, "metadata": {}, "outputs": [ { @@ -271,7 +272,7 @@ "[1, 2, 7, 4, 5]" ] }, - "execution_count": 9, + "execution_count": 82, "metadata": {}, "output_type": "execute_result" } @@ -282,7 +283,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 83, "metadata": {}, "outputs": [], "source": [ @@ -310,89 +311,46 @@ }, { "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "q = [3, 9, 6, 6, 15, 10, 12, 29, 37, 21] \n", - " p = [20, 40, 140, 80, 100] \n", - " k = [-2.0, 0.0, 25.0, 7.0, 12.0]\n" - ] - } - ], - "source": [ - "print(\"q = \",q,'\\n',\"p = \",p,'\\n','k = ',k)" - ] - }, - { - "cell_type": "code", - "execution_count": 12, + "execution_count": 93, "metadata": {}, "outputs": [ { "data": { - "image/png": "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\n", "text/plain": [ - "
    " + "[(0, 1), (0, 2), (0, 3), (0, 4)]" ] }, - "execution_count": 12, + "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "from qiskit.circuit import QuantumCircuit, Parameter\n", - "\n", - "# create the parameter\n", - "phi = Parameter('phi')\n", - "qc = QuantumCircuit(1)\n", - "\n", - "# parameterize the rotation\n", - "qc.rx(2*phi, 0)\n", - "qc.rz(2*phi,0)\n", - "qc.draw()\n", - "\n", - "# bind the parameters after circuit to create a bound circuit\n", - "bc = qc.bind_parameters({phi: 3.14})\n", - "\n", - "bc.measure_all()\n", - "bc.draw(\"mpl\")" + "G.find_edges(0)" ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 84, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "3\n", - "9\n", - "6\n", - "6\n", - "15\n", - "10\n", - "12\n", - "29\n", - "37\n", - "21\n" + "q = [3, 9, 6, 6, 15, 10, 12, 29, 37, 21] \n", + " p = [20, 40, 140, 80, 100] \n", + " k = [-2.0, 0.0, 25.0, 7.0, 12.0]\n" ] } ], "source": [ - "for edge in G.edges:\n", - " print(q[G.edges.index(edge)])" + "print(\"q = \",q,'\\n',\"p = \",p,'\\n','k = ',k)" ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 85, "metadata": {}, "outputs": [ { @@ -402,7 +360,7 @@ "
    " ] }, - "execution_count": 14, + "execution_count": 85, "metadata": {}, "output_type": "execute_result" } @@ -446,7 +404,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 86, "metadata": {}, "outputs": [], "source": [ @@ -467,7 +425,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 87, "metadata": {}, "outputs": [ { @@ -476,7 +434,7 @@ "-20" ] }, - "execution_count": 16, + "execution_count": 87, "metadata": {}, "output_type": "execute_result" } @@ -497,27 +455,7 @@ }, { "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[0, 0, 0, 0, 1]" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "list(reversed(x))" - ] - }, - { - "cell_type": "code", - "execution_count": 18, + "execution_count": 88, "metadata": {}, "outputs": [], "source": [ @@ -552,7 +490,7 @@ " for j in range(0,G.n_nodes):\n", " if (i,j) in G.edges:\n", " q_part+= x[i]*x[j]*q[G.edges.index((i,j))]\n", - " obj = q_part - p_part \n", + " obj = 2*q_part - p_part \n", " return obj\n", "\n", "def compute_expectation(counts, G):\n", @@ -660,36 +598,12 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 89, "metadata": {}, "outputs": [], "source": [ - "# class QAOA:\n", - "# # counts: dict\n", - "# def __init__(self, graph, initial_parameters):\n", - "# self.graph = graph\n", - "# self.initial_parameters = initial_parameters\n", - " \n", - "# backend = Aer.get_backend('qasm_simulator')\n", - "# backend.shots = 1024\n", - "# qc_res = create_qaoa_circ(graph, optimization(graph,initial_parameters,backend).x)\n", - "# counts = backend.run(qc_res, seed_simulator=10).result().get_counts()\n", - "# self.counts = counts\n", - " \n", - "# def result(self):\n", - "# pass\n", - "\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [], - "source": [ - "depth = 20\n", - "initial_parameters = [0.5,0.5]*depth\n", + "depth = 5\n", + "initial_parameters = [1.0,1.0]*depth\n", "\n", "backend = Aer.get_backend('qasm_simulator')\n", "backend.shots = 2048\n", @@ -701,47 +615,47 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "{'11011': 61,\n", - " '10111': 58,\n", - " '11000': 67,\n", - " '01010': 60,\n", - " '10001': 61,\n", - " '00100': 59,\n", - " '00011': 52,\n", - " '01110': 76,\n", - " '10000': 60,\n", - " '10101': 75,\n", + "{'01111': 64,\n", + " '11010': 72,\n", " '11001': 67,\n", - " '10100': 67,\n", - " '11101': 49,\n", - " '00110': 68,\n", - " '00111': 74,\n", - " '01100': 68,\n", - " '00010': 73,\n", - " '11100': 62,\n", - " '11110': 70,\n", - " '00001': 51,\n", - " '01101': 56,\n", - " '11010': 61,\n", - " '01000': 61,\n", - " '01111': 63,\n", - " '00101': 58,\n", - " '01001': 68,\n", - " '10011': 62,\n", - " '10110': 56,\n", - " '10010': 71,\n", + " '10011': 79,\n", + " '00110': 60,\n", + " '00010': 69,\n", + " '10001': 73,\n", + " '01010': 61,\n", + " '01110': 66,\n", + " '11000': 59,\n", + " '10111': 63,\n", + " '01000': 65,\n", + " '11011': 59,\n", " '11111': 58,\n", - " '00000': 79,\n", - " '01011': 77}" + " '10110': 67,\n", + " '10010': 73,\n", + " '00101': 76,\n", + " '01001': 68,\n", + " '01100': 59,\n", + " '00111': 60,\n", + " '01011': 69,\n", + " '00000': 64,\n", + " '00011': 77,\n", + " '00100': 55,\n", + " '10101': 58,\n", + " '10000': 48,\n", + " '11110': 53,\n", + " '11100': 69,\n", + " '10100': 48,\n", + " '11101': 63,\n", + " '01101': 69,\n", + " '00001': 57}" ] }, - "execution_count": 21, + "execution_count": 90, "metadata": {}, "output_type": "execute_result" } @@ -753,17 +667,17 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 91, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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    " ] }, - "execution_count": 22, + "execution_count": 91, "metadata": {}, "output_type": "execute_result" } From 11ae63f0c5b8c5d3d557944d4ff32ef95e7cadf8 Mon Sep 17 00:00:00 2001 From: JPazem <109220752+JPazem@users.noreply.github.com> Date: Wed, 27 Jul 2022 12:10:00 +0200 Subject: [PATCH 09/39] Add files via upload --- .../space_debris_collection_Pennylane.ipynb | 810 ++++++++++++++++++ 1 file changed, 810 insertions(+) create mode 100644 team 8/space_debris_collection_Pennylane.ipynb diff --git a/team 8/space_debris_collection_Pennylane.ipynb b/team 8/space_debris_collection_Pennylane.ipynb new file mode 100644 index 0000000..070948f --- /dev/null +++ b/team 8/space_debris_collection_Pennylane.ipynb @@ -0,0 +1,810 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "space_debris_collection_Pennylane.ipynb", + "provenance": [], + "collapsed_sections": [] + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "iEYhchm4dvze", + "outputId": "3df98194-d82b-419d-f467-9e09b432bc9e" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n", + "Collecting pennylane\n", + " Downloading PennyLane-0.24.0-py3-none-any.whl (957 kB)\n", + "\u001b[K |████████████████████████████████| 957 kB 5.3 MB/s \n", + "\u001b[?25hCollecting pennylane-lightning>=0.24\n", + " Downloading PennyLane_Lightning-0.24.0-cp37-cp37m-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (9.3 MB)\n", + "\u001b[K |████████████████████████████████| 9.3 MB 14.0 MB/s \n", + "\u001b[?25hRequirement already satisfied: appdirs in /usr/local/lib/python3.7/dist-packages (from pennylane) (1.4.4)\n", + "Collecting toml\n", + " Downloading toml-0.10.2-py2.py3-none-any.whl (16 kB)\n", + "Requirement already satisfied: networkx in /usr/local/lib/python3.7/dist-packages (from pennylane) (2.6.3)\n", + "Collecting semantic-version==2.6\n", + " Downloading semantic_version-2.6.0-py3-none-any.whl (14 kB)\n", + "Collecting retworkx\n", + " Downloading retworkx-0.11.0-cp37-cp37m-manylinux_2_5_x86_64.manylinux1_x86_64.manylinux_2_12_x86_64.manylinux2010_x86_64.whl (1.6 MB)\n", + "\u001b[K |████████████████████████████████| 1.6 MB 36.5 MB/s \n", + "\u001b[?25hRequirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from pennylane) (1.7.3)\n", + "Requirement already satisfied: cachetools in /usr/local/lib/python3.7/dist-packages (from pennylane) (4.2.4)\n", + "Collecting autoray>=0.3.1\n", + " Downloading autoray-0.3.2-py3-none-any.whl (36 kB)\n", + "Requirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from pennylane) (1.21.6)\n", + "Requirement already satisfied: autograd in /usr/local/lib/python3.7/dist-packages (from pennylane) (1.4)\n", + "Collecting ninja\n", + " Downloading ninja-1.10.2.3-py2.py3-none-manylinux_2_5_x86_64.manylinux1_x86_64.whl (108 kB)\n", + "\u001b[K |████████████████████████████████| 108 kB 53.9 MB/s \n", + "\u001b[?25hRequirement already satisfied: future>=0.15.2 in /usr/local/lib/python3.7/dist-packages (from autograd->pennylane) (0.16.0)\n", + "Installing collected packages: ninja, toml, semantic-version, retworkx, pennylane-lightning, autoray, pennylane\n", + "Successfully installed autoray-0.3.2 ninja-1.10.2.3 pennylane-0.24.0 pennylane-lightning-0.24.0 retworkx-0.11.0 semantic-version-2.6.0 toml-0.10.2\n", + "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n", + "Requirement already satisfied: networkx in /usr/local/lib/python3.7/dist-packages (2.6.3)\n" + ] + } + ], + "source": [ + "import sys\n", + "!{sys.executable} -m pip install pennylane\n", + "!{sys.executable} -m pip install networkx" + ] + }, + { + "cell_type": "code", + "source": [ + "import networkx as nx\n", + "import pennylane as qml\n", + "from pennylane import numpy as np \n", + "import matplotlib.pyplot as plt" + ], + "metadata": { + "id": "vTd6PsprHhIm" + }, + "execution_count": 2, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "# Space debris optimization" + ], + "metadata": { + "id": "wr3gMLPUepdb" + } + }, + { + "cell_type": "markdown", + "source": [ + "In this work, we solve the combinatorial optimization problem of space debris collection. A challenge for space agencies, satellite producers and any actor involved in space travel is to avoid space debris. In spite of possibly small sizes, their speeds on orbits make any collision with satellite or spacecraft threaten the success of space expeditions with major damage. Therefore, a major concern is to collect these debris and destroy them at the entrance of the atmosphere." + ], + "metadata": { + "id": "FdAx9nEVeytw" + } + }, + { + "cell_type": "markdown", + "source": [ + "The problem is the following. Debris collection journeys are expensive, since the quantity of fuels used to propel the engins is massive, and the capacity of each space craft limits the amount of space garbage that can be collected. To optimize each trip to space, we must therefore seek debris located at particular locations, such that they minimize the distance and hence the fuel consumption, and they maximize the quantity of trash collected. We solve the latter problem first, and add further constraints to the problem progressively." + ], + "metadata": { + "id": "sMUPN0CCfzsU" + } + }, + { + "cell_type": "markdown", + "source": [ + "### Formulation of the cost function " + ], + "metadata": { + "id": "wKXwHlEhP2_-" + } + }, + { + "cell_type": "markdown", + "source": [ + "Let us first consider the problem of maximization of the volume of trash that is collected. This task is related to the knapsack problem. \n", + "\n", + "We start with a set of N debris. We encode the information about the debris to collect in a bitstring:\n", + "\\begin{equation}\n", + "z = z_1 z_2 \\cdots z_N, \\text{where } z_i = \\begin{cases}\n", + "1, & \\text{if debris i is collected} \\\\\n", + "0, & \\text{if otherwise.}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "To solve the problem with brute force method, we must inspect all possible bitstrings $z$ and pick the one that maximizes the volume of the debris collected. Therefore, it is a combinatorial optimization problem. To formulate it, we pair each debris $i$ with its weight/size $w_i$. The debris locations can be reported on a graph with edge set $E$ and vertex set $V$ such that $G = \\{E,V\\}$. Each vertex is associated with a weight, and each edge $i -j$ with a distance $d_{ij}$. With these notations, we encode the problem into the cost function:\n", + "\\begin{equation}\n", + "C(z) = (V-\\sum_{i=1}^{N} w_i z_i)^2 + \\sum_{i, j=1}^{N} d_{ij} z_i z_j\n", + "\\end{equation}\n", + "where the first term corresponds to the knapsack problem and the second aims at minimizing the travelled distance. To simplify the implementation, the constant term can be removed:\n", + "\\begin{align}\n", + "C(z) &= (-2V\\sum_{i=1}^{N} w_i z_i + 2\\sum_{ii} g_{ij} -\\sum_{j 1]\n", + "light_edges = [(u, v) for (u, v, d) in G.edges(data=True) if d[\"weight\"] <= 1]\n", + "pos = nx.spring_layout(G, seed=11) \n", + "nx.draw_networkx_nodes(G, pos, node_size=700, node_color=\"r\")\n", + "nx.draw_networkx_edges(G, pos, edgelist=heavy_edges, width=6)\n", + "nx.draw_networkx_edges(G, pos, edgelist=light_edges, width=6, edge_color=\"b\", style=\"dashed\")\n", + "nx.draw_networkx_labels(G, pos, font_size=20, font_family=\"sans-serif\")\n", + "edge_labels = nx.get_edge_attributes(G, \"weight\")\n", + "nx.draw_networkx_edge_labels(G, pos, edge_labels)\n", + " \n", + "#nx.draw(G, with_labels=True, alpha=0.8, node_size=300)\n", + "\n", + "N_vertices = 3\n", + "G = nx.Graph()\n", + "G.add_edge('0', '1', weight = 1)\n", + "G.add_edge('1', '2', weight = 10)\n", + "G.add_edge('2', '0', weight = 10)\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 248 + }, + "id": "987QfIbfgt6D", + "outputId": "58c32d84-d971-4483-9a0c-a6ef1e78600c" + }, + "execution_count": 172, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "We implement the QAOA algorithm on this data set. We choose:\n", + "- Mixer Hamiltonian: $\\hat{H}_M = \\sum_{i=0}^{N-1} X_i$\n", + "- Problem Hamiltonin as defined above\n", + "\n", + "For an approximate Trotterization with p steps, the evolution yields the following state:\n", + "\\begin{equation}\n", + "|\\overrightarrow{\\gamma}, \\overrightarrow{\\beta}\\rangle = e^{i\\beta_p H_M} e^{i\\gamma_p H_P} \\cdots e^{i\\beta_1 H_M} e^{i\\gamma_1 H_P}|+\\rangle^{\\otimes{N}}\n", + "\\end{equation}\n", + "where $|+\\rangle^{\\otimes{N}} = \\frac{1}{\\sqrt{2^N}} \\sum_{z\\in \\{0,1\\}^N} |z\\rangle $ is an equal superposition of all bitstrings." + ], + "metadata": { + "id": "QiItM9uZKZoU" + } + }, + { + "cell_type": "code", + "source": [ + "dev = qml.device(\"default.qubit\", wires=len(G.nodes()), shots= 1024)\n", + "\n", + "@qml.qnode(dev)\n", + "def QAOA_Circuit(G, weights, V, p, angles):\n", + " N_vertices = len(G.nodes())\n", + " wires = range(N_vertices)\n", + " distances = nx.get_edge_attributes(G, \"weight\")\n", + "\n", + " # Initialize the states\n", + " for i in range(N_vertices):\n", + " qml.Hadamard(wires=wires[i])\n", + "\n", + " # Apply QAOA\n", + " gammas = angles[:p]\n", + " beta = angles[p:]\n", + "\n", + " problem_coef = []\n", + " problem_operators = []\n", + "\n", + " for step in range(0, p):\n", + " \n", + " # Apply the problem Hamiltonian\n", + " \n", + " for i in range(0, N_vertices):\n", + " coef_single = V*weights[i] - sum([v for k,v in distances.items() if str(i) in k])\n", + " qml.RZ(coef_single*gammas[step], wires=wires[i])\n", + " if step == 1:\n", + " problem_coef += [coef_single]\n", + " problem_operators += [qml.PauliZ(wires=wires[i])]\n", + "\n", + " for j in range(i+1, N_vertices):\n", + " coef_double = (1/2*weights[i]*weights[j] + 1/4*nx.get_edge_attributes(G, \"weight\")[(str(i), str(j))])\n", + " qml.MultiRZ(gammas[step]*coef_double, wires=[wires[i]]+[wires[j]])\n", + " if step == 1:\n", + " problem_coef += [coef_double]\n", + " problem_operators += [qml.PauliZ(wires[i]) @ qml.PauliZ(wires[j])]\n", + "\n", + "\n", + " # Apply the mixer Hamiltonian\n", + " for i in range(0, N_vertices):\n", + " qml.RX(beta[step], wires=wires[i])\n", + "\n", + " # Compute the expectation value of the problem Hamiltonian\n", + " # problem_H = qml.Hamiltonian(problem_coef, problem_operators)\n", + "\n", + " return qml.expval(qml.Hamiltonian(problem_coef, problem_operators))\n" + ], + "metadata": { + "id": "zc9MhBK3MJqV" + }, + "execution_count": 154, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "@qml.qnode(dev)\n", + "def QAOA_Circuit_optimized_probas(G, weights, V, p, angles):\n", + " N_vertices = len(G.nodes())\n", + " wires = range(N_vertices)\n", + " distances = nx.get_edge_attributes(G, \"weight\")\n", + "\n", + " # Initialize the states\n", + " for i in range(N_vertices):\n", + " qml.Hadamard(wires=wires[i])\n", + "\n", + " # Apply QAOA\n", + " gammas = angles[:p]\n", + " beta = angles[p:]\n", + "\n", + " for step in range(0, p):\n", + " \n", + " # Apply the problem Hamiltonian\n", + " \n", + " for i in range(0, N_vertices):\n", + " coef_single = V*weights[i] - sum([v for k,v in distances.items() if str(i) in k])\n", + " qml.RZ(coef_single*gammas[step], wires=wires[i])\n", + "\n", + " for j in range(i+1, N_vertices):\n", + " coef_double = (1/2*weights[i]*weights[j] + 1/4*nx.get_edge_attributes(G, \"weight\")[(str(i), str(j))])\n", + " qml.MultiRZ(gammas[step]*coef_double, wires=[wires[i]]+[wires[j]])\n", + "\n", + " # Apply the mixer Hamiltonian\n", + " for i in range(0, N_vertices):\n", + " qml.RX(beta[step], wires=wires[i])\n", + "\n", + " return qml.probs(wires)" + ], + "metadata": { + "id": "ZKp_UBGi23J6" + }, + "execution_count": 155, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Optimize the angles\n", + "def cost_function(G, weights, V, p, angles):\n", + " def optimizable_object(angles):\n", + " cost_exp_val = QAOA_Circuit(G, weights, V, p, angles)\n", + " return cost_exp_val\n", + " return optimizable_object" + ], + "metadata": { + "id": "i3CKY8f0mdV1" + }, + "execution_count": 156, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Parameters\n", + "V = 10\n", + "# weights = np.array([1,2,7,4,5], requires_grad=False)\n", + "weights = np.array([5,5,100], requires_grad=False)\n", + "p=2\n", + "\n", + "#angles = np.array(2*p*[np.pi/4], requires_grad=True)\n", + "angles = np.array(2*p*[1])\n", + "shots=1024\n", + "\n", + "dev = qml.device(\"default.qubit\", wires=len(G.nodes()), shots=shots)" + ], + "metadata": { + "id": "7hZXeG4dOj1w" + }, + "execution_count": 173, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "circuit = QAOA_Circuit(G, weights, V, p, angles)" + ], + "metadata": { + "id": "c2H1BfBmu6Ma" + }, + "execution_count": 174, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "from scipy.optimize import minimize\n", + "cost = cost_function(G, weights, V, p, angles)\n", + "optimized_params = minimize(cost, angles, method='COBYLA')\n", + "optimized_angles = optimized_params.x\n", + "\n", + "#optimizer = qml.GradientDescentOptimizer(stepsize=0.8)\n", + "#cost = cost_function(G, weights, V, p, angles)\n", + "#for k in range(100):\n", + "# if k % 5 == 0:\n", + "# print(f\"Step {k}, cost: {cost(angles)}\")\n", + "# angles = optimizer.step(cost, angles)\n", + "#optimized_angles = angles" + ], + "metadata": { + "id": "t-XpCGgc1edP" + }, + "execution_count": 175, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "proba_opt = QAOA_Circuit_optimized_probas(G, weights, V, p, optimized_angles)\n", + "exp_val_opt = QAOA_Circuit(G, weights, V, p, optimized_angles)\n", + "#probas_opt = result(0)\n", + "#exp_val = result(1)\n", + "print(exp_val_opt)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "jvZnSGY8BgR8", + "outputId": "a277e098-05d4-40c0-c2cb-6aee20d453c2" + }, + "execution_count": 176, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "-925.29443359375\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [ + "xlabels = [str(bin(i)[2:]) for i in range(len(proba_opt))]\n", + "for x in range(len(xlabels)):\n", + " while len(xlabels[x]))" + ] + }, + "metadata": {}, + "execution_count": 177 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": "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\n" + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "source": [ + "print(np.max(proba_opt))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "yYn1_QjXbPaX", + "outputId": "41f618b2-3bcf-428d-c3a5-fae180e0ddcc" + }, + "execution_count": 162, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "0.1328125\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## Classical algorithm" + ], + "metadata": { + "id": "3biD-ZFOZB5U" + } + }, + { + "cell_type": "code", + "source": [ + "# Brute force\n", + "def classical_cost_calculator(z, G, weights, V):\n", + " weights = np.array(weights)\n", + " distances = nx.get_edge_attributes(G, \"weight\")\n", + " cost = []\n", + " for number in range(len(z)):\n", + " z_vector = [int(z[number][-1])]\n", + " for i in reversed(range(0,len(weights)-1)):\n", + " z_vector = z_vector + [int(z[number][i])]\n", + " z_vector = np.array(z_vector, requires_grad=False)\n", + "\n", + " cost_n = (V-np.dot(weights,z_vector))**2 # - np.dot(weights,z_vector)\n", + " for i in range(len(G.nodes())):\n", + " for j in range(i+1, len(G.nodes())):\n", + " cost_n += distances[(str(i), str(j))] * z_vector[i] * z_vector[j]\n", + " cost = cost + [cost_n]\n", + " return cost\n", + "\n", + "def int_to_binary(G):\n", + " N = len(G.nodes())\n", + " n_list = list(range(2**N))\n", + "\n", + " def binary_filler(z,N):\n", + " while len(z))" + ] + }, + "metadata": {}, + "execution_count": 179 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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\n" + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "source": [ + "print(np.min(classical_cost))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "1ISZliobdc2N", + "outputId": "e41383c8-b6fc-42e2-c2b5-2181f3205470" + }, + "execution_count": 110, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "-9\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [ + "classical_cost" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "yl52JAZOeCU1", + "outputId": "d9b30313-f964-4ab6-afcc-68d920e2d2f6" + }, + "execution_count": 143, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[[100,\n", + " 81,\n", + " 64,\n", + " 50,\n", + " 9,\n", + " 6,\n", + " 2,\n", + " 4,\n", + " 36,\n", + " 27,\n", + " 18,\n", + " 14,\n", + " 2,\n", + " 9,\n", + " 13,\n", + " 25,\n", + " 25,\n", + " 17,\n", + " 11,\n", + " 8,\n", + " 6,\n", + " 14,\n", + " 21,\n", + " 34,\n", + " 2,\n", + " 4,\n", + " 6,\n", + " 13,\n", + " 40,\n", + " 58,\n", + " 73,\n", + " 96]]" + ] + }, + "metadata": {}, + "execution_count": 143 + } + ] + }, + { + "cell_type": "code", + "source": [ + "bin(6)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 37 + }, + "id": "cgoBw-pIkiN2", + "outputId": "e8058a4d-2c83-44ea-ec17-275e83e61e57" + }, + "execution_count": 125, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "'0b110'" + ], + "application/vnd.google.colaboratory.intrinsic+json": { + "type": "string" + } + }, + "metadata": {}, + "execution_count": 125 + } + ] + }, + { + "cell_type": "code", + "source": [ + "" + ], + "metadata": { + "id": "KKEpG2iLwPm7" + }, + "execution_count": null, + "outputs": [] + } + ] +} \ No newline at end of file From fbb42bbe7b0a62721235fd09bceaa3d047f1e0c8 Mon Sep 17 00:00:00 2001 From: Jitesh Lalwani <64247212+ab-jiteshlalwani@users.noreply.github.com> Date: Wed, 27 Jul 2022 16:29:23 +0530 Subject: [PATCH 10/39] Minor changes to business application readme --- team 8/Business_Application.md | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/team 8/Business_Application.md b/team 8/Business_Application.md index 755887f..2df1a92 100644 --- a/team 8/Business_Application.md +++ b/team 8/Business_Application.md @@ -6,7 +6,7 @@ The debris includes rocket thrusters, abandoned satellites, and most importantly ![Space Debris](./images/space_debris.jpg) -### Problems Created by Space Debris +### Why Space Debris is a Problem? There were approximately 128 million pieces of debris under 1 cm (0.4 in), about 900,000 pieces between 1 and 10 cm, and approximately 34,000 pieces larger than 10 cm (3.9 in) in orbit around the Earth as of January 2019. Space debris orbits around the earth at tremendous speeds - about 15,700 miles per hour (25,265 kph) in low Earth orbit which is 10 times the speed of a bullet. So there is a possibility that active satellites and spacecraft could be damaged by space debris. Space travel is also at risk due to all this debris. @@ -44,13 +44,15 @@ We gather open source space debris data and encode it for quantum computers. Our As a pre-processing step, we also use AI to clean and rank debris according to size, collection cost, etc. ### Business Model -Yearly Subscription: Our solution is scalable and can be used by several space companies or agencies with no or minimal changes. Our model returns the optimal path for satellite vessels to collect as much debris as possible in one pass. +**Yearly Subscription:** We offer both on-premises and cloud deployment options for our model on a yearly subscription basis. + +Our solution is scalable and can be used by several space companies or agencies with no or minimal changes. Our model returns the optimal path for satellite vessels to collect as much debris as possible in one pass. + -We offer both on-premises and cloud deployment options for our model on a yearly subscription basis. ### References: * https://en.wikipedia.org/wiki/Space_debris * https://www.youtube.com/watch?v=Ctvzf_p0qUA * https://www.cbsnews.com/news/space-junk-damage-international-space-station * https://www.reuters.com/lifestyle/science/international-space-station-swerves-dodge-space-junk-2021-12-03 -* https://en.wikipedia.org/wiki/Knapsack_problem \ No newline at end of file +* https://en.wikipedia.org/wiki/Knapsack_problem From a859bc1e72cd98966b1abf4f8bc2826383bfc29c Mon Sep 17 00:00:00 2001 From: JPazem <109220752+JPazem@users.noreply.github.com> Date: Wed, 27 Jul 2022 13:24:56 +0200 Subject: [PATCH 11/39] Create ReadMe.md --- team 8/ReadMe.md | 1 + 1 file changed, 1 insertion(+) create mode 100644 team 8/ReadMe.md diff --git a/team 8/ReadMe.md b/team 8/ReadMe.md new file mode 100644 index 0000000..8b13789 --- /dev/null +++ b/team 8/ReadMe.md @@ -0,0 +1 @@ + From 76f9f33f4343172fab51d91a04e9a934aaf009c4 Mon Sep 17 00:00:00 2001 From: JPazem <109220752+JPazem@users.noreply.github.com> Date: Wed, 27 Jul 2022 13:39:17 +0200 Subject: [PATCH 12/39] Update Business_Application.md --- team 8/Business_Application.md | 14 ++++++++++---- 1 file changed, 10 insertions(+), 4 deletions(-) diff --git a/team 8/Business_Application.md b/team 8/Business_Application.md index 2df1a92..0398cd2 100644 --- a/team 