CapstoneProject

This repository contains the Python code and simulations used in my Capstone Project for my undergraduate degree in Theoretical Physics at Trinity College Dublin: "Perfect Quantum State Transfer in Chaotic Systems". This project was supervised by Dr. Shane Dooley of the Dublin Institute of Advanced Studies.

This purpose of code written for this project was to construct the following

• An exact representation of a heisenberg spin chain capable of Perfect Quantum State Transfer.
• Local Projection Operators and Random Local Interactions to construct Quantum Many Body Scars
• Methods for computing the evolution of the system under the Schrodinger Eqn.
• Methods for computing and analysing the spectrum of the hamiltonian, including eigenvalue gap statistics, Von Neumann Entropy, and Expectation Values of Eiegenstates w.r.t the Projection Operators
• Visualisation methods, including plotting and animation

Project Structure

The repository is organized into the following directories and files:

• main_system/: Contains the primary class that models and simulates the XX-Scar system. This class includes methods for system construction, simulation, and visualization.

  • Qudit_Chain_OOP.py: Main OOP class for the simulation.

• other_systems/: Houses code for alternative or work-in-progress simulations that are based on variations of the primary system.

  • QutritEntanglementSharing.py: Simulations of an alternative quantum system.

• snippets/: Includes smaller code snippets or scripts for testing, plotting, or experimenting with various methods used in the project.

  • ClassDefinition.py: The initialisation of the class quditChain
  • ProjectorsConstruction.py: A function to generate the projectors used in the Shiriashi-Mori Hamiltonian
  • GenerateSM_Hamiltonian.py: A set of functions to generate the Shiriashi-Mori Hamiltonian
  • SchmidtSVN.py: A function compute the Von Neumann Entropy of the Eigenstates of the hamiltonian, using a schmidt decompositon.
  • XXHamiltonianGeneration.py: A set of functions to generate the XX Hamiltonian
  • Solve.py: A function to simulate the evolution of the sytem

• requirements.txt: A list of Python packages required to run the code.

Installation

To run the code locally, clone the repository and install the dependencies:

git clone https://github.com/yourusername/CapstoneProject.git
cd CapstoneProject
pip install -r requirements.txt