Qiskit Cayley Codes

quantum-error-correction
coding-theory
graph-theory
CSS quantum code construction from Cayley graphs, via the Couvreur-Delfosse-Zémor construction
Published

August 22, 2026

STATUS · Qiskit Ecosystem submission in review · PyPI v0.1.1

What it does

A CSS quantum code construction package implementing the Couvreur-Delfosse-Zémor (CDZ) construction — building quantum error-correcting codes directly from Cayley graphs on a group and a chosen generating set, rather than from a hand-designed stabilizer layout. The n=4 case reproduces the [[8,4,2]] code and is validated directly against Theorem 10 of the CDZ paper.

Where the two research threads meet

This is the point where the number-theory/graph-theory background behind this portfolio and the Qiskit-facing tooling work actually converge on the same object: a Cayley graph is simultaneously a group-theoretic construction and a graph one, and the CDZ construction turns its combinatorial structure directly into a quantum code’s stabilizer structure.

Open, and documented as open

Two issues are tracked openly rather than papered over: a self-orthogonality condition that needs checking outside the specific case of F₂ⁿ, and a parameter mismatch between the ISIT conference version and the arXiv version of the CDZ paper that hasn’t been fully reconciled yet. Neither blocks the validated [[8,4,2]] case, but both are real open items, not resolved footnotes.