8/Business_Application.md +++ b/team 8/Business_Application.md @@ -25,11 +25,15 @@ NASA and the Canadian Space Agency first noticed the damage on Canadarm2 on May ### Space Debris Removal Optimization In space debris removal optimization, the goal is to create an optimal path for satellite vessels to collect as much debris as possible in one pass, while saving fuel. As a result, space debris collection will take fewer days overall. -A space debris removal optimization could also be described as combinatorial optimization, which is searching for maxima (or minima) of an objective function F whose domain is a discrete but large configuration space (in contrast to an N-dimensional continuous space). +A space debris removal optimization could also be described as combinatorial optimization problem, which is searching for maxima (or minima) of an objective function F whose domain is a discrete but large configuration space (in contrast to an N-dimensional continuous space). ![Space Debris](./images/knapsack.png) -This can be also considered as a Knapsack problem where the goal is to determine the number of items each with a weight and value to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. According to its name, it refers to the problem of filling a fixed-size knapsack with valuable items when constrained by a fixed size. A similar problem occurs when decision-makers have to select from a set of non-divisible projects or tasks within a fixed budget or timeframe. +This can be also considered as a Knapsack problem where the goal is to determine the number of items each with a weight and value to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. According to its name, it refers to the problem of filling a fixed-size knapsack with valuable items when constrained by a fixed size. A similar problem occurs when decision-makers have to select from a set of non-divisible projects or tasks within a fixed budget or timeframe. + +To optimize the path and take into account the resources required to travel, we add complexity to the problem. The new term is related to the Traveling Salesman Problem (TSP) whose goal is to optimize a path on a graph, such that all nodes are visited and each road is taken only once. In our case, we want to maximize the amount of nodes visited, representing the debris that are collected, while minimizing the length of the path, indicated by weights on the edges of the graph. + +The two problems that represent the situation of debris collection are known to be computationally hard to solve on classical computers: for large amounts of debris, it may take more that the age of the universe to solve. ### Potential Customers * Space agencies, like NASA, ESA, etc, are potential customers because space debris can hinder their missions. @@ -39,9 +43,9 @@ This can be also considered as a Knapsack problem where the goal is to determine ### Architecture -We gather open source space debris data and encode it for quantum computers. Our model is platform agnostic and can be run either on IBM hardware or Xanadu hardware. In the near future, it will be also possible to run our model on quantum annealers such as D-Wave hardware. +We gather open source space debris data and encode it for quantum computers. Our first model leverages gate-based quantum computing using the QAOA algorithm. It is platform agnostic and can be run either on IBM hardware or Xanadu hardware. In the near future, it will be also possible to run our model on quantum annealers such as D-Wave hardware. -As a pre-processing step, we also use AI to clean and rank debris according to size, collection cost, etc. +As a pre-processing step, we also use AI to clean and rank debris according to size, collection cost, etc. This process reduces the size of the problem to solve according to the collection priorities and makes the program more efficient to run. ### Business Model **Yearly Subscription:** We offer both on-premises and cloud deployment options for our model on a yearly subscription basis. @@ -56,3 +60,5 @@ Our solution is scalable and can be used by several space companies or agencies * https://www.cbsnews.com/news/space-junk-damage-international-space-station * https://www.reuters.com/lifestyle/science/international-space-station-swerves-dodge-space-junk-2021-12-03 * https://en.wikipedia.org/wiki/Knapsack_problem +* E. Farhi, J. Goldstone, and S. 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8/Business_Application.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/team 8/Business_Application.md b/team 8/Business_Application.md index 0398cd2..7bdcba4 100644 --- a/team 8/Business_Application.md +++ b/team 8/Business_Application.md @@ -31,6 +31,8 @@ A space debris removal optimization could also be described as combinatorial opt This can be also considered as a Knapsack problem where the goal is to determine the number of items each with a weight and value to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. According to its name, it refers to the problem of filling a fixed-size knapsack with valuable items when constrained by a fixed size. A similar problem occurs when decision-makers have to select from a set of non-divisible projects or tasks within a fixed budget or timeframe. +![Space Debris](./images/TSP.jpeg) + To optimize the path and take into account the resources required to travel, we add complexity to the problem. The new term is related to the Traveling Salesman Problem (TSP) whose goal is to optimize a path on a graph, such that all nodes are visited and each road is taken only once. In our case, we want to maximize the amount of nodes visited, representing the debris that are collected, while minimizing the length of the path, indicated by weights on the edges of the graph. The two problems that represent the situation of debris collection are known to be computationally hard to solve on classical computers: for large amounts of debris, it may take more that the age of the universe to solve. 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zXx!^z+B1XMe9;Y0P{@?JWoo~&dc49->)*0X%YWQ@8uVCp${kR;`Pfu+=6zYe9n1N;gY1>F zXSy-(2c>98+OaVds}YPTP?VBqshW~_ybYA818-$@TAe<9`Y{{hkEVvlpcK=%R|6<~ zNcqj%*}wN}do2CEAw^~B>k#GWH%S&J=Bd5<**e`TdCm=QP=QkoBo=R7det=&xbQZM zQ*4ECU{U`op|xhfaVC;wzJ{nc$e1xprGr6YDD;?}~a$xl=RVP5IvF@Ohh-!?hPC zv!-phDpWe@sMzNl92?vZo!hr_dwHgbZsKayS1R5A_X>%=+3F~Gt7Iv#QC8t0br(#4fEdMFn1OxxkL1FPfR@A#<=&D!Xb{!Kb9+`@h+Vx?+YI9 z^kOkt|IKG5)6ru*ELSG+WsWp>q!+Yqg{x}|cs|JzGz!{o-MmdKI;Vst0OZ*TVgLXD literal 0 HcmV?d00001 From e19763ffe54ada89098c102f48186194c7011dcf Mon Sep 17 00:00:00 2001 From: JPazem <109220752+JPazem@users.noreply.github.com> Date: Wed, 27 Jul 2022 14:29:17 +0200 Subject: [PATCH 16/39] Add files via upload --- .../space_debris_collection_Pennylane.ipynb | 274 ++++++++++-------- 1 file changed, 146 insertions(+), 128 deletions(-) diff --git a/team 8/space_debris_collection_Pennylane.ipynb b/team 8/space_debris_collection_Pennylane.ipynb index 070948f..1f98fe3 100644 --- a/team 8/space_debris_collection_Pennylane.ipynb +++ b/team 8/space_debris_collection_Pennylane.ipynb @@ -135,12 +135,12 @@ "\n", "To solve the problem with brute force method, we must inspect all possible bitstrings $z$ and pick the one that maximizes the volume of the debris collected. Therefore, it is a combinatorial optimization problem. To formulate it, we pair each debris $i$ with its weight/size $w_i$. The debris locations can be reported on a graph with edge set $E$ and vertex set $V$ such that $G = \\{E,V\\}$. Each vertex is associated with a weight, and each edge $i -j$ with a distance $d_{ij}$. With these notations, we encode the problem into the cost function:\n", "\\begin{equation}\n", - "C(z) = (V-\\sum_{i=1}^{N} w_i z_i)^2 + \\sum_{i, j=1}^{N} d_{ij} z_i z_j\n", + "C(z) = (V-\\sum_{i=1}^{N} w_i z_i)^2 + \\sum_{ii} g_{ij} -\\sum_{j)" + "([0,\n", + " 1,\n", + " 2,\n", + " 3,\n", + " 4,\n", + " 5,\n", + " 6,\n", + " 7,\n", + " 8,\n", + " 9,\n", + " 10,\n", + " 11,\n", + " 12,\n", + " 13,\n", + " 14,\n", + " 15,\n", + " 16,\n", + " 17,\n", + " 18,\n", + " 19,\n", + " 20,\n", + " 21,\n", + " 22,\n", + " 23,\n", + " 24,\n", + " 25,\n", + " 26,\n", + " 27,\n", + " 28,\n", + " 29,\n", + " 30,\n", + " 31],\n", + " )" ] }, "metadata": {}, - "execution_count": 177 + "execution_count": 268 }, { "output_type": "display_data", @@ -549,7 +602,7 @@ "text/plain": [ "

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tniaznZ2Zz+o2MBCfdZOZW4AtTeeIiNszc6TpHN2YrR6z1WO2egY1Wz+nbiaBM9uWl1Trum4TEYuBU2i9KdvPXEnSHOqn6HcAyyLinIg4gdabq9s6ttkGXFE9Xg3ckq1zQtuANRFxYkScAywDvjU70SVJ/eh56iYzpyJiPXAzrcsrt2bm7ojYBNyemduATwKfjYg9wAFaBwOq7a4H7gSmgL/JzCfm6GeZDY2fPjoGs9VjtnrMVs9AZuv5Zqwk6Tebd8ZKUuEsekkqnEUvSYWz6IGIOC0iTms6hyTNhQVb9BFxVkSMR8SDwDeBb0XEA9W6pc2mG3wRMRwRL6m+hpvO00tEDDWdQWrKgr3qJiL+F/gwcMPhSz6rD1y7FHhrZr6syXzTiYhdmbm8wec/D/g4rZviDt/8tgT4OfDXmfntprIdS0Tcl5lnDUCOYeCManEyM+9vMk8/ImIoMw82nCFofU7WU/sO+FYOcIFFxAsy84dN54CFXfR3Z+ay4x2bDxHxJ9MNAR+f7vMs5kNE3AH8RWZ+s2P9y4DrMvMPm0kGEfG26YaAd2ZmY6fnflMPkND8QTIiLgQ+BtzNkfvuubT23VebynYsTe+3dgPxWTcN2RkRH6P1qZs/qdadSesO3+80lqrlc8B/AN2Ows+c5yydTu4seYDMvC0iTm4iUJt/Aj5I6+a8Tk2fpvw00x8gPwU0doCschzrINn0aa+PABcc/hsXh1V3228HXthEqCrDv043BPz2fGY5loVc9G+i9Tn6/8iRvw4evtO3Sd8DPpSZ3+8ciIgLGsjT7ssRcROtPzTTfoB8E/CVxlK1fBu4MTN3dg5ExJUN5Gk3yAdIGOyD5GJgf5f1k8BvzXOWTm8GNgCPdRl7wzxnmdaCPXUzyCLij4B7M/O+LmMjmXl7A7HaM1xE628NHHGAzMztzaWCiHg+8FBmHvUxsREx3OT58OqV3+/T/QD54/aP/W5CRHwD+NtpDpI/ycwzu0ybF9VfqftTWn8Lo33frQGuz8x/bjDbLcC7MvMbXcZ+nJnnNBDrKAu26KtP2XwL8DqOLKwvAp/MzF83lU1lGtQDJDx1kDyQmQ92GWv0IFlleCHd992dzaVqXZoN/CozH20yRy8Luej/i9YbYZ/h6V8Ll9A6R39aZr6+wWyHD0J/DPxetXrgD0IRsSUz1/Xecv4NcjZpri3kov9RZj7veMfmw4AfhKa7ciWA72bmkvnMc0SAwc52CvAOWq9Kh2m90f4ArYP35sz8eVPZ4Ih8rwOezYDlm05EfDkzL2o6RzeDlG0hvxl7ICIuBb6QmU8CRMQzaF1H/3CjyWBFlwPNfuC2iPhRE4HaPAjcS6s8D8tq+dmNJHraIGe7HrgFGMvMnwJExO8Aa6uxC5uLBjydb7Qj3xU0nC8iXjLdEHDefGY5KsAAZ2u3kF/RLwXeD4zRevUMrcuhbgU2Vn/MvBERcRtwDd0PQm/LzJUNZrsbeNU0bxQ3/abdIGe7KzOff7xj82WQ80XEE8B/c+QB/LCXZeZJ8xzpKYOcrd2CfUWfmfsi4j20rpk/4s3YJku+sobWQejaiOg8CK1pLFXLh4FTgaPKFPjAPGfpNMjZ7o2Ivwc+c/iNzeou2bU8fSVJkwY53w9o3YNwd+dARJitDwv5Ff0/0CrNcY68224NMJ6Zm5vKBtNeZfDFzPxBc6laIuIFdL8CwmzTiIhTgY20sh0+jXQ/rfs2Nmdmo6cLBzlfRKwGdmXmXV3GXpeZNzYQ6/DzD2y2dgu56H8EvKjzCpbq7+LubvgjEAb2IFS96vuzKlv7G8Vmqyki3pyZn2o6x3QGOZ/Z+rOQi/6HwGsy896O9WcDX234nOQgH4TMNssG6TNRuhnkfGbrz4I9Rw+8Ffh69Qbe4XNpZ9H6oKRG71IEnqR1/fy9Het/txprktlqiIjvTTdE63LLRg1yPrPN3IIt+sz8SkQ8j6M/+nTH4Y8tbtAgH4TMVs8w8BqOvnQ3gKNun2/AIOcz2wwt2KIHqC5dvK3pHJ0G+SBkttq+BAxl5h2dAxExMf9xjjLI+cw2Qwv2HL0kLRRNf/yoJGmOWfSSVDiLXpIKZ9FLUuH+H7nluYdoKrPqAAAAAElFTkSuQmCC\n" 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\n" }, "metadata": { "needs_background": "light" @@ -567,15 +620,15 @@ "base_uri": "https://localhost:8080/" }, "id": "yYn1_QjXbPaX", - "outputId": "41f618b2-3bcf-428d-c3a5-fae180e0ddcc" + "outputId": "2cb54657-7908-4f74-9e6a-80390a98e333" }, - "execution_count": 162, + "execution_count": 267, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ - "0.1328125\n" + "0.14453125\n" ] } ] @@ -626,18 +679,9 @@ "metadata": { "id": "4ngBq0Z0ZEhO" }, - "execution_count": 178, + "execution_count": 253, "outputs": [] }, - { - "cell_type": "markdown", - "source": [ - "$C(z) = -\\sum w_i z_i + (v-\\sum w_i z_i)^2 + \\sum d_{ij}z_iz_j$" - ], - "metadata": { - "id": "hqrHAoCQ13fE" - } - }, { "cell_type": "code", "source": [ @@ -654,22 +698,54 @@ "metadata": { "colab": { "base_uri": "https://localhost:8080/", - "height": 291 + "height": 848 }, "id": "VaOZyX-kdT0T", - "outputId": "85e4d793-b0d3-47d7-880c-598656091f8a" + "outputId": "f0d56a73-c634-44c2-be2f-9d7a39fb1355" }, - "execution_count": 179, + "execution_count": 254, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ - "([0, 1, 2, 3, 4, 5, 6, 7], )" + "([0,\n", + " 1,\n", + " 2,\n", + " 3,\n", + " 4,\n", + " 5,\n", + " 6,\n", + " 7,\n", + " 8,\n", + " 9,\n", + " 10,\n", + " 11,\n", + " 12,\n", + " 13,\n", + " 14,\n", + " 15,\n", + " 16,\n", + " 17,\n", + " 18,\n", + " 19,\n", + " 20,\n", + " 21,\n", + " 22,\n", + " 23,\n", + " 24,\n", + " 25,\n", + " 26,\n", + " 27,\n", + " 28,\n", + " 29,\n", + " 30,\n", + " 31],\n", + " )" ] }, "metadata": {}, - "execution_count": 179 + "execution_count": 254 }, { "output_type": "display_data", @@ -677,7 +753,7 @@ "text/plain": [ "
