Quantum_Battleships

A quantum version of the traditional battleship game

Overview

We made a quantum version of Battleships that you can play in a Jupyter Notebook. You have two actions on any grid square:

• Scan (quantum): Use a small quantum circuit to “peek” without fully looking.
• Fire (classical): Try to hit a ship.

The scan uses EV bomb testing ideas (interaction-free hints) and the Quantum Zeno effect (many tiny checks).

How to Use

The main page of our game

There're several parts on our UI.

On the top-left corner, there's the board of AI, where you can select a square, choose an action mode and adjust the parameters.

On the bottom-left corner, there's your board. You can see your ships and AI's movement here.

Once you select a square on AI's board, you can choose an action mode and adjust the parameters on the right of the page, then press 'Confirm! '. The results (hit/miss/found without exploded/exploded) will shown in the 'Stats' block.

After you took an action, please press 'AI Move' bottom, then AI will choose square/action mode/parameters and action.

There are 4 symbols in the game:

    symbols = {
        "O": " ",        # white label means the grid is never scanned or fired. 
        "X": "❌",       # means there is a ship hitted in the grid. 
        "M": "⭕️",       # means the grid is fired, but there's no ship here. 
        "S": "🟨",       # means the grid is scanned, and there's probably a ship. 
        "NS": "🟩",      # means the grid is scanned, and there's not likely a ship. 
    }

After an action, you'll be able to see the page like:

Your and AI's scores are shown on the right side of the string 'AI' and 'You'. That score is calculated using measurement times, hits, misses, etc. The detailed explanation of how to calculate the score is on the Score&Cost part.

A statistic log is printed below your grid. That's 2 dictionary like:

    usage = {
        'shots': 0,
        'measuments': 0,
        'positives': 0,
        'explosions': 0,
        'fire times': 0,
        'hits': 0,
        'misses': 0,
    }

Code: Quantum Engine

One qubit only.

From the outcomes we label each scan as:

• found (dark event seen) → likely ship,

• explodes (rare penalty event), or

• no_ship.

  QuantumEngine1 is the quantum scanning engine used in the Quantum Battleships game. It checks a board square using a Quantum Zeno / EV-style probe to guess whether a ship is there while spending as few resources as possible

How does it work?

• It normally uses Qiskit + AerSimulator to run a single-qubit circuit.
• The probe applies many tiny rotations. If a ship is present, the engine performs mid-circuit measurements + reset each step, then one final readout.
• It counts two important types of events:
  • dark → hint that a ship is present
  • exploded → rare but a stronger sign of a ship (and gives a penalty)
• It also calculates a Wilson confidence interval to show how confident we are about “ship present”.

Key methods

Method	Purpose
_zeno_counts_qiskit(...)	Runs the real quantum circuit and returns statistics (dark, exploded, counts).
_zeno_counts_proxy(...)	A simple probability-based fallback if Qiskit/Aer is not available.
_wilson_ci(...)	Gives a confidence range for the probability of “ship found”.
probe(...)	Main public method: scans a board square and returns results + cost + UI stats.

Code: AI

In AI Strategy part, we use Bayesian Belief Algorithm to improve its E.V. Score. First, we choose target among max-prob untargeted cells.Second, we consider the neighborhood of it and use Suggest method to adjust the next target. Finally, use update method to update the coordinate to choose for next step. We use In-place bayesian-like local update (reference rules) to update the label. After that, the next action depends on the status, that is whether Explodes, Found or Miss. If miss, continue to search for the next position. If explodes, Fire directly at the same position. If Found, continue to search around it.

Code: Other Classes

Board

Board state The class holds two 10×10 grids—one for the opponent and one for the player—plus two lists of ship coordinate sets for each side.

Game

Class Game shows the flow line of how ships are scaned or fired.The method ai_take_turn shows how AI will take strategy to improve its ev score.

UI

Finally, when it runs, we defind the functions on_scan and on_fire to show how it is demonstrated by the User Interface. Then display the UI.