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

Comments: 80 pages, plus a separate supplement. This work is accompanied by a full proof of the relation reduction solved without AI assistance and a machine-checked Agda formalisation, both available in public repositories linked in the paper

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

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

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

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)

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
• A quasiparticle-protected superconducting qubit
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians