Completeness for Fault Equivalence of Clifford ZX Diagrams

arXiv:2510.08477 · quant-ph · Submitted 2025-10-09 · Read on arXiv

quant-ph

Submitted: 2025-10-09

Updated: 2026-10-13

Code: https://github.com/paritea/paritea

Terminology

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

Sources

• The ZX-calculus is complete for stabilizer quantum mechanics
• Complete equational theories for classical and quantum Gaussian relations
• The code distance of Floquet codes
• Unifying flavors of fault tolerance with the ZX calculus
• Interacting Quantum Observables: Categorical Algebra and Diagrammatics
• Designing fault-tolerant circuits using detector error models
• Spacetime codes of Clifford circuits
• An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation
• Opportunities and Challenges in Fault-Tolerant Quantum Computation
• Quantum computing with Qiskit
• A universal completion of the ZX-calculus
• The Qupit Stabiliser ZX-travaganza: Simplified Axioms, Normal Forms and Graph-Theoretic Simplification
• Fault Tolerance by Construction
• The Focked-up ZX Calculus: Picturing Continuous-Variable Quantum Computation
• ZX-calculus for the working quantum computer scientist

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