Teaching

Matrix Exponential Visualizer

An interactive Python notebook that visualizes the matrix exponential in real-time for $2 \times 2$ matrices. Built as a conceptual tool to illustrate the flow generated by a matrix in the plane, this project bridges linear algebra, differential equations, and Lie group theory.

Apr 20, 2025

Bloch Sphere Visualization

An interactive visualization tool for exploring the Bloch sphere representation of qubit states and unitary operations. Built with ipywidgets, this app lets users intuitively rotate states on the sphere using SU(2) matrices and observe their geometric action in real time.

Apr 18, 2025

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.

Apr 15, 2025

KAK Decomposition for Quantum Circuits

A Python notebook exploring the KAK decomposition of SU(4) as a tool for visualizing and optimizing two-qubit quantum gates. This project illustrates how Lie group structure can inform circuit simplification and variational ansatz design in quantum machine learning.

Apr 10, 2025

Visualizing Representations of 𝔰𝔩(2,ℂ)

An interactive notebook that illustrates representations of the Lie algebra $\mathfrak{sl}(2, \mathbb{C})$ by implementing the action of its generators on homogeneous polynomials. Designed for Lecture 4 (Representation Theory) of the Lie Groups with Applications course at Quantum Formalism.

Feb 22, 2025

Visualizing the Lie Bracket in 𝖘𝖚(2)

An interactive 3D notebook for visualizing the Lie bracket structure of 𝖘𝖚(2) using a geometric cross-product analogy. Developed as a demonstration for Lecture 3 (Matrix Lie Algebras) in the Lie Groups with Applications course at Quantum Formalism.

Jan 22, 2025