Color code with a logical control-S gate using transversal T rotations

2024/11/22 by Benjamin J. Brown, Brown, Benjamin J. · 1 voice · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Physics and Astronomy · #Cellular Automata and Applications #DNA and Biological Computing #FOS: Physical sciences #Quantum Physics (quant-ph) #graph theory and CDMA systems #quant-ph

paper · pdf · doi:10.48550/arxiv.2411.15035

openalex publication_date 2024/11/22 · arxiv published 2024/11/22 · arxiv updated 2025/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

The color code has been invaluable for the development of the theory of fault-tolerant logic gates using transversal rotations. Three-dimensional examples of the color code have shown us how its structure, specifically the intersection of the supports of logical operators, can give rise to non-Clifford T and CCZ gates. Here we present a color code with a logical control-S gate that is accomplished with transversal T and T^† rotations on its physical qubits.

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Discussions

• To those that may have noticed v1 on arXiv, the published article comes with an expanded discussion on the results as supplemental information. This new material is also included as an appendix on the [bsky, 2 points, 0 comments]

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