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Limitations on transversal gates for hypergraph product codes

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arxiv 2012.05842 v1 pith:OV5MSYTL submitted 2020-12-10 quant-ph

Simon Burton , Dan Browne This is my paper · ORCID
classification quant-ph
keywords codesgateshypergraphproductrestrictedtransversalanalyzeargument
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We analyze the structure of the logical operators from a class of quantum codes that generalizes the surface codes. These are the hypergraph product codes, restricted to the vertical sector. By generalizing an argument of Bravyi and K\"onig, we find that transversal gates for these codes must be restricted to the Clifford group.

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  1. Transversal Gates for Highly Asymmetric qLDPC Codes

    quant-ph 2025-06 conditional novelty 6.0 of 10

    First qLDPC code constructions with transversal non-Clifford phase gates, obtained by embedding a local code with the desired transversal gate into a Tanner-based hypergraph or balanced product code, at the cost of O(...

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