qsec/qmath.py at master · 2forts/qsec · GitHub

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#
#Comparator circuit. It only uses 1 ancilla input
#@version 1.0
#@author: Francisco Orts <francisco.orts@ual.es>. The circuit used to compute the
#addition and the subtraction is proposed in  https://dl.acm.org/doi/abs/10.1145/2491682.
#On the other hand, the design of the circuit used to compute the squaring is presented
#in https://dl.acm.org/doi/10.1007/s00034-017-0631-5
#

from projectq.ops import X, CNOT, Toffoli

#IMPORTANT: In the paper, the adder without input carry of https://dl.acm.org/doi/abs/10.1145/2491682.
#is used to perform the subractions. Here, the version with input carry is used to test the two adders.
#Please, adapt method addingNoCarryInput() (the adder withouth input carry) if you want to use that
#version. Contact me if you need help with that version (<francisco.orts@ual.es>).
#bb.cin is reverted to be used in the two subtractions.
def subtractingX(eng, bb):
    #Step 1
    X | bb.cin
    X | bb.xj0
    X | bb.xj1
    X | bb.xj2

    #Step 2
    CNOT | (bb.xi0, bb.xj0)
    CNOT | (bb.xi1, bb.xj1)
    CNOT | (bb.xi2, bb.xj2)

    #Step 3
    CNOT | (bb.xi0, bb.cin)

    #Step 4
    CNOT | (bb.xi1, bb.xi0)

    #Step 5
    Toffoli | (bb.cin, bb.xj0, bb.xi0)
    CNOT | (bb.xi2, bb.xi1)

    #Step 6
    Toffoli | (bb.xi0, bb.xj1, bb.xi1)

    #Step 8
    X | bb.xj0
    X | bb.xj1
    CNOT | (bb.xi1, bb.xj2)

    #Step 9
    X | bb.xj1
    Toffoli | (bb.xi0, bb.xj1, bb.xi1)
    X | bb.xj1
    CNOT | (bb.xi0, bb.xj1)

    #Step 10
    X | bb.xj0
    Toffoli | (bb.cin, bb.xj0, bb.xi0)
    X | bb.xj0
    CNOT | (bb.cin, bb.xj0)
    X | bb.xj1
    CNOT | (bb.xi2, bb.xi1)

    #Step 12
    X | bb.xj0
    CNOT | (bb.xi1, bb.xi0)

    #Step 13
    CNOT | (bb.xi0, bb.cin)

    #Step 15
    CNOT | (bb.xi0, bb.xj0)
    CNOT | (bb.xi1, bb.xj1)
    CNOT | (bb.xi2, bb.xj2)
    X | bb.cin

def subtractingY(eng, bb):
    #Step 1
    X | bb.cin
    X | bb.yj0
    X | bb.yj1
    X | bb.yj2

    #Step 2
    CNOT | (bb.yi0, bb.yj0)
    CNOT | (bb.yi1, bb.yj1)
    CNOT | (bb.yi2, bb.yj2)

    #Step 3
    CNOT | (bb.yi0, bb.cin)

    #Step 4
    CNOT | (bb.yi1, bb.yi0)

    #Step 5
    Toffoli | (bb.cin, bb.yj0, bb.yi0)
    CNOT | (bb.yi2, bb.yi1)

    #Step 6
    Toffoli | (bb.yi0, bb.yj1, bb.yi1)

    #Step 8
    X | bb.yj0
    X | bb.yj1
    CNOT | (bb.yi1, bb.yj2)

    #Step 9
    X | bb.yj1
    Toffoli | (bb.yi0, bb.yj1, bb.yi1)
    X | bb.yj1
    CNOT | (bb.yi0, bb.yj1)

    #Step 10
    X | bb.yj0
    Toffoli | (bb.cin, bb.yj0, bb.yi0)
    X | bb.yj0
    CNOT | (bb.cin, bb.yj0)
    X | bb.yj1
    CNOT | (bb.yi2, bb.yi1)

    #Step 12
    X | bb.yj0
    CNOT | (bb.yi1, bb.yi0)

    #Step 13
    CNOT | (bb.yi0, bb.cin)

    #Step 15
    CNOT | (bb.yi0, bb.yj0)
    CNOT | (bb.yi1, bb.yj1)
    CNOT | (bb.yi2, bb.yj2)
    X | bb.cin

def UNCOMPUTEsubtracting(bb):
    #Uncompute Y
    #Step 15
    X | bb.cin
    CNOT | (bb.yi2, bb.yj2)
    CNOT | (bb.yi1, bb.yj1)
    CNOT | (bb.yi0, bb.yj0)