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\n" 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\n" }, "metadata": { "needs_background": "light" @@ -688,22 +764,23 @@ { "cell_type": "code", "source": [ - "print(np.min(classical_cost))" + "min_cost = np.min(classical_cost)\n", + "print(min_cost)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "1ISZliobdc2N", - "outputId": "e41383c8-b6fc-42e2-c2b5-2181f3205470" + "outputId": "817f3496-215d-4c07-ad3d-659daef2e304" }, - "execution_count": 110, + "execution_count": 255, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ - "-9\n" + "2\n" ] } ] @@ -711,87 +788,28 @@ { "cell_type": "code", "source": [ - "classical_cost" + "optimal_packages= np.where(np.array(classical_cost) == np.min(classical_cost))[0]\n", + "optimal_bitstrings = [bin(optimal_packages[i])[2:] for i in range(len(optimal_packages))]\n", + "for i in range(len(optimal_bitstrings)):\n", + " while len(optimal_bitstrings[i])< N_vertices:\n", + " optimal_bitstrings[i] = '0' + optimal_bitstrings[i]\n", + "print(\"The optimal trajectories are: \", optimal_bitstrings)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, - "id": "yl52JAZOeCU1", - "outputId": "d9b30313-f964-4ab6-afcc-68d920e2d2f6" + "id": "KKEpG2iLwPm7", + "outputId": "ccee5148-5e25-482d-9d21-9a7b02e7dd1b" }, - "execution_count": 143, + "execution_count": 256, "outputs": [ { - "output_type": "execute_result", - "data": { - "text/plain": [ - "[[100,\n", - " 81,\n", - " 64,\n", - " 50,\n", - " 9,\n", - " 6,\n", - " 2,\n", - " 4,\n", - " 36,\n", - " 27,\n", - " 18,\n", - " 14,\n", - " 2,\n", - " 9,\n", - " 13,\n", - " 25,\n", - " 25,\n", - " 17,\n", - " 11,\n", - " 8,\n", - " 6,\n", - " 14,\n", - " 21,\n", - " 34,\n", - " 2,\n", - " 4,\n", - " 6,\n", - " 13,\n", - " 40,\n", - " 58,\n", - " 73,\n", - " 96]]" - ] - }, - "metadata": {}, - "execution_count": 143 - } - ] - }, - { - "cell_type": "code", - "source": [ - "bin(6)" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 37 - }, - "id": "cgoBw-pIkiN2", - "outputId": "e8058a4d-2c83-44ea-ec17-275e83e61e57" - }, - "execution_count": 125, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "'0b110'" - ], - "application/vnd.google.colaboratory.intrinsic+json": { - "type": "string" - } - }, - "metadata": {}, - "execution_count": 125 + "output_type": "stream", + "name": "stdout", + "text": [ + "The optimal trajectories are: ['00110', '01100', '11000']\n" + ] } ] }, @@ -801,7 +819,7 @@ "" ], "metadata": { - "id": "KKEpG2iLwPm7" + "id": "x7J3X509RWXn" }, "execution_count": null, "outputs": [] From 6193bc863459e717fc16efa19003155c462db92e Mon Sep 17 00:00:00 2001 From: JPazem <109220752+JPazem@users.noreply.github.com> Date: Wed, 27 Jul 2022 14:31:28 +0200 Subject: [PATCH 17/39] Add files via upload --- team 8/images/SpaceDebrisGraph.jpeg | Bin 0 -> 432638 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 team 8/images/SpaceDebrisGraph.jpeg diff --git a/team 8/images/SpaceDebrisGraph.jpeg 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z8(1AYv`Ns!HGVTIl^D09@Z2meXoppbsReQ8A&~QIcr$BwLb?A|BL@+5CtMsSb=daC z-dzV@&kSH$D!+c1tttg5Fxz7x>EhL_X9Q!Gsf+oM)Am=&?hbu^hMuW79GE>Um^>vL zfl|6o?mVRd;${Rtm^S8VxJsM-YpdfA3#|WymMHWe0o?t4qc*oY0o~w%7@bOkCY}a%6bV^ zhE=bJ-YzDchlSL$6K`gHpE2wC#X>6G3BXhK#}GkH30J+3h{K%YS;~-Yi+9t=vv}%XE@SO)gdG<6+2;G<;|E6 z2v&Nx4Bp4QppEMiO460BlQ8(%;>#Fm#q%{FPZk=x#l0c Date: Wed, 27 Jul 2022 15:53:58 +0300 Subject: [PATCH 18/39] Add files via upload --- team 8/Debris_Removal_Model.ipynb | 382 +++++++++++++++--------------- team 8/dummy_graph_option.png | Bin 0 -> 28698 bytes 2 files changed, 191 insertions(+), 191 deletions(-) create mode 100644 team 8/dummy_graph_option.png diff --git a/team 8/Debris_Removal_Model.ipynb b/team 8/Debris_Removal_Model.ipynb index 4a684c3..8ce98d1 100644 --- a/team 8/Debris_Removal_Model.ipynb +++ b/team 8/Debris_Removal_Model.ipynb @@ -141,7 +141,7 @@ }, { "cell_type": "code", - "execution_count": 78, + "execution_count": 197, "metadata": {}, "outputs": [ { @@ -176,12 +176,12 @@ }, { "cell_type": "code", - "execution_count": 79, + "execution_count": 232, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
    " ] @@ -193,13 +193,13 @@ } ], "source": [ - "graph_drawing(G,'done',bitstring = [1,1,1,0,1],filename = 'dummy_graph_option.png')\n", + "graph_drawing(G,'done',bitstring = [1,1,1,0,0],filename = 'dummy_graph_option.png')\n", "# graph_drawing(G,'done',bitstring = [1,0,1],filename = 'dummy_graph_option.png')" ] }, { "cell_type": "code", - "execution_count": 80, + "execution_count": 199, "metadata": {}, "outputs": [ { @@ -208,7 +208,7 @@ "[1, 2, 7, 4, 5]" ] }, - "execution_count": 80, + "execution_count": 199, "metadata": {}, "output_type": "execute_result" } @@ -219,7 +219,7 @@ }, { "cell_type": "code", - "execution_count": 81, + "execution_count": 200, "metadata": {}, "outputs": [ { @@ -228,7 +228,7 @@ "True" ] }, - "execution_count": 81, + "execution_count": 200, "metadata": {}, "output_type": "execute_result" } @@ -251,19 +251,17 @@ "Calculation of the hamiltonian coefficients \n", "\n", "\\begin{equation}\n", - "H = \\sum_{(i,j) \\in E} q_{ij} \\frac{1}{2} (1 - \\hat{Z_i} \\hat{Z_j}) - \\sum_{i=1}^{N} k_i \\hat{Z_i}\n", + "H = \\sum_{i=1}^{N} (h_i - \\sum_{j \\not= i} g_{ij}) \\, Z_i + \\sum_{i" ] }, - "execution_count": 85, + "execution_count": 205, "metadata": {}, "output_type": "execute_result" } @@ -380,12 +423,12 @@ "gamma = Parameter(\"$\\\\gamma$\")\n", "qc_p_1 = QuantumCircuit(nqubits)\n", "for edge in G.edges: # pairs of nodes\n", - " qc_p_1.rzz(2 * gamma * q[G.edges.index(edge)], edge[0], edge[1])\n", + " qc_p_1.rzz(2 * gamma * g[edge[0], edge[1]], edge[0], edge[1])\n", " qc_p_1.barrier()\n", "\n", "qc_p_2 = QuantumCircuit(nqubits)\n", "for i in range(0, nqubits):\n", - " qc_p_2.rz((2 * gamma * k[i] * (-1)),i) # we added (-1) as in H we have -k_iZ_i\n", + " qc_p_2.rz(2 * gamma * k[i],i)\n", " qc_p_2.barrier()\n", " \n", "qc_0 = QuantumCircuit(nqubits)\n", @@ -404,7 +447,7 @@ }, { "cell_type": "code", - "execution_count": 86, + "execution_count": 206, "metadata": {}, "outputs": [], "source": [ @@ -413,49 +456,69 @@ ] }, { - "cell_type": "markdown", + "cell_type": "code", + "execution_count": 207, "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.5\n", + "8.0\n", + "5.0\n", + "5.5\n", + "14.5\n", + "9.0\n", + "11.0\n", + "28.5\n", + "36.0\n", + "20.5\n" + ] + } + ], "source": [ - "Here we create the QAOA model to **minimize** the function: \n", - "\n", - "\\begin{equation}\n", - "C(\\vec{x}) = - \\sum_{i=1}^{N} p_i x_i + \\sum_{i,j=1}^{N} x_i x_j q_{ij} \n", - " \\end{equation} " + "for edge in G.edges: # pairs of nodes\n", + " print(2*g[edge[0], edge[1]])\n", + " " ] }, { "cell_type": "code", - "execution_count": 87, + "execution_count": 208, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "-20" + "[0, 0, 1, 0, 1]" ] }, - "execution_count": 87, + "execution_count": 208, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "x = [1,0,0,0,0]\n", - "obj = 0\n", - "q_part = 0\n", - "p_part = 0\n", - "for i in range(0,G.n_nodes):\n", - " p_part += p[i]*x[i]\n", - " for j in range(0,G.n_nodes):\n", - " if (i,j) in G.edges:\n", - " q_part+= x[i]*x[j]*q[G.edges.index((i,j))]\n", - "obj = q_part - p_part \n", - "obj" + "x = \"00101\"\n", + "x = list(map(int,list(x)))\n", + "x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we create the QAOA model to **minimize** the function: \n", + "\n", + "\\begin{equation}\n", + "C(\\vec{x}) = -2V \\sum_{i=1}^{N} w_i z_i + \\sum_{i" - ] - }, - "execution_count": 91, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "plot_histogram(counts, figsize=(16, 10), color=None, number_to_keep=None,\n", - " sort='asc', target_string=None, legend=None,\n", - " bar_labels=True, title=\"Final Distribution\", ax=None)" - ] - }, - { - "cell_type": "code", - "execution_count": 23, + "cell_type": "markdown", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
    " - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - } - ], "source": [ - "from qiskit import BasicAer\n", - "qc = QuantumCircuit(2)\n", - "# qc.h(0) \n", - "qc.x(0) \n", - "qc.measure_all() \n", - "qasm_sim = BasicAer.get_backend('qasm_simulator') #this time we call the qasm simulator\n", - "result = execute(qc, qasm_sim, shots=100).result() # NOTICE: we can skip some steps by doing .result() directly, we could go further!\n", - "counts = result.get_counts() #this time, we are not getting the state, but the counts!\n", - "qc.draw(\"mpl\")" + "## Final results " ] }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 231, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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"text/plain": [ - "
    " + "
    " ] }, - "execution_count": 24, + "execution_count": 231, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "plot_histogram(counts) " + "plot_histogram(counts, figsize=(16, 10), color=None, number_to_keep=None,\n", + " sort='asc', target_string=None, legend=None,\n", + " bar_labels=True, title=\"Final Distribution\", ax=None)" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { diff --git a/team 8/dummy_graph_option.png b/team 8/dummy_graph_option.png new file mode 100644 index 0000000000000000000000000000000000000000..e27e24c1eed6212c78b4484fcac12823bdb87ca6 GIT binary patch literal 28698 zcmeFY_cxqh)IK~+5IxbO1~U@9MG1yP38O~uErRI1_k;+djou@f5JZVOAs9V`kP*EN z5{%wrbnor?Jn#Gd4d1oCKUibUy64>c?6b?Yuf0#)Q*BjBGG;Om2t)~2Q`Q542oA6R zZW06E{1{(|2RaY8Wpv;E$+DB?GRSz$WF4dS(nu{Xo=sf^-mvO742oR)3mSP^8*3@ymeC0 zSiAm$*hEnZ_!L9aGy@N$5oC@eiuPtx)I__#743Z<3H7ymE6M{FC}sgZ@7R#e0YB{r 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zA2e97a$s3G;(=r)w@p`)(wpq%*tc$&P;~10F+kZqVBNV}&*%4cRDp1pz`nVE&YA*z z(j9Pc6r)5&$o|mnu~nb@6~t$#O*`Hp=^w=C|1>!CuI{62?HRtHuc25hVnSiWG*4kb z+3%qqC8k{A#r;iMwrhTVU I#p>z*0YhLpiU0rr literal 0 HcmV?d00001 From 723223f84dc2676212c41829d57170115a6921ea Mon Sep 17 00:00:00 2001 From: VasilyBokov <62181457+VasilyBokov@users.noreply.github.com> Date: Wed, 27 Jul 2022 15:57:07 +0300 Subject: [PATCH 19/39] Add files via upload --- team 8/Debris_Removal_Model_Qiskit.ipynb | 779 +++++++++++++++++++++++ 1 file changed, 779 insertions(+) create mode 100644 team 8/Debris_Removal_Model_Qiskit.ipynb diff --git a/team 8/Debris_Removal_Model_Qiskit.ipynb b/team 8/Debris_Removal_Model_Qiskit.ipynb new file mode 100644 index 0000000..456aae3 --- /dev/null +++ b/team 8/Debris_Removal_Model_Qiskit.ipynb @@ -0,0 +1,779 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import networkx as nx # tool to handle general Graphs \n", + "import matplotlib.pyplot as plt \n", + "from matplotlib import cm\n", + "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n", + "from typing import Any, Dict, List, Tuple\n", + "from qiskit import Aer, IBMQ\n", + "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit, transpile, assemble\n", + "from qiskit.providers.ibmq import least_busy\n", + "from qiskit.tools.monitor import job_monitor\n", + "from qiskit.visualization import plot_histogram" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Firstly, we define a class we can draw a graph in convinient way\n", + "class GraphModel:\n", + " \n", + " n_nodes: int\n", + " edges: List[Tuple[int, int]]\n", + " graph: nx.Graph\n", + " \n", + " def __init__(self, n_nodes, edges, weights, distancies, qaoa_solve=None):\n", + " \n", + " self.n_nodes = n_nodes\n", + " self.edges = edges\n", + " self.weights = weights\n", + " self.distancies = distancies\n", + " self.graph = nx.Graph()\n", + " self.graph.add_nodes_from(np.arange(0,n_nodes,1))\n", + " self.graph.add_edges_from(edges)\n", + " #self.qaoa_solve = qaoa_solve\n", + " \n", + " def draw_raw_graph(self):\n", + " \n", + " # Generate plot of the Graph\n", + " colors = ['cornflowerblue' for node in self.graph.nodes()]\n", + " default_axes = plt.axes(frameon=False)\n", + " random_pos = nx.random_layout(self.graph, seed=42)\n", + " pos = nx.spring_layout(self.graph, pos=random_pos)\n", + "\n", + " nx.draw_networkx_nodes(self.graph, node_color=colors, node_size=900,pos = pos, \n", + " alpha=1, ax=default_axes) \n", + " nx.draw_networkx_edges(self.graph, pos = pos, width=8,alpha=1,ax=default_axes,\n", + " edge_color=\"tab:gray\")\n", + " nx.draw_networkx_labels(self.graph, pos = pos, font_size=22, font_color=\"white\")\n", + "\n", + "\n", + " def draw_done_graph(self,bitstring):\n", + " \n", + " # Draw a graph in accordance with its bitstring\n", + " color_map = []\n", + " edgelist_different = []\n", + " edgelist_same = []\n", + " default_axes = plt.axes(frameon=False)\n", + " default_axes.axis('off')\n", + " random_pos = nx.random_layout(self.graph, seed=42)\n", + " pos = nx.spring_layout(self.graph, pos=random_pos)\n", + " \n", + " if bitstring == None:\n", + " self.draw_raw_graph()\n", + " else:\n", + " for i in bitstring:\n", + " if i > 0:\n", + " color_map.append('red')\n", + " else: \n", + " color_map.append('cornflowerblue')\n", + "# for edge in self.edges:\n", + "# if bitstring[edge[0]] != bitstring[edge[1]]:\n", + "# edgelist_different.append(edge)\n", + "# else:\n", + "# edgelist_same.append(edge)\n", + " \n", + " nx.draw_networkx_nodes(self.graph, node_color=color_map, node_size=900,pos = pos, \n", + " alpha=1, ax=default_axes) \n", + " nx.draw_networkx_edges(self.graph, pos = pos, edgelist = self.edges, \n", + " width=8,alpha=1,ax=default_axes,edge_color=\"tab:grey\")\n", + "# nx.draw_networkx_edges(self.graph, pos = pos, edgelist = edgelist_different,\n", + "# width=8,alpha=1,ax=default_axes, edge_color=\"tab:red\")\n", + " nx.draw_networkx_labels(self.graph, pos = pos, font_size=22, font_color=\"white\")\n", + " \n", + " def connections(self, node): \n", + " connection_list = []\n", + " for edge in self.edges:\n", + " if (edge[0] == node):\n", + " connection_list.append(edge[1])\n", + " elif (edge[1] == node):\n", + " connection_list.append(edge[0])\n", + " connection_list = list(dict.fromkeys(connection_list))\n", + " return connection_list\n", + " \n", + " # This function returns all edges corresponding