Quantum Time-Evolution Simulations

Trotterization for 1D Infinite Potential Well and Harmonic Oscillator

This repository contains two Jupyter notebooks where I simulate the real-time dynamics of simple 1D quantum systems using Suzuki–Trotter product-formula methods. The goal is to show how well Trotterization captures continuous time evolution when the Hamiltonian is discretized and represented on a qubit register.

What’s inside

1. Trotter_1D_Infinite_Potential_Well_Time_Evolution.ipynb Models a particle in a box. I discretize the spatial domain, build the kinetic-energy operator, map it to qubits, Trotterize the unitary, and track the wavepacket spreading over time.

2. Trot_Harmonic_Oscillator_Time_Evolution.ipynb Simulates the 1D harmonic oscillator. Same workflow. Better-behaved dynamics. A good testbed for seeing how phase, squeezing, and revival patterns emerge through Trotter steps.

What the notebooks cover

• Discretization of 1D Hamiltonians
• Basis mapping to qubit operators
• First-order and higher-order Suzuki–Trotter expansions
• Building and running quantum circuits
• Extracting statevectors and plotting probability distributions
• Comparing numerical evolution with textbook results

Requirements

• Python 3.x
• NumPy, SciPy
• Matplotlib
• Qiskit (Aer for simulation)

Install everything quickly:

pip install qiskit numpy scipy matplotlib

How to run

Clone the repo, open the notebooks in Jupyter or VS Code, and run the cells top to bottom. All plots and animations are generated inside the notebook.

If you want, I can also create a more polished long version, add badges, or generate a proper project structure with CONTRIBUTING, requirements.txt, environment.yml, etc.