Simulating an iSWAP Gate with Coupled Qubits

This repository contains the simulation code for a Quantum Mechanics 2 (QM-2) course project. The objective is to simulate the time evolution of coupled qubits under an XY Hamiltonian to realize an iSWAP gate using Trotterization.

Project Overview

The project simulates the Hamiltonian: $$ H = g(X \otimes X + Y \otimes Y) $$

This interaction naturally gives rise to the iSWAP gate, which exchanges the amplitudes of the $|01\rangle$ and $|10\rangle$ states with a phase factor.

Key Features

• Trotterization: Implements time evolution using the Trotter-Suzuki decomposition.
• Circuit Visualization: Visualizes the quantum circuit decomposition into basis gates.
• Simulations:
  1. Single iSWAP: Demonstrates the state swap from $|01\rangle$ to $|10\rangle$.
  2. Time Evolution: Plots the probability of states $|01\rangle$ and $|10\rangle$ over time.
  3. Double iSWAP: Shows that applying the operation twice returns the system to the initial state (with a phase).

Files

• final.ipynb: The main Jupyter Notebook containing the complete simulation code and results.
• project_report.pdf: The detailed project report and documentation.
• images/: Directory containing the generated simulation plots.

Getting Started

Prerequisites

Ensure you have Python installed. You can install the required dependencies using pip:

pip install -r requirements.txt

Running the Simulation

Open the final.ipynb notebook to run the simulations:

jupyter notebook final.ipynb

Note: The notebook generates plots in the current directory. The canonical versions are stored in the images/ directory.

Results

Key simulation results:

Evolution

Single iSWAP

Double iSWAP

License

This project was developed for academic purposes.