    #Step 13
    CNOT | (bb.yi0, bb.cin)

    #Step 12
    X | bb.yj0
    CNOT | (bb.yi1, bb.yi0)

    #Step 10
    CNOT | (bb.yi2, bb.yi1)
    X | bb.yj1
    CNOT | (bb.cin, bb.yj0)
    X | bb.yj0
    Toffoli | (bb.cin, bb.yj0, bb.yi0)
    X | bb.yj0

    #Step 9
    CNOT | (bb.yi0, bb.yj1)
    X | bb.yj1
    Toffoli | (bb.yi0, bb.yj1, bb.yi1)
    X | bb.yj1

    #Step 8
    CNOT | (bb.yi1, bb.yj2)
    X | bb.yj1
    X | bb.yj0

    #Step 6
    Toffoli | (bb.yi0, bb.yj1, bb.yi1)

    #Step 5
    CNOT | (bb.yi2, bb.yi1)
    Toffoli | (bb.cin, bb.yj0, bb.yi0)

    #Step 4
    CNOT | (bb.yi1, bb.yi0)

    #Step 3
    CNOT | (bb.yi0, bb.cin)

    #Step 2
    CNOT | (bb.yi0, bb.yj0)
    CNOT | (bb.yi1, bb.yj1)
    CNOT | (bb.yi2, bb.yj2)

    #Step 1
    X | bb.cin
    X | bb.yj0
    X | bb.yj1
    X | bb.yj2

    #Uncompute X
    #Step 15
    X | bb.cin
    CNOT | (bb.xi2, bb.xj2)
    CNOT | (bb.xi1, bb.xj1)
    CNOT | (bb.xi0, bb.xj0)

    #Step 13
    CNOT | (bb.xi0, bb.cin)

    #Step 12
    CNOT | (bb.xi1, bb.xi0)
    X | bb.xj0

    #Step 10
    CNOT | (bb.xi2, bb.xi1)
    X | bb.xj1
    CNOT | (bb.cin, bb.xj0)
    X | bb.xj0
    Toffoli | (bb.cin, bb.xj0, bb.xi0)
    X | bb.xj0

    #Step 9
    CNOT | (bb.xi0, bb.xj1)
    X | bb.xj1
    Toffoli | (bb.xi0, bb.xj1, bb.xi1)
    X | bb.xj1

    #Step 8
    CNOT | (bb.xi1, bb.xj2)
    X | bb.xj1
    X | bb.xj0

    #Step 6
    Toffoli | (bb.xi0, bb.xj1, bb.xi1)

    #Step 5
    CNOT | (bb.xi2, bb.xi1)
    Toffoli | (bb.cin, bb.xj0, bb.xi0)

    #Step 4
    CNOT | (bb.xi1, bb.xi0)

    #Step 3
    CNOT | (bb.xi0, bb.cin)

    #Step 2
    CNOT | (bb.xi0, bb.xj0)
    CNOT | (bb.xi1, bb.xj1)
    CNOT | (bb.xi2, bb.xj2)

    #Step 1
    X | bb.cin
    X | bb.xj0
    X | bb.xj1
    X | bb.xj2

#Squaring circuit
def squaringX(bb):
    #Step 1
    #X | ai0
    #X | ai3
    #X | ai4

    #Step 2
    Toffoli | (bb.xj0, bb.xj1, bb.ai2)

    #Step 3
    Toffoli | (bb.xj0, bb.xj2, bb.ai3)

    #Step 4
    Toffoli | (bb.xj1, bb.xj2, bb.ai4)

    #Step 5
    Toffoli | (bb.xj1, bb.ai2, bb.ai5)
    CNOT | (bb.xj1, bb.ai2)

    #Step 6
    #ControlledGate(X, 3) | (ai0, ai3, ai5, ai6)
    Toffoli | (bb.ai0, bb.ai3, bb.ai5)

    #Step 7
    #ControlledGate(X, 3) | (xj2, ai4, ai6, ai7)
    #Toffoli | (xj2, ai4, ai6)

def squaringY(bb):
    #Step 1
    #X | bi0
    #X | bi3
    #X | bi4

    #Step 2
    Toffoli | (bb.yj0, bb.yj1, bb.bi2)

    #Step 3
    Toffoli | (bb.yj0, bb.yj2, bb.bi3)

    #Step 4
    Toffoli | (bb.yj1, bb.yj2, bb.bi4)

    #Step 5
    Toffoli | (bb.yj1, bb.bi2, bb.bi5)
    CNOT | (bb.yj1, bb.bi2)

    #Step 6
    #ControlledGate(X, 3) | (bi0, bi3, bi5, bi6)
    Toffoli | (bb.bi0, bb.bi3, bb.bi5)

