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CSS-T codes are a class of stabilizer codes introduced by Rengaswamy et al with desired properties for quantum fault-tolerance. In this work, we comprehensively study non-degenerate CSS-T codes built from Reed-Muller codes. These classical codes allow for constructing optimal CSS-T code families with nonvanishing asymptotic rates up to 12 and possibly diverging minimum distance when non-degenerate.

We propose a new systematic construction of CSS-T codes from any given CSS code using a map Ï•. When Ï• is the identity map I, we retrieve the construction of hu2021mitigating and use it to prove the existence of asymptotically good binary CSS-T codes, resolving a previously open problem in the literature, and of asymptotically good quantum LDPC CSS-T codes.

In this paper, we introduce the Union-Intersection Union-Find (UIUF) algorithm for decoding depolarizing errors in topological codes, combining the strengths of iterative and standard Union-Find (UF) decoding. While iterative UF improves performance at moderate error rates, it lacks an error correction guarantee. To address this, we develop UIUF, which maintains the enhanced performance of iterative UF while ensuring error correction up to half the code distance.

We introduce a new erasure decoder that applies to arbitrary quantum LDPC codes. Dubbed the cluster decoder, it generalizes the decomposition idea of Vertical-Horizontal (VH) decoding introduced by Connolly et al. in 2022. Like the VH decoder, the idea is to first run the peeling decoder and then post-process the resulting stopping set. The cluster decoder breaks the stopping set into a tree of clusters, which can be solved sequentially via Gaussian Elimination.