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Quantum Weight Enumerators for Real Codes with $X$ and $Z$ Exactly Transversal

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arxiv 2306.12526 v2 pith:OZTNUDOO submitted 2023-06-21 quant-ph

Eric Kubischta , Ian Teixeira , J. Maxwell Silvester This is my paper · ORCID
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keywords codeerrorcorrectingenumeratorsexactlyidentitiesquantumreal
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abstract

In this note we show that the weight enumerators of a real quantum error correcting code with $ X $ and $ Z $ exactly transversal must satisfy certain identities. One consequence of these identities is that if the code is error detecting then it is automatically error correcting for free; implying a relationship between transversality and code distance.

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Cited by 1 Pith paper

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  1. Time-Reversal Selection Rules