    #Step 7
    #ControlledGate(X, 3) | (yj2, bi4, bi6, bi7)
    #Toffoli | (yj2, bi4, bi6)

def UNCOMPUTEsquaring(bb):
    #Uncompute Y
    #Step 6
    Toffoli | (bb.bi0, bb.bi3, bb.bi5)

    #Step 5
    CNOT | (bb.yj1, bb.bi2)
    Toffoli | (bb.yj1, bb.bi2, bb.bi5)

    #Step 4
    Toffoli | (bb.yj1, bb.yj2, bb.bi4)

    #Step 3
    Toffoli | (bb.yj0, bb.yj2, bb.bi3)

    #Step 2
    Toffoli | (bb.yj0, bb.yj1, bb.bi2)

    #Uncompute X
    #Step 6
    Toffoli | (bb.ai0, bb.ai3, bb.ai5)

    #Step 5
    CNOT | (bb.xj1, bb.ai2)
    Toffoli | (bb.xj1, bb.ai2, bb.ai5)

    #Step 4
    Toffoli | (bb.xj1, bb.xj2, bb.ai4)

    #Step 3
    Toffoli | (bb.xj0, bb.xj2, bb.ai3)

    #Step 2
    Toffoli | (bb.xj0, bb.xj1, bb.ai2)

def addingNoCarryInput(bb):
    #Step 2
    CNOT | (bb.ai1, bb.bi1)
    CNOT | (bb.ai2, bb.bi2)
    CNOT | (bb.ai5, bb.bi5)

    #Step 3
    CNOT | (bb.ai5, bb.z)

    #Step 4
    CNOT | (bb.ai2, bb.ai5)

    #Step 5
    CNOT | (bb.ai1, bb.ai2)

    #Step 6
    Toffoli | (bb.yj0, bb.xj0, bb.ai1)

    #Step 7
    Toffoli | (bb.bi1, bb.ai1, bb.ai2)

    #Step 8
    Toffoli | (bb.bi2, bb.ai2, bb.ai5)

    #Step 9
    Toffoli | (bb.ai5, bb.bi5, bb.z)
    CNOT | (bb.ai5, bb.bi5)

    #Step 10
    Toffoli | (bb.ai2, bb.bi2, bb.ai5)
    CNOT | (bb.ai2, bb.bi2)

    #Step 11
    Toffoli | (bb.ai1, bb.bi1, bb.ai2)
    CNOT | (bb.ai1, bb.bi1)

    #Step 12
    Toffoli | (bb.xj0, bb.yj0, bb.ai1)
    CNOT | (bb.xj0, bb.yj0)

    #Step 13
    CNOT | (bb.ai1, bb.ai2)

    #Step 14
    CNOT | (bb.ai2, bb.bi5)

    #Step 15
    CNOT | (bb.ai1, bb.bi1)
    CNOT | (bb.ai2, bb.bi2)
    CNOT | (bb.ai5, bb.bi5)

def UNCOMPUTEaddingNoCarryInput(bb):
    #Step 15
    CNOT | (bb.ai1, bb.bi1)
    CNOT | (bb.ai2, bb.bi2)
    CNOT | (bb.ai5, bb.bi5)

    #Step 14
    CNOT | (bb.ai2, bb.bi5)

    #Step 13
    CNOT | (bb.ai1, bb.ai2)

    #Step 12
    CNOT | (bb.xj0, bb.yj0)
    Toffoli | (bb.xj0, bb.yj0, bb.ai1)

    #Step 11
    CNOT | (bb.ai1, bb.bi1)
    Toffoli | (bb.ai1, bb.bi1, bb.ai2)

    #Step 10
    CNOT | (bb.ai2, bb.bi2)
    Toffoli | (bb.ai2, bb.bi2, bb.ai5)

    #Step 9
    CNOT | (bb.ai5, bb.bi5)
    Toffoli | (bb.ai5, bb.bi5, bb.z)

    #Step 8
    Toffoli | (bb.bi2, bb.ai2, bb.ai5)

    #Step 7
    Toffoli | (bb.bi1, bb.ai1, bb.ai2)

    #Step 6
    Toffoli | (bb.yj0, bb.xj0, bb.ai1)

    #Step 5
    CNOT | (bb.ai1, bb.ai2)

    #Step 4
    CNOT | (bb.ai2, bb.ai5)

    #Step 3
    CNOT | (bb.ai5, bb.z)

    #Step 2
    CNOT | (bb.ai1, bb.bi1)
    CNOT | (bb.ai2, bb.bi2)
    CNOT | (bb.ai5, bb.bi5)