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.

The KAK decomposition expresses any element of SU(4) as a product of local SU(2) × SU(2) gates and a diagonal entangling gate, and plays a central role in understanding two-qubit gate equivalence classes. Also created as supplemental material for the Lie Groups with Applications course with Quantum Formalism.

This notebook includes:

• A pedagogical walkthrough of SU(4) → KAK decomposition via Lie theory
• A variational QML approach via Pennylane automatic differentiation
• Numerical simulation and timing benchmarks using scipy.linalg, and pennylane

Use cases:

• Design of efficient two-qubit gates
• Benchmarking quantum compilation algorithms
• Educational demo for quantum circuits and Lie algebras

GitHub:
kak-decomposition-qml