Quantum Prisoner's Dilemma Simulation

This Jupyter Notebook implements a simulation of the Quantum Prisoner's Dilemma (QPD) game with multiple players, incorporating quantum strategies and knowledge sharing mechanisms. It uses Qiskit for quantum circuit construction and execution, either on a simulator or real quantum hardware.

Description

The notebook explores a multi-player extension of the Prisoner's Dilemma where one player employs a quantum strategy, while others use classical strategies. Key features include:

• Strategy Gates: Quantum gates representing player strategies based on parameters like theta, phi, and lambda.
• Payoff Calculation: Custom payoff matrices for cooperation and defection.
• Knowledge Sharing: Optional sharing of quantum states between games via entanglement.
• Experimentation: Runs simulations for different quantum players in a network defined by an adjacency matrix.
• Logging: Outputs game results, payoffs, and statistics to a CSV file.

The simulation supports both simulated (using AerSimulator) and real quantum processing unit (QPU) modes.

Requirements

• Python 3.8+
• Qiskit
• Qiskit Aer
• Qiskit IBM Runtime (for QPU mode)
• NumPy
• Pandas
• NetworkX
• Plotly
• SciPy

Installation

1. Install required packages:

   pip install qiskit qiskit-aer qiskit-ibm-runtime numpy pandas networkx plotly scipy
   

2. For QPU access, set up your IBM Quantum account and obtain an API token.

Usage

1. Open the notebook in Jupyter or VS Code.
2. Configure parameters in the main block:
   • knowledge_sharing: Boolean for enabling knowledge sharing.
   • adj_matrix: NumPy array defining player connections.
   • logfile: Path to the output CSV file.
   • mode: "simulated" or "qpu".
3. Run the notebook. It will simulate games for each player as the quantum player and log results.
4. Visualize the quantum circuit using circ.draw(output="mpl").

Example output includes average payoffs per player, computed from the logfile.

Output

• Logfile: CSV file with columns for game results, player payoffs, and metadata.
• Circuit Visualization: Matplotlib plot of the quantum circuit.
• Analysis: Use get_results() to compute mean payoffs from the logfile.

Notes

• Payoff values are arbitrarily chosen for simplicity.
• Ensure the adjacency matrix is symmetric for undirected graphs.
• For QPU mode, replace the token with your own and select an available backend.