to certain node of the graph G \n", + " def find_edges(self, node): \n", + " connection_edges = []\n", + " for edge in self.edges:\n", + " if (edge[0] == node):\n", + " connection_edges.append(edge)\n", + " elif (edge[1] == node):\n", + " connection_edges.append(edge)\n", + " connection_edges = list(dict.fromkeys(connection_edges)) \n", + " return connection_edges" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def graph_drawing(G,regime, *args, **kwargs):\n", + " bitstring = kwargs.get('bitstring', None)\n", + " filename = kwargs.get('filename', None)\n", + " figure, axes = plt.subplots(frameon=False)\n", + " axes.axis('off')\n", + " # Turn off tick labels\n", + " req_dpi = 100 \n", + " figure.set_size_inches(500 / float(req_dpi), \n", + " 500 / float(req_dpi)) \n", + " if regime == 'raw':\n", + " G.draw_raw_graph()\n", + " elif regime == 'done':\n", + " G.draw_done_graph(bitstring)\n", + " else:\n", + " raise ValueError('Regime is wrong')\n", + " \n", + " figure.savefig(filename, format='png',\n", + " transparent=True, dpi=req_dpi) " + ] + }, + { + "cell_type": "code", + "execution_count": 197, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Example of drawing method of the class GrapgModel\n", + "n_nodes = 5\n", + "E = [(0,1),(0,2),(0,3), (0,4),(1,2),(1,3), (1,4), (2,3), (2,4),(3,4) ]\n", + "weghts_list = [1,2,7,4,5]\n", + "distancies_list = [1,2,2,1,1,2,2,1,2,1]\n", + "G = GraphModel(n_nodes, E, weghts_list, distancies_list )\n", + "graph_drawing(G,'raw',filename = 'dummy_graph.png')\n", + "\n", + "# n_nodes = 3\n", + "# E = [(0,1),(0,2),(1,2)]\n", + "# weghts_list = [5,5,100]\n", + "# distancies_list = [1,1,10]\n", + "# G = GraphModel(n_nodes, E, weghts_list, distancies_list )\n", + "# graph_drawing(G,'raw',filename = 'dummy_graph.png')" + ] + }, + { + "cell_type": "code", + "execution_count": 232, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "graph_drawing(G,'done',bitstring = [1,1,1,0,0],filename = 'dummy_graph_option.png')\n", + "# graph_drawing(G,'done',bitstring = [1,0,1],filename = 'dummy_graph_option.png')" + ] + }, + { + "cell_type": "code", + "execution_count": 199, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[1, 2, 7, 4, 5]" + ] + }, + "execution_count": 199, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.weights" + ] + }, + { + "cell_type": "code", + "execution_count": 200, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 200, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(G.distancies) == len(G.edges)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Circuit construction" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calculation of the hamiltonian coefficients \n", + "\n", + "\\begin{equation}\n", + "H = \\sum_{i=1}^{N} (h_i - \\sum_{j \\not= i} g_{ij}) \\, Z_i + \\sum_{i" + ] + }, + "execution_count": 231, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot_histogram(counts, figsize=(16, 10), color=None, number_to_keep=None,\n", + " sort='asc', target_string=None, legend=None,\n", + " bar_labels=True, title=\"Final Distribution\", ax=None)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "00111 corresponds to 0,1,2 nodes are occupied" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.12" + } 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z%0h34dmq3`f_VseJjpqB=_>iX{t(E9R0ae29qzG!E1Mvsr92qw?9pL8TNE}HdMrXz z#7Bcc_{r^p8_R6KTDb!8lzfOiEci`H7dUZqD?dt?4Gz$F2(h^h$e8EuA@0JDUiwwgT zM#gjBLd7Sa62sp=1(&U*aDatDx`_?g(f+^7*8bm}bpQALd)PC|xTx}c-`h|9z=eWj NFfD^SrMK+D{y(Kxe Date: Wed, 27 Jul 2022 15:59:56 +0300 Subject: [PATCH 22/39] Delete Debris_Removal_Model.ipynb --- team 8/Debris_Removal_Model.ipynb | 770 ------------------------------ 1 file changed, 770 deletions(-) delete mode 100644 team 8/Debris_Removal_Model.ipynb diff --git a/team 8/Debris_Removal_Model.ipynb b/team 8/Debris_Removal_Model.ipynb deleted file mode 100644 index 8ce98d1..0000000 --- a/team 8/Debris_Removal_Model.ipynb +++ /dev/null @@ -1,770 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import networkx as nx # tool to handle general Graphs \n", - "import matplotlib.pyplot as plt \n", - "from matplotlib import cm\n", - "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n", - "from typing import Any, Dict, List, Tuple\n", - "from qiskit import Aer, IBMQ\n", - "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit, transpile, assemble\n", - "from qiskit.providers.ibmq import least_busy\n", - "from qiskit.tools.monitor import job_monitor\n", - "from qiskit.visualization import plot_histogram" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "# Firstly, we define a class we can draw a graph in convinient way\n", - "class GraphModel:\n", - " \n", - " n_nodes: int\n", - " edges: List[Tuple[int, int]]\n", - " graph: nx.Graph\n", - " \n", - " def __init__(self, n_nodes, edges, weights, distancies, qaoa_solve=None):\n", - " \n", - " self.n_nodes = n_nodes\n", - " self.edges = edges\n", - " self.weights = weights\n", - " self.distancies = distancies\n", - " self.graph = nx.Graph()\n", - " self.graph.add_nodes_from(np.arange(0,n_nodes,1))\n", - " self.graph.add_edges_from(edges)\n", - " #self.qaoa_solve = qaoa_solve\n", - " \n", - " def draw_raw_graph(self):\n", - " \n", - " # Generate plot of the Graph\n", - " colors = ['cornflowerblue' for node in self.graph.nodes()]\n", - " default_axes = plt.axes(frameon=False)\n", - " random_pos = nx.random_layout(self.graph, seed=42)\n", - " pos = nx.spring_layout(self.graph, pos=random_pos)\n", - "\n", - " nx.draw_networkx_nodes(self.graph, node_color=colors, node_size=900,pos = pos, \n", - " alpha=1, ax=default_axes) \n", - " nx.draw_networkx_edges(self.graph, pos = pos, width=8,alpha=1,ax=default_axes,\n", - " edge_color=\"tab:gray\")\n", - " nx.draw_networkx_labels(self.graph, pos = pos, font_size=22, font_color=\"white\")\n", - "\n", - "\n", - " def draw_done_graph(self,bitstring):\n", - " \n", - " # Draw a graph in accordance with its bitstring\n", - " color_map = []\n", - " edgelist_different = []\n", - " edgelist_same = []\n", - " default_axes = plt.axes(frameon=False)\n", - " default_axes.axis('off')\n", - " random_pos = nx.random_layout(self.graph, seed=42)\n", - " pos = nx.spring_layout(self.graph, pos=random_pos)\n", - " \n", - " if bitstring == None:\n", - " self.draw_raw_graph()\n", - " else:\n", - " for i in bitstring:\n", - " if i > 0:\n", - " color_map.append('red')\n", - " else: \n", - " color_map.append('cornflowerblue')\n", - "# for edge in self.edges:\n", - "# if bitstring[edge[0]] != bitstring[edge[1]]:\n", - "# edgelist_different.append(edge)\n", - "# else:\n", - "# edgelist_same.append(edge)\n", - " \n", - " nx.draw_networkx_nodes(self.graph, node_color=color_map, node_size=900,pos = pos, \n", - " alpha=1, ax=default_axes) \n", - " nx.draw_networkx_edges(self.graph, pos = pos, edgelist = self.edges, \n", - " width=8,alpha=1,ax=default_axes,edge_color=\"tab:grey\")\n", - "# nx.draw_networkx_edges(self.graph, pos = pos, edgelist = edgelist_different,\n", - "# width=8,alpha=1,ax=default_axes, edge_color=\"tab:red\")\n", - " nx.draw_networkx_labels(self.graph, pos = pos, font_size=22, font_color=\"white\")\n", - " \n", - " def connections(self, node): \n", - " connection_list = []\n", - " for edge in self.edges:\n", - " if (edge[0] == node):\n", - " connection_list.append(edge[1])\n", - " elif (edge[1] == node):\n", - " connection_list.append(edge[0])\n", - " connection_list = list(dict.fromkeys(connection_list))\n", - " return connection_list\n", - " \n", - " # This function returns all edges corresponding to certain node of the graph G \n", - " def find_edges(self, node): \n", - " connection_edges = []\n", - " for edge in self.edges:\n", - " if (edge[0] == node):\n", - " connection_edges.append(edge)\n", - " elif (edge[1] == node):\n", - " connection_edges.append(edge)\n", - " connection_edges = list(dict.fromkeys(connection_edges)) \n", - " return connection_edges" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "def graph_drawing(G,regime, *args, **kwargs):\n", - " bitstring = kwargs.get('bitstring', None)\n", - " filename = kwargs.get('filename', None)\n", - " figure, axes = plt.subplots(frameon=False)\n", - " axes.axis('off')\n", - " # Turn off tick labels\n", - " req_dpi = 100 \n", - " figure.set_size_inches(500 / float(req_dpi), \n", - " 500 / float(req_dpi)) \n", - " if regime == 'raw':\n", - " G.draw_raw_graph()\n", - " elif regime == 'done':\n", - " G.draw_done_graph(bitstring)\n", - " else:\n", - " raise ValueError('Regime is wrong')\n", - " \n", - " figure.savefig(filename, format='png',\n", - " transparent=True, dpi=req_dpi) " - ] - }, - { - "cell_type": "code", - "execution_count": 197, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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    " - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# Example of drawing method of the class GrapgModel\n", - "n_nodes = 5\n", - "E = [(0,1),(0,2),(0,3), (0,4),(1,2),(1,3), (1,4), (2,3), (2,4),(3,4) ]\n", - "weghts_list = [1,2,7,4,5]\n", - "distancies_list = [1,2,2,1,1,2,2,1,2,1]\n", - "G = GraphModel(n_nodes, E, weghts_list, distancies_list )\n", - "graph_drawing(G,'raw',filename = 'dummy_graph.png')\n", - "\n", - "# n_nodes = 3\n", - "# E = [(0,1),(0,2),(1,2)]\n", - "# weghts_list = [5,5,100]\n", - "# distancies_list = [1,1,10]\n", - "# G = GraphModel(n_nodes, E, weghts_list, distancies_list )\n", - "# graph_drawing(G,'raw',filename = 'dummy_graph.png')" - ] - }, - { - "cell_type": "code", - "execution_count": 232, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
    " - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "graph_drawing(G,'done',bitstring = [1,1,1,0,0],filename = 'dummy_graph_option.png')\n", - "# graph_drawing(G,'done',bitstring = [1,0,1],filename = 'dummy_graph_option.png')" - ] - }, - { - "cell_type": "code", - "execution_count": 199, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[1, 2, 7, 4, 5]" - ] - }, - "execution_count": 199, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "G.weights" - ] - }, - { - "cell_type": "code", - "execution_count": 200, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "True" - ] - }, - "execution_count": 200, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "len(G.distancies) == len(G.edges)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Circuit construction" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Calculation of the hamiltonian coefficients \n", - "\n", - "\\begin{equation}\n", - "H = \\sum_{i=1}^{N} (h_i - \\sum_{j \\not= i} g_{ij}) \\, Z_i + \\sum_{i" - ] - }, - "execution_count": 231, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "plot_histogram(counts, figsize=(16, 10), color=None, number_to_keep=None,\n", - " sort='asc', target_string=None, legend=None,\n", - " bar_labels=True, title=\"Final Distribution\", ax=None)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.12" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} From 264075946d12d2369ece74826b7a3d7243581ec1 Mon Sep 17 00:00:00 2001 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zCQOX4SOj+Vq#i2Hu%M@z^4S?ND>FpOBiPmUj2V(BZx)BAdQjRDtdENjrAKT1a>1YE zJMu&n`OsW3nmnC3S>b*^=H$hEF12U8BK1?CjmbNezRU&m=*ofHoHmMp^jy3-L!6GN zLGrfqaCwN2o*FOSdMU%34D_9W$M}s2i`W)P7~|T;D9#Y`QxsWj?sWiVgJRiFN(;1; zvlZQ6jMIL`%M<|-E`!S86Me$odG)?CpQ+4@rxd_4Kt4==cym8HLhtuI_e!${+Wp{0 z;V&0$UJ8RwErS$Uuh^6PcyyW1CYn(H}?U+KHMha#l}Rv zA2e97a$s3G;(=r)w@p`)(wpq%*tc$&P;~10F+kZqVBNV}&*%4cRDp1pz`nVE&YA*z z(j9Pc6r)5&$o|mnu~nb@6~t$#O*`Hp=^w=C|1>!CuI{62?HRtHuc25hVnSiWG*4kb z+3%qqC8k{A#r;iMwrhTVU I#p>z*0YhLpiU0rr literal 0 HcmV?d00001 From a2751fb1b8509cff566b29634d820da8735e586d Mon Sep 17 00:00:00 2001 From: Jitesh Lalwani <64247212+ab-jiteshlalwani@users.noreply.github.com> Date: Wed, 27 Jul 2022 18:35:47 +0530 Subject: [PATCH 24/39] Added Fujitsu example --- team 8/Business_Application.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/team 8/Business_Application.md b/team 8/Business_Application.md index 7bdcba4..d8f4a96 100644 --- a/team 8/Business_Application.md +++ b/team 8/Business_Application.md @@ -41,7 +41,8 @@ The two problems that represent the situation of debris collection are known to * Space agencies, like NASA, ESA, etc, are potential customers because space debris can hinder their missions. * Governments around the world are also our potential customers since space debris can interfere with satellite operations as this is a matter of national security. In addition, it is related to the sustainability of space. * Space companies such as SpaceX and OneWeb, which plan to deploy 40,000+ satellites in the near future, will also be interested in our product since they wish to avoid collisions with space debris. -* We believe that startups such as CleanSpace, Astroscale, and others who are interested in space debris removal will be interested in our product since they want to collect more space debris with less cost and mission time. +* We believe that startups such as CleanSpace, Astroscale, and others who are interested in space debris removal will be interested in our product since they want to collect more space debris with less cost and mission time.
