Hamiltonian Simulation — TFIM and Trotterization

A Python notebook exploring Hamiltonian simulation of the Transverse Field Ising Model (TFIM) using Trotter–Suzuki approximations. This project provides a self-contained, pedagogical example of how to approximate time evolution $e^{-iHt}$ for non-commuting Hamiltonians.

Topics covered include:

• Definition and matrix representation of the TFIM Hamiltonian
• Exact diagonalization of small systems using NumPy
• First- and second-order Trotterization of the time evolution operator
• Lie-theoretic perspective on operator splitting and BCH approximations

The notebook is designed as supplemental material for the Lie Groups with Applications course with Quantum Formalism.

GitHub:
hamiltonian-simulation-tfim-trotter