Quantum Computation and Nonlinear Oscillators

This repository contains code and results for simulating the classical and quantum dynamics of nonlinear oscillators, specifically the Duffing oscillator model. The project explores the behavior of quantum states—such as coherent and Schrödinger cat states—under a nonlinear Hamiltonian, visualized using tools like Wigner functions.

View the full report here

Overview

The simulation and analysis in this project cover:

• Classical dynamics of the Duffing oscillator using numerical solvers
• Quantum evolution using the QuTiP library
• Investigation of coherent and Schrödinger cat states
• Visualization with Wigner functions in phase space

Key Features

• Classical Duffing oscillator simulation using scipy.integrate.odeint
• Quantum simulations with qutip.mesolve
• Expectation values: ⟨x(t)⟩ and ⟨p(t)⟩
• Wigner function rendering with qutip.wigner

Files Included

• osc.ipynb: Jupyter notebook containing all code and plots
• tex/: Directory containing main.tex and key result visualizations
• paper.pdf: IEEE-style report summarizing the work
• README.md: This file

Images

Classical Duffing Oscillator

Quantum Coherent State Evolution

Quantum Cat State Evolution

Wigner Function of Coherent State

Wigner Function of Cat State

Requirements

• Python 3.8+
• QuTiP
• NumPy
• SciPy
• Matplotlib

Install dependencies with:

pip install -r requirements.txt