    +For e.g: Fujitsu worked with Glasgow University and Astroscale to demonstrate quantum advantage in space debris removal. The team designed an optimal mission in just 0.083 seconds using quantum inspired algorithms that reduced fuel costs by 25% and overall mission days by 23%. In addition, they were awarded £1 million in grants from the UK government. ### Architecture From 1e2dee42984c725573c00b841fa7f1134601e0b4 Mon Sep 17 00:00:00 2001 From: JPazem <109220752+JPazem@users.noreply.github.com> Date: Wed, 27 Jul 2022 15:23:51 +0200 Subject: [PATCH 25/39] Add files via upload --- team 8/Technical_Explanation.ipynb | 128 +++++++++++++++++++++++++++++ 1 file changed, 128 insertions(+) create mode 100644 team 8/Technical_Explanation.ipynb diff --git a/team 8/Technical_Explanation.ipynb b/team 8/Technical_Explanation.ipynb new file mode 100644 index 0000000..ba7f72e --- /dev/null +++ b/team 8/Technical_Explanation.ipynb @@ -0,0 +1,128 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "030bde69-364a-46c8-b41b-13e0892a6d24", + "metadata": {}, + "source": [ + "# Technical solution to space debris collection\n", + "\n", + "Here, we formulate the problem to solve to optimize space cleaning. " + ] + }, + { + "cell_type": "markdown", + "id": "69f1bc92-9639-46da-98cc-89805327de17", + "metadata": {}, + "source": [ + "The problem of trash in space has become a boiling issue: objects are orbiting around the earth, endangering the space expeditions. They are composed of dysfunctional instruments that are no longer in use, or broken parts that were torn apart from a larger device. In spite of being mostly very small, they travel at such impressive speeds that by Newton's law, any shock with one of these could cause tremendous damage to a space ship or a satellite. Since these space expeditions are very costly, it is a major challenge to avoid them, and to remove them from space in the long term. Therefore, the challenge of cleaning space has been undertaken by companies, space agencies and public institutions.\n", + "\n", + "To optimize their travel and collection schedule, two main constraints should be fulfilled:\n", + "1) Since the space ship has limited capacity, it can only collect so much that it can contain.\n", + "2) Fuel can also be contained in limited amounts, and is in itself very expensive. It is hence desirable to travel the longest distance that the fuel quantity allows.\n", + "\n", + "To formulate it simply, the challenge is to find the shortest path between debris that gathers the most of them, within the capactity of the ship. Using brute force, one would have to try all possible combinations of debris to find the one that fulfills these conditions the best. It is therefore a combinatorial optimization problem that would grow exponentially in the number of debris to choose from. It is therefore unscalable and untractable to classical computer at large scales. To circumvent this delicate issue, we propose to use a quantum-classical algorithm to get a better solution than a classical computer could get. Using the gate-based model in quantum computing, we solve the problem with the Quantum Approximate Optimization Algorithm.\n", + "\n", + "## Cost function \n", + "\n", + "To perform the optimization, we first express the problem in a cost function that we attempt to minimize. We start with a set of N debris. We encode the information about the debris in a bitstring:\\begin{equation}\n", + "z = z_1 z_2 \\cdots z_N, \\text{where } z_i = \\begin{cases}\n", + "1, & \\text{if debris i is collected} \\\\\n", + "0, & \\text{if otherwise.}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "To solve the problem with brute force method, we must inspect all possible bitstrings $z$ and pick the one that maximizes the volume of the debris collected. Therefore, it is a combinatorial optimization problem. To formulate it, we pair each debris $i$ with its weight/size $w_i$. The debris locations can be reported on a graph with edge set $E$ and vertex set $V$ such that $G = \\{E,V\\}$. Each vertex is associated with a weight, and each edge $i -j$ with a distance $d_{ij}$. With these notations, we encode the problem into the cost function:\n", + "\\begin{equation}\n", + "C(z) = (V-\\sum_{i=1}^{N} w_i z_i)^2 + \\sum_{ii} g_{ij} -\\sum_{j Date: Wed, 27 Jul 2022 18:55:55 +0530 Subject: [PATCH 26/39] Add files via upload QA added with Dwave --- team 8/space_debris_collection_QA_Dwave.ipynb | 589 ++++++++++++++++++ 1 file changed, 589 insertions(+) create mode 100644 team 8/space_debris_collection_QA_Dwave.ipynb diff --git a/team 8/space_debris_collection_QA_Dwave.ipynb b/team 8/space_debris_collection_QA_Dwave.ipynb new file mode 100644 index 0000000..044857e --- /dev/null +++ b/team 8/space_debris_collection_QA_Dwave.ipynb @@ -0,0 +1,589 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "space_debris_collection_QA_Dwave.ipynb", + "provenance": [] + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "code", + "execution_count": 117, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "iEYhchm4dvze", + "outputId": "90f67db7-edf5-4af7-ddcb-bf7187df8779" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n", + "Requirement already satisfied: pennylane in /usr/local/lib/python3.7/dist-packages (0.24.0)\n", + "Requirement already satisfied: autoray>=0.3.1 in /usr/local/lib/python3.7/dist-packages (from pennylane) (0.3.2)\n", + "Requirement already satisfied: networkx in /usr/local/lib/python3.7/dist-packages (from pennylane) (2.6.3)\n", + "Requirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from pennylane) (1.21.6)\n", + "Requirement already satisfied: appdirs in /usr/local/lib/python3.7/dist-packages (from pennylane) (1.4.4)\n", + "Requirement already satisfied: cachetools in /usr/local/lib/python3.7/dist-packages (from pennylane) (4.2.4)\n", + "Requirement already satisfied: semantic-version==2.6 in /usr/local/lib/python3.7/dist-packages (from pennylane) (2.6.0)\n", + "Requirement already satisfied: autograd in /usr/local/lib/python3.7/dist-packages (from pennylane) (1.4)\n", + "Requirement already satisfied: retworkx in /usr/local/lib/python3.7/dist-packages (from pennylane) (0.11.0)\n", + "Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from pennylane) (1.7.3)\n", + "Requirement already satisfied: pennylane-lightning>=0.24 in /usr/local/lib/python3.7/dist-packages (from pennylane) (0.24.0)\n", + "Requirement already satisfied: toml in /usr/local/lib/python3.7/dist-packages (from pennylane) (0.10.2)\n", + "Requirement already satisfied: ninja in /usr/local/lib/python3.7/dist-packages (from pennylane-lightning>=0.24->pennylane) (1.10.2.3)\n", + "Requirement already satisfied: future>=0.15.2 in /usr/local/lib/python3.7/dist-packages (from autograd->pennylane) (0.16.0)\n", + "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n", + "Requirement already satisfied: networkx in /usr/local/lib/python3.7/dist-packages (2.6.3)\n" + ] + } + ], + "source": [ + "import sys\n", + "!{sys.executable} -m pip install pennylane\n", + "!{sys.executable} -m pip install networkx" + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Space debris optimization" + ], + "metadata": { + "id": "wr3gMLPUepdb" + } + }, + { + "cell_type": "markdown", + "source": [ + "In this work, we solve the combinatorial optimization problem of space debris collection. A challenge for space agencies, satellite producers and any actor involved in space travel is to avoid space debris. In spite of possibly small sizes, their speeds on orbits make any collision with satellite or spacecraft threaten the success of space expeditions with major damage. Therefore, a major concern is to collect these debris and destroy them at the entrance of the atmosphere." + ], + "metadata": { + "id": "FdAx9nEVeytw" + } + }, + { + "cell_type": "markdown", + "source": [ + "The problem is the following. Debris collection journeys are expensive, since the quantity of fuels used to propel the engins is massive, and the capacity of each space craft limits the amount of space garbage that can be collected. To optimize each trip to space, we must therefore seek debris located at particular locations, such that they minimize the distance and hence the fuel consumption, and they maximize the quantity of trash collected. We solve the latter problem first, and add further constraints to the problem progressively." + ], + "metadata": { + "id": "sMUPN0CCfzsU" + } + }, + { + "cell_type": "markdown", + "source": [ + "Let us first consider the problem of maximization of the volume of trash that is collected. This task is related to the knapsack problem. \n", + "\n", + "We start with a set of N debris. We encode the information about the debris to collect in a bitstring:\n", + "\\begin{equation}\n", + "z = z_1 z_2 \\cdots z_N, \\text{where } z_i = \\begin{cases}\n", + "1, & \\text{if debris i is collected} \\\\\n", + "0, & \\text{if otherwise.}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "To solve the problem with brute force method, we must inspect all possible bitstrings $z$ and pick the one that maximizes the volume of the debris collected. Therefore, it is a combinatorial optimization problem. To formulate it, we pair each debris $i$ with its weight/size $w_i$. The debris locations can be reported on a graph with edge set $E$ and vertex set $V$ such that $G = \\{E,V\\}$. Each vertex is associated with a weight, and each edge $i -j$ with a distance $d_{ij}$. With these notations, we encode the problem into the cost function:\n", + "\\begin{equation}\n", + "C(z) = (V-\\sum_{i=1}^{N} w_i z_i)^2 + \\sum_{i 1]\n", + "light_edges = [(u, v) for (u, v, d) in G.edges(data=True) if d[\"weight\"] <= 1]\n", + "pos = nx.spring_layout(G, seed=11) \n", + "nx.draw_networkx_nodes(G, pos, node_size=700, node_color=\"r\")\n", + "nx.draw_networkx_edges(G, pos, edgelist=heavy_edges, width=6)\n", + "nx.draw_networkx_edges(G, pos, edgelist=light_edges, width=6, edge_color=\"b\", style=\"dashed\")\n", + "nx.draw_networkx_labels(G, pos, font_size=20, font_family=\"sans-serif\")\n", + "edge_labels = nx.get_edge_attributes(G, \"weight\")\n", + "nx.draw_networkx_edge_labels(G, pos, edge_labels)" + ], + "metadata": { + "id": "987QfIbfgt6D", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 427 + }, + "outputId": "02129067-7847-4e2e-8d0c-374b26094829" + }, + "execution_count": 119, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "{('0', '1'): Text(-0.31213490044069825, 0.0229285235823255, '1'),\n", + " ('0', '2'): Text(0.18180059090333675, -0.7976561108038269, '2'),\n", + " ('0', '3'): Text(-0.6981592185316541, -0.4262551763130149, '2'),\n", + " ('0', '4'): Text(0.2340158724740534, -0.207744883060842, '1'),\n", + " ('1', '2'): Text(0.26598412752594675, 0.16442417717540436, '1'),\n", + " ('1', '3'): Text(-0.6139756819090442, 0.5358251116662163, '2'),\n", + " ('1', '4'): Text(0.3181994090966634, 0.7543354049183892, '2'),\n", + " ('2', '3'): Text(-0.12004019056500914, -0.28475952271993604, '1'),\n", + " ('2', '4'): Text(0.8121349004406984, -0.06624922946776313, '2'),\n", + " ('3', '4'): Text(-0.0678249089942925, 0.30515170502304884, '1')}" + ] + }, + "metadata": {}, + "execution_count": 119 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "!pip install dwave-ocean-sdk" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "_zjw_nquuQYx", + "outputId": "40039bad-3ab6-4931-b9c8-8c3e60db11a6" + }, + "execution_count": 120, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n", + "Requirement already satisfied: dwave-ocean-sdk in /usr/local/lib/python3.7/dist-packages (5.3.0)\n", + "Requirement already satisfied: dimod==0.11.3 in /usr/local/lib/python3.7/dist-packages (from dwave-ocean-sdk) (0.11.3)\n", + "Requirement already satisfied: dwave-system==1.15.0 in /usr/local/lib/python3.7/dist-packages (from dwave-ocean-sdk) (1.15.0)\n", + "Requirement already satisfied: dwave-tabu==0.4.5 in /usr/local/lib/python3.7/dist-packages (from dwave-ocean-sdk) (0.4.5)\n", + "Requirement already satisfied: dwave-cloud-client==0.10.1 in /usr/local/lib/python3.7/dist-packages (from dwave-ocean-sdk) (0.10.1)\n", + "Requirement already satisfied: penaltymodel==1.0.2 in /usr/local/lib/python3.7/dist-packages (from dwave-ocean-sdk) (1.0.2)\n", + "Requirement already satisfied: dwave-inspector==0.3.0 in /usr/local/lib/python3.7/dist-packages (from dwave-ocean-sdk) (0.3.0)\n", + "Requirement already satisfied: dwave-networkx==0.8.12 in /usr/local/lib/python3.7/dist-packages (from dwave-ocean-sdk) (0.8.12)\n", + "Requirement already satisfied: dwave-greedy==0.2.5 in /usr/local/lib/python3.7/dist-packages (from