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

Terminology

• Quantum Circuits — 2× in this paper · explained in 2 episodes
• Adjacency Matrix — 1× in this paper · explained in 1 episode
• 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

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