A Complete and Natural Rule Set for Multi-Qudit Clifford Circuits in All Odd Prime Dimensions

arXiv:2609.40106 · quant-ph · Submitted 2026-09-30 · Read on arXiv

quant-ph

Submitted: 2026-09-30

Updated: 2026-10-05

Code: https://github.com/onestruggler/acir

Project page: https://tikzit.github.io/index.html

Terminology

• Induction Hypothesis — 6× in this paper
• Quantum Circuits — 6× in this paper · explained in 2 episodes
• Verification — 6× in this paper · explained in 2 episodes
• Distillation — 3× in this paper · explained in 2 episodes
• Formal Verification — 2× in this paper · explained in 2 episodes
• Stabilizer States — 2× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Axioms — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• IEEE Symposium on Logic in Computer Science — 1× in this paper
• Quantum Physics — 1× in this paper · explained in 10 episodes
• Steering — 1× in this paper · explained in 2 episodes

Sources

• Simpler Presentations for Many Fragments of Quantum Circuits
• GCAMPS: A Scalable Classical Simulator for Qudit Systems
• Group Representations, Error Bases and Quantum Codes
• Non-binary Unitary Error Bases and Quantum Codes
• Classical simulation of quantum computation, the Gottesman-Knill theorem, and slightly beyond
• A universal completion of the ZX-calculus
• Qudit-based quantum error-correcting codes from irreducible representations of SU(d)

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