dwave-ocean-sdk) (0.2.5)\n", + "Requirement already satisfied: dwavebinarycsp==0.2.0 in /usr/local/lib/python3.7/dist-packages (from dwave-ocean-sdk) (0.2.0)\n", + "Requirement already satisfied: dwave-neal==0.5.9 in /usr/local/lib/python3.7/dist-packages (from dwave-ocean-sdk) (0.5.9)\n", + "Requirement already satisfied: dwave-preprocessing==0.4.0 in /usr/local/lib/python3.7/dist-packages (from dwave-ocean-sdk) (0.4.0)\n", + "Requirement already satisfied: minorminer==0.2.9 in /usr/local/lib/python3.7/dist-packages (from dwave-ocean-sdk) (0.2.9)\n", + "Requirement already satisfied: dwave-hybrid==0.6.8 in /usr/local/lib/python3.7/dist-packages (from dwave-ocean-sdk) (0.6.8)\n", + "Requirement already satisfied: numpy<2.0.0,>=1.17.3 in /usr/local/lib/python3.7/dist-packages (from dimod==0.11.3->dwave-ocean-sdk) (1.21.6)\n", + "Requirement already satisfied: plucky>=0.4.3 in /usr/local/lib/python3.7/dist-packages (from dwave-cloud-client==0.10.1->dwave-ocean-sdk) (0.4.3)\n", + "Requirement already satisfied: diskcache>=5.2.1 in /usr/local/lib/python3.7/dist-packages (from dwave-cloud-client==0.10.1->dwave-ocean-sdk) (5.4.0)\n", + "Requirement already satisfied: click>=7.0 in /usr/local/lib/python3.7/dist-packages (from dwave-cloud-client==0.10.1->dwave-ocean-sdk) (7.1.2)\n", + "Requirement already satisfied: requests[socks]>=2.18 in /usr/local/lib/python3.7/dist-packages (from dwave-cloud-client==0.10.1->dwave-ocean-sdk) (2.23.0)\n", + "Requirement already satisfied: pydantic>=1.7.3 in /usr/local/lib/python3.7/dist-packages (from dwave-cloud-client==0.10.1->dwave-ocean-sdk) (1.9.1)\n", + "Requirement already satisfied: python-dateutil>=2.7 in /usr/local/lib/python3.7/dist-packages (from dwave-cloud-client==0.10.1->dwave-ocean-sdk) (2.8.2)\n", + "Requirement already satisfied: homebase>=1.0 in /usr/local/lib/python3.7/dist-packages (from dwave-cloud-client==0.10.1->dwave-ocean-sdk) (1.0.1)\n", + "Requirement already satisfied: importlib-metadata>=1.0 in /usr/local/lib/python3.7/dist-packages (from dwave-greedy==0.2.5->dwave-ocean-sdk) (4.12.0)\n", + "Requirement already satisfied: networkx in /usr/local/lib/python3.7/dist-packages (from dwave-hybrid==0.6.8->dwave-ocean-sdk) (2.6.3)\n", + "Requirement already satisfied: Flask>=1.1.1 in /usr/local/lib/python3.7/dist-packages (from dwave-inspector==0.3.0->dwave-ocean-sdk) (1.1.4)\n", + "Requirement already satisfied: importlib-resources>=3.2.0 in /usr/local/lib/python3.7/dist-packages (from dwave-inspector==0.3.0->dwave-ocean-sdk) (5.8.0)\n", + "Requirement already satisfied: fasteners in /usr/local/lib/python3.7/dist-packages (from minorminer==0.2.9->dwave-ocean-sdk) (0.17.3)\n", + "Requirement already satisfied: rectangle-packer>=2.0.1 in /usr/local/lib/python3.7/dist-packages (from minorminer==0.2.9->dwave-ocean-sdk) (2.0.1)\n", + "Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from minorminer==0.2.9->dwave-ocean-sdk) (1.7.3)\n", + "Requirement already satisfied: Werkzeug<2.0,>=0.15 in /usr/local/lib/python3.7/dist-packages (from Flask>=1.1.1->dwave-inspector==0.3.0->dwave-ocean-sdk) (1.0.1)\n", + "Requirement already satisfied: itsdangerous<2.0,>=0.24 in /usr/local/lib/python3.7/dist-packages (from Flask>=1.1.1->dwave-inspector==0.3.0->dwave-ocean-sdk) (1.1.0)\n", + "Requirement already satisfied: Jinja2<3.0,>=2.10.1 in /usr/local/lib/python3.7/dist-packages (from Flask>=1.1.1->dwave-inspector==0.3.0->dwave-ocean-sdk) (2.11.3)\n", + "Requirement already satisfied: zipp>=0.5 in /usr/local/lib/python3.7/dist-packages (from importlib-metadata>=1.0->dwave-greedy==0.2.5->dwave-ocean-sdk) (3.8.1)\n", + "Requirement already satisfied: typing-extensions>=3.6.4 in /usr/local/lib/python3.7/dist-packages (from importlib-metadata>=1.0->dwave-greedy==0.2.5->dwave-ocean-sdk) (4.1.1)\n", + "Requirement already satisfied: MarkupSafe>=0.23 in /usr/local/lib/python3.7/dist-packages (from Jinja2<3.0,>=2.10.1->Flask>=1.1.1->dwave-inspector==0.3.0->dwave-ocean-sdk) (2.0.1)\n", + "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.7/dist-packages (from python-dateutil>=2.7->dwave-cloud-client==0.10.1->dwave-ocean-sdk) (1.15.0)\n", + "Requirement already satisfied: urllib3!=1.25.0,!=1.25.1,<1.26,>=1.21.1 in /usr/local/lib/python3.7/dist-packages (from requests[socks]>=2.18->dwave-cloud-client==0.10.1->dwave-ocean-sdk) (1.24.3)\n", + "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.7/dist-packages (from requests[socks]>=2.18->dwave-cloud-client==0.10.1->dwave-ocean-sdk) (2022.6.15)\n", + "Requirement already satisfied: chardet<4,>=3.0.2 in /usr/local/lib/python3.7/dist-packages (from requests[socks]>=2.18->dwave-cloud-client==0.10.1->dwave-ocean-sdk) (3.0.4)\n", + "Requirement already satisfied: idna<3,>=2.5 in /usr/local/lib/python3.7/dist-packages (from requests[socks]>=2.18->dwave-cloud-client==0.10.1->dwave-ocean-sdk) (2.10)\n", + "Requirement already satisfied: PySocks!=1.5.7,>=1.5.6 in /usr/local/lib/python3.7/dist-packages (from requests[socks]>=2.18->dwave-cloud-client==0.10.1->dwave-ocean-sdk) (1.7.1)\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [ + "\n", + "from dwave.system.samplers import DWaveSampler\n", + "from dwave.system.composites import EmbeddingComposite\n", + "import numpy as np" + ], + "metadata": { + "id": "U9UX8YnHg4DJ" + }, + "execution_count": 121, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "from collections import defaultdict" + ], + "metadata": { + "id": "D4bYyUHD92e0" + }, + "execution_count": 122, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "Q = defaultdict(int)" + ], + "metadata": { + "id": "rH9taLW50UtQ" + }, + "execution_count": 123, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "w = [1,2,7,4,5]" + ], + "metadata": { + "id": "6Vk1R4N0Do1s" + }, + "execution_count": 124, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Constraint Knapsack enncoded\n", + "for i in range(len(w)):\n", + " for j in range(i+1,len(w)):\n", + " # print(i,j)\n", + " # print()\n", + " # print(2*w[i]*w[j])\n", + " Q[(i,j)] = 2*w[i]*w[j]\n", + " \n", + " " + ], + "metadata": { + "id": "eolHbTxjEHMf" + }, + "execution_count": 125, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "Q" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "YDO2DtLIHfz-", + "outputId": "dacd6dd7-8e23-491b-acd3-b63e2a32ddd5" + }, + "execution_count": 126, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "defaultdict(int,\n", + " {(0, 1): 4,\n", + " (0, 2): 14,\n", + " (0, 3): 8,\n", + " (0, 4): 10,\n", + " (1, 2): 28,\n", + " (1, 3): 16,\n", + " (1, 4): 20,\n", + " (2, 3): 56,\n", + " (2, 4): 70,\n", + " (3, 4): 40})" + ] + }, + "metadata": {}, + "execution_count": 126 + } + ] + }, + { + "cell_type": "code", + "source": [ + "for i in range(len(w)):\n", + " # print(i,i)\n", + " Q[(i,i)] = -19*w[i]+w[i]" + ], + "metadata": { + "id": "ISBmL_SAOmmQ" + }, + "execution_count": 127, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "Q" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "e1IQe3nzPwa8", + "outputId": "de330812-e036-481b-d78d-db1507a79c72" + }, + "execution_count": 128, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "defaultdict(int,\n", + " {(0, 0): -18,\n", + " (0, 1): 4,\n", + " (0, 2): 14,\n", + " (0, 3): 8,\n", + " (0, 4): 10,\n", + " (1, 1): -36,\n", + " (1, 2): 28,\n", + " (1, 3): 16,\n", + " (1, 4): 20,\n", + " (2, 2): -126,\n", + " (2, 3): 56,\n", + " (2, 4): 70,\n", + " (3, 3): -72,\n", + " (3, 4): 40,\n", + " (4, 4): -90})" + ] + }, + "metadata": {}, + "execution_count": 128 + } + ] + }, + { + "cell_type": "code", + "source": [ + "distances = nx.get_edge_attributes(G, \"weight\")" + ], + "metadata": { + "id": "Ue3pREmUhSry" + }, + "execution_count": 129, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "#Objective TSP encoded\n", + "for i in range(len(w)):\n", + " for j in range(i+1,len(w)):\n", + " # print(i,j)\n", + " # print(distances[(str(i),str(j))])\n", + " # print()\n", + " Q[(i,j)] += distances[(str(i),str(j))]" + ], + "metadata": { + "id": "TRpjNAJOR6b2" + }, + "execution_count": 130, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "Q" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "etHe5AhTgorW", + "outputId": "9be79d07-9824-4557-8d4f-43713aa1e6e3" + }, + "execution_count": 131, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "defaultdict(int,\n", + " {(0, 0): -18,\n", + " (0, 1): 5,\n", + " (0, 2): 16,\n", + " (0, 3): 10,\n", + " (0, 4): 11,\n", + " (1, 1): -36,\n", + " (1, 2): 29,\n", + " (1, 3): 18,\n", + " (1, 4): 22,\n", + " (2, 2): -126,\n", + " (2, 3): 57,\n", + " (2, 4): 72,\n", + " (3, 3): -72,\n", + " (3, 4): 41,\n", + " (4, 4): -90})" + ] + }, + "metadata": {}, + "execution_count": 131 + } + ] + }, + { + "cell_type": "code", + "source": [ + "sampler = DWaveSampler(token = '##############')\n", + "sampler = EmbeddingComposite(sampler)" + ], + "metadata": { + "id": "C_f4fG7Yjsgt" + }, + "execution_count": 132, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "response = sampler.sample_qubo(Q, num_reads = 1000)" + ], + "metadata": { + "id": "NTtKZYCfhvdX" + }, + "execution_count": 133, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "response" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "HtyEp8vOiX9f", + "outputId": "1e97780a-7ca5-490f-b6c8-2a3eea9a4ab5" + }, + "execution_count": 134, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "SampleSet(rec.array([([0, 0, 1, 0, 1], -144., 395, 0. ),\n", + " ([0, 0, 1, 1, 0], -141., 294, 0. ),\n", + " ([1, 0, 1, 0, 1], -135., 74, 0. ),\n", + " ([0, 1, 1, 0, 0], -133., 71, 0. ),\n", + " ([1, 0, 1, 1, 0], -133., 34, 0. ),\n", + " ([0, 1, 1, 1, 0], -130., 29, 0. ),\n", + " ([1, 1, 1, 0, 0], -130., 26, 0. ),\n", + " ([0, 1, 1, 0, 1], -129., 25, 0. ),\n", + " ([1, 0, 1, 0, 0], -128., 13, 0. ),\n", + " ([0, 0, 1, 0, 0], -126., 15, 0. ),\n", + " ([0, 0, 0, 1, 1], -121., 7, 0. ),\n", + " ([0, 0, 1, 1, 1], -118., 1, 0. ),\n", + " ([1, 0, 0, 1, 1], -118., 4, 0. ),\n", + " ([1, 1, 1, 1, 0], -117., 3, 0. ),\n", + " ([0, 1, 0, 1, 1], -117., 4, 0. ),\n", + " ([1, 1, 1, 0, 1], -115., 1, 0. ),\n", + " ([1, 1, 0, 1, 1], -109., 2, 0. ),\n", + " ([1, 1, 1, 1, 0], -117., 2, 0.2)],\n", + " dtype=[('sample', 'i1', (5,)), ('energy', ' Date: Wed, 27 Jul 2022 15:27:30 +0200 Subject: [PATCH 27/39] Add files via upload --- .../space_debris_collection_Pennylane.ipynb | 50 ------------------- 1 file changed, 50 deletions(-) diff --git a/team 8/space_debris_collection_Pennylane.ipynb b/team 8/space_debris_collection_Pennylane.ipynb index 1f98fe3..1ee916e 100644 --- a/team 8/space_debris_collection_Pennylane.ipynb +++ b/team 8/space_debris_collection_Pennylane.ipynb @@ -123,8 +123,6 @@ { "cell_type": "markdown", "source": [ - "Let us first consider the problem of maximization of the volume of trash that is collected. This task is related to the knapsack problem. \n", - "\n", "We start with a set of N debris. We encode the information about the debris to collect in a bitstring:\n", "\\begin{equation}\n", "z = z_1 z_2 \\cdots z_N, \\text{where } z_i = \\begin{cases}\n", @@ -181,54 +179,6 @@ "id": "lMeZrSQhQddb" } }, - { - "cell_type": "markdown", - "source": [ - "### Potentially wrong Hamiltonian WARNING" - ], - "metadata": { - "id": "G9JYbEBzQNKq" - } - }, - { - "cell_type": "markdown", - "source": [ - "The second step is to convert this cost function into a Hamiltonian with $\\hat{Z}$ operators acting on one and two qubits (Ising Hamiltonian). We realize the following mapping:\n", - "\\begin{equation}\n", - "z_i \\longrightarrow \\hat{Z_i} \n", - "\\end{equation}\n", - "where the quantum operator acts as:\n", - "\\begin{equation}\n", - "\\hat{Z_i} |z_i\\rangle = \n", - "\\begin{cases}\n", - "-1, & \\text{if } |z_i\\rangle = |1\\rangle \\\\\n", - "1, & \\text{if } |z_i\\rangle = |0\\rangle.\n", - "\\end{cases}\n", - "\\end{equation}\n", - "\n", - "The resulting problem Hamiltonian is:\n", - "\\begin{equation}\n", - "\\hat{H}_P = -2V \\sum_{i=1}^{N} w_i \\hat{Z_i} + \\sum_{i Date: Wed, 27 Jul 2022 15:33:57 +0200 Subject: [PATCH 28/39] Update ReadMe.md --- team 8/ReadMe.md | 10 ++++++++++ 1 file changed, 10 insertions(+) diff --git a/team 8/ReadMe.md b/team 8/ReadMe.md index 8b13789..eccc22a 100644 --- a/team 8/ReadMe.md +++ b/team 8/ReadMe.md @@ -1 +1,11 @@ +# Space debris collection +In this repository, you can find: +* Our [business proposal](.\Business_Application.md) +* A [technical explanation](.\Technical_Explanation.ipynb) of what algorithm does and how it works on this problem +* Our codes for: + * [Quantum Annealing](.\space_debris_collection_QA_Dwave.ipynb) + * [QAOA with Pennylane](.\space_debris_collection_Pennylane.ipynb) + * [QAOA with Qiskit](.