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arXiv · 2509.06865

A Class of Cyclic Quantum Codes

Matthew B. Hastings
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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.

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Matthew B. Hastings. 2025-09-08. A Class of Cyclic Quantum Codes. https://arxiv.org/abs/2509.06865

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