A Class of Cyclic Quantum Codes

Matthew B. Hastings (Sep 09 2025).

Abstract: We introduce a class of cyclic quantum codes, basing the construction not on the simplicity of the stabilizers, but rather on the simplicity of preparation of a code state (at least in the absence of noise). We show how certain known codes, such as a certain family of rotated two-dimensional toric codes, fall into this class, and we also give certain other examples at small sizes found by computer search. We finally discuss fault tolerant preparation of these codes.

Arxiv: https://arxiv.org/abs/2509.06865