\Debris_Removal_Model_Qiskit.ipynb) + + From 74c82a6158156f0bf590ca3d80b69280c8e8f047 Mon Sep 17 00:00:00 2001 From: AmitPatel-ArtificialBrain <106136305+AmitPatel-ArtificialBrain@users.noreply.github.com> Date: Wed, 27 Jul 2022 19:06:20 +0530 Subject: [PATCH 29/39] Update space_debris_collection_QA_Dwave.ipynb typo fixed in QA_dwave file --- team 8/space_debris_collection_QA_Dwave.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/team 8/space_debris_collection_QA_Dwave.ipynb b/team 8/space_debris_collection_QA_Dwave.ipynb index 044857e..a80a535 100644 --- a/team 8/space_debris_collection_QA_Dwave.ipynb +++ b/team 8/space_debris_collection_QA_Dwave.ipynb @@ -568,7 +568,7 @@ { "cell_type": "markdown", "source": [ - "As you can see the best solution we have got is [0,0,1,0,1] where 1 denotes w2 and w4 i.e 7 and 5 which is a total 11 which shows it has maximized the weights of debris usually we should have got results less than 10 which was our max weight but we have all constant terms from cost function that's why didn't got our desired total weight less than 10. After post processing we can easily find the optimum solution by going through the rest of the probabilities which satisfy the constraint." + "As you can see the best solution we have got is [0,0,1,0,1] where 1 denotes w2 and w4 i.e 7 and 5 which is a total 11 which shows it has maximized the weights of debris usually we should have got results less than 10 which was our max weight but we have all constant terms removed from cost function that's why didn't got our desired total weight less than 10. After post processing we can easily find the optimum solution by going through the rest of the probabilities which satisfy the constraint." ], "metadata": { "id": "CVXyNECPwgjE" @@ -586,4 +586,4 @@ "outputs": [] } ] -} \ No newline at end of file +} From 8b44dd2234fceccb27344c611b57c9e50a3f4c89 Mon Sep 17 00:00:00 2001 From: JPazem <109220752+JPazem@users.noreply.github.com> Date: Wed, 27 Jul 2022 15:37:49 +0200 Subject: [PATCH 30/39] Update ReadMe.md --- team 8/ReadMe.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/team 8/ReadMe.md b/team 8/ReadMe.md index eccc22a..727f50c 100644 --- a/team 8/ReadMe.md +++ b/team 8/ReadMe.md @@ -8,4 +8,4 @@ In this repository, you can find: * [QAOA with Pennylane](.\space_debris_collection_Pennylane.ipynb) * [QAOA with Qiskit](.\Debris_Removal_Model_Qiskit.ipynb) - + Here is a link to our presentation slides: https://docs.google.com/presentation/d/1zBIP7QOgtwzTeTv0sfvOP2ZzHSZc5o7bAlzJogANkA8/edit?usp=sharing From 3965609ea4f64392c39f6192ed8e937a8ecc4b8d Mon Sep 17 00:00:00 2001 From: JPazem <109220752+JPazem@users.noreply.github.com> Date: Wed, 27 Jul 2022 15:38:40 +0200 Subject: [PATCH 31/39] Update ReadMe.md --- team 8/ReadMe.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/team 8/ReadMe.md b/team 8/ReadMe.md index 727f50c..25c768b 100644 --- a/team 8/ReadMe.md +++ b/team 8/ReadMe.md @@ -1,5 +1,7 @@ # Space debris collection +We propose an efficient solution to optimize space expedition to collect space garbage. + In this repository, you can find: * Our [business proposal](.\Business_Application.md) * A [technical explanation](.\Technical_Explanation.ipynb) of what algorithm does and how it works on this problem From c29fa09d7dcd304a4d997800f7aa8368a39592d2 Mon Sep 17 00:00:00 2001 From: JPazem <109220752+JPazem@users.noreply.github.com> Date: Wed, 27 Jul 2022 15:42:35 +0200 Subject: [PATCH 32/39] Update ReadMe.md --- team 8/ReadMe.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/team 8/ReadMe.md b/team 8/ReadMe.md index 25c768b..e1a4c82 100644 --- a/team 8/ReadMe.md +++ b/team 8/ReadMe.md @@ -1,6 +1,8 @@ # Space debris collection -We propose an efficient solution to optimize space expedition to collect space garbage. +Welcome to our repository! Here, we propose an efficient solution to optimize space expedition to collect space garbage. + +![SpaceGraph](.\images\SpaceDebrisGraph.jpeg) In this repository, you can find: * Our [business proposal](.\Business_Application.md) From 5b6d2342b8b5399ff9327f7e4fa31ccb037a891b Mon Sep 17 00:00:00 2001 From: JPazem <109220752+JPazem@users.noreply.github.com> Date: Wed, 27 Jul 2022 15:42:56 +0200 Subject: [PATCH 33/39] Update ReadMe.md --- team 8/ReadMe.md | 2 -- 1 file changed, 2 deletions(-) diff --git a/team 8/ReadMe.md b/team 8/ReadMe.md index e1a4c82..998931c 100644 --- a/team 8/ReadMe.md +++ b/team 8/ReadMe.md @@ -2,8 +2,6 @@ Welcome to our repository! Here, we propose an efficient solution to optimize space expedition to collect space garbage. -![SpaceGraph](.\images\SpaceDebrisGraph.jpeg) - In this repository, you can find: * Our [business proposal](.\Business_Application.md) * A [technical explanation](.\Technical_Explanation.ipynb) of what algorithm does and how it works on this problem From 0d1da267cccd3b495f368b24dbe301771daa6c83 Mon Sep 17 00:00:00 2001 From: JPazem <109220752+JPazem@users.noreply.github.com> Date: Wed, 27 Jul 2022 15:44:51 +0200 Subject: [PATCH 34/39] Update ReadMe.md --- team 8/ReadMe.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/team 8/ReadMe.md b/team 8/ReadMe.md index 998931c..fdefa29 100644 --- a/team 8/ReadMe.md +++ b/team 8/ReadMe.md @@ -6,8 +6,8 @@ In this repository, you can find: * Our [business proposal](.\Business_Application.md) * A [technical explanation](.\Technical_Explanation.ipynb) of what algorithm does and how it works on this problem * Our codes for: - * [Quantum Annealing](.\space_debris_collection_QA_Dwave.ipynb) - * [QAOA with Pennylane](.\space_debris_collection_Pennylane.ipynb) - * [QAOA with Qiskit](.\Debris_Removal_Model_Qiskit.ipynb) + * [Quantum Annealing](.\space_debris_collection_QA_Dwave.ipynb) : space_debris_collection_QA_Dwave.ipynb + * [QAOA with Pennylane](.\space_debris_collection_Pennylane.ipynb) : space_debris_collection_Pennylane.ipynb + * [QAOA with Qiskit](.\Debris_Removal_Model_Qiskit.ipynb): Debris_Removal_Model_Qiskit.ipynb Here is a link to our presentation slides: https://docs.google.com/presentation/d/1zBIP7QOgtwzTeTv0sfvOP2ZzHSZc5o7bAlzJogANkA8/edit?usp=sharing From f96af3295f5334362cb906ae1c5721e3865a5c8a Mon Sep 17 00:00:00 2001 From: JPazem <109220752+JPazem@users.noreply.github.com> Date: Wed, 27 Jul 2022 15:45:23 +0200 Subject: [PATCH 35/39] Update ReadMe.md --- team 8/ReadMe.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/team 8/ReadMe.md b/team 8/ReadMe.md index fdefa29..5b43cfa 100644 --- a/team 8/ReadMe.md +++ b/team 8/ReadMe.md @@ -3,8 +3,8 @@ Welcome to our repository! Here, we propose an efficient solution to optimize space expedition to collect space garbage. In this repository, you can find: -* Our [business proposal](.\Business_Application.md) -* A [technical explanation](.\Technical_Explanation.ipynb) of what algorithm does and how it works on this problem +* Our [business proposal](.\Business_Application.md) : Business_Application.md +* A [technical explanation](.\Technical_Explanation.ipynb) of what algorithm does and how it works on this problem : Technical_Explanation.ipynb * Our codes for: * [Quantum Annealing](.\space_debris_collection_QA_Dwave.ipynb) : space_debris_collection_QA_Dwave.ipynb * [QAOA with Pennylane](.\space_debris_collection_Pennylane.ipynb) : space_debris_collection_Pennylane.ipynb From b7d476f5dd26d57e9d04b42105e4bdb89735ad41 Mon Sep 17 00:00:00 2001 From: VasilyBokov <62181457+VasilyBokov@users.noreply.github.com> Date: Wed, 27 Jul 2022 16:47:00 +0300 Subject: [PATCH 36/39] Update ReadMe.md --- team 8/ReadMe.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/team 8/ReadMe.md b/team 8/ReadMe.md index 5b43cfa..9638df5 100644 --- a/team 8/ReadMe.md +++ b/team 8/ReadMe.md @@ -8,6 +8,6 @@ In this repository, you can find: * Our codes for: * [Quantum Annealing](.\space_debris_collection_QA_Dwave.ipynb) : space_debris_collection_QA_Dwave.ipynb * [QAOA with Pennylane](.\space_debris_collection_Pennylane.ipynb) : space_debris_collection_Pennylane.ipynb - * [QAOA with Qiskit](.\Debris_Removal_Model_Qiskit.ipynb): Debris_Removal_Model_Qiskit.ipynb + * [QAOA with Qiskit](https://github.com/ab-jiteshlalwani/Hackathon2022/blob/main/team%208/Debris_Removal_Model_Qiskit.ipynb): Debris_Removal_Model_Qiskit.ipynb Here is a link to our presentation slides: https://docs.google.com/presentation/d/1zBIP7QOgtwzTeTv0sfvOP2ZzHSZc5o7bAlzJogANkA8/edit?usp=sharing From db2945f663cf20e701c009d851d2b6cf378c1f5b Mon Sep 17 00:00:00 2001 From: VasilyBokov <62181457+VasilyBokov@users.noreply.github.com> Date: Wed, 27 Jul 2022 16:48:50 +0300 Subject: [PATCH 37/39] Update ReadMe.md --- team 8/ReadMe.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/team 8/ReadMe.md b/team 8/ReadMe.md index 9638df5..f60e898 100644 --- a/team 8/ReadMe.md +++ b/team 8/ReadMe.md @@ -3,11 +3,11 @@ Welcome to our repository! Here, we propose an efficient solution to optimize space expedition to collect space garbage. In this repository, you can find: -* Our [business proposal](.\Business_Application.md) : Business_Application.md -* A [technical explanation](.\Technical_Explanation.ipynb) of what algorithm does and how it works on this problem : Technical_Explanation.ipynb +* Our [business proposal](https://github.com/ab-jiteshlalwani/Hackathon2022/blob/main/team%208/Business_Application.md) : Business_Application.md +* A [technical explanation](https://github.com/ab-jiteshlalwani/Hackathon2022/blob/main/team%208/Technical_Explanation.ipynb) of what algorithm does and how it works on this problem : Technical_Explanation.ipynb * Our codes for: - * [Quantum Annealing](.\space_debris_collection_QA_Dwave.ipynb) : space_debris_collection_QA_Dwave.ipynb - * [QAOA with Pennylane](.\space_debris_collection_Pennylane.ipynb) : space_debris_collection_Pennylane.ipynb + * [Quantum Annealing](https://github.com/ab-jiteshlalwani/Hackathon2022/blob/main/team%208/space_debris_collection_QA_Dwave.ipynb) : space_debris_collection_QA_Dwave.ipynb + * [QAOA with Pennylane](https://github.com/ab-jiteshlalwani/Hackathon2022/blob/main/team%208/space_debris_collection_Pennylane.ipynb) : space_debris_collection_Pennylane.ipynb * [QAOA with Qiskit](https://github.com/ab-jiteshlalwani/Hackathon2022/blob/main/team%208/Debris_Removal_Model_Qiskit.ipynb): Debris_Removal_Model_Qiskit.ipynb Here is a link to our presentation slides: https://docs.google.com/presentation/d/1zBIP7QOgtwzTeTv0sfvOP2ZzHSZc5o7bAlzJogANkA8/edit?usp=sharing From 5140ab257854b77987590adace4520551a52a7fd Mon Sep 17 00:00:00 2001 From: AmitPatel-ArtificialBrain <106136305+AmitPatel-ArtificialBrain@users.noreply.github.com> Date: Wed, 27 Jul 2022 19:34:11 +0530 Subject: [PATCH 38/39] Update Technical_Explanation.ipynb report added for Dwave --- team 8/Technical_Explanation.ipynb | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/team 8/Technical_Explanation.ipynb b/team 8/Technical_Explanation.ipynb index ba7f72e..359f3ff 100644 --- a/team 8/Technical_Explanation.ipynb +++ b/team 8/Technical_Explanation.ipynb @@ -95,6 +95,11 @@ "\n", "5) Use a classical optimizer to select the $\\gamma$ and $\\beta$ that minimize this expectation value.\n", "6) Run the QAOA circuit one more time and select the most probable basis state: it contains the answer to the problem." + + "##Quantum Annealing QUBO algorithm", + "\n", + "To solve the problem with Quantum Annealers, we need to convert our cost function to QUBO equation and then to QUBO matrix, as Dwave provides a high-level quantum annealing software that automatically creates embedding, normalizing, and scaling biases and couplers and provides results, following QUBO is:" + "\begin{align}C(z) &= \sum_{i=1}^{N} w_i z_i + 2\sum_{i Date: Wed, 27 Jul 2022 16:14:56 +0200 Subject: [PATCH 39/39] Add files via upload --- team 8/Technical_Explanation.ipynb | 5 ----- 1 file changed, 5 deletions(-) diff --git a/team 8/Technical_Explanation.ipynb b/team 8/Technical_Explanation.ipynb index 359f3ff..ba7f72e 100644 --- a/team 8/Technical_Explanation.ipynb +++ b/team 8/Technical_Explanation.ipynb @@ -95,11 +95,6 @@ "\n", "5) Use a classical optimizer to select the $\\gamma$ and $\\beta$ that minimize this expectation value.\n", "6) Run the QAOA circuit one more time and select the most probable basis state: it contains the answer to the problem." - - "##Quantum Annealing QUBO algorithm", - "\n", - "To solve the problem with Quantum Annealers, we need to convert our cost function to QUBO equation and then to QUBO matrix, as Dwave provides a high-level quantum annealing software that automatically creates embedding, normalizing, and scaling biases and couplers and provides results, following QUBO is:" - "\begin{align}C(z) &= \sum_{i=1}^{N} w_i z_i + 2\sum_{i