Simulating Clifford Circuits with Gaussian Elimination

arXiv:2511.06127 · quant-ph, cs.NA, math.NA · Submitted 2025-11-08 · Read on arXiv

quant-ph, cs.NA, math.NA

Submitted: 2025-11-08

Updated: 2026-10-10

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Quantum Circuits — 2× in this paper · explained in 2 episodes
• Adjacency Matrix — 1× in this paper
• Entanglement — 1× in this paper · explained in 4 episodes
• ZX-calculus — 1× in this paper · explained in 2 episodes

Sources

• On Self-Dual Quantum Codes, Graphs, and Boolean Functions
• Pivoting makes the ZX-calculus complete for real stabilizers
• The Heisenberg Representation of Quantum Computers
• Stabilizer Circuits, Quadratic Forms, and Computing Matrix Rank
• Learning stabilizer states by Bell sampling
• Sparse LDL, LU, and inverse butterfly factorization via tree decomposition

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Incoherent Imaging with Spatially Structured Quantum Probes
• A quasiparticle-protected superconducting qubit
• Theory of quantum-enhanced interferometry with general Markovian light sources