Open Quantum System Dynamics with OQuPy

This repository contains a compact portfolio project on open quantum system dynamics using OQuPy.

The project focuses on the dynamics of a two-level quantum system coupled to a bosonic environment, illustrating key physical concepts such as decoherence, relaxation, memory effects, and non-Markovian dynamics.

Overview

Open quantum systems are quantum systems that interact with an external environment. Instead of evolving purely unitarily, their dynamics can include dissipation, decoherence, relaxation, and memory effects.

OQuPy is a Python package designed to simulate non-Markovian open quantum systems using process tensors and tensor-network-based methods.

Physical Model

The main example considered in this repository is a two-level system described by a Hamiltonian of the form

$$H_S = \frac{\epsilon}{2}\sigma_z + \frac{\Delta}{2}\sigma_x,$$

where:

• $\epsilon$ is the energy bias;
• $\Delta$ is the tunneling amplitude;
• $\sigma_x$ and $\sigma_z$ are Pauli matrices.

The system is coupled to a bosonic environment through an operator such as

$$A = \sigma_z.$$

This type of model is closely related to the spin-boson model, which is widely used to study decoherence and relaxation in quantum systems.

Goals

This repository aims to demonstrate:

• construction of a simple open quantum system model;
• simulation of time-dependent reduced dynamics;
• computation of expectation values such as $\langle \sigma_z(t) \rangle$ and $\langle \sigma_x(t) \rangle$;
• visualization of decoherence and relaxation;
• reproducible scientific Python workflows using OQuPy.

Repository Structure

open-quantum-system-dynamics-oqupy/
├── README.md
├── requirements.txt
├── src/
│   ├── run_oqupy_dynamics.py
│   └── plot_results.py
├── results/
│   └── .gitkeep
└── figures/
    └── .gitkeep

Planned Workflow

1. Define the two-level quantum system.
2. Define the system-environment coupling.
3. Specify bath correlations.
4. Run the OQuPy dynamics simulation.
5. Save expectation values.
6. Generate plots of open-system dynamics.

Requirements

numpy
matplotlib
oqupy

Install dependencies with:

pip install -r requirements.txt

Expected Outputs

The project will generate:

• numerical data in results/;
• plots of time-dependent expectation values in figures/;
• examples of decoherence and relaxation dynamics.

Example Results

The simulation generates time-dependent expectation values for a two-level quantum system coupled to a bosonic environment.

Open-System Expectation Values

Status

This repository is under active development.

The first version focuses on a minimal two-level-system example using OQuPy.

Author

Thiago Rocha Girão Souza
PhD Candidate in Physics
Quantum Computing | Quantum Dynamics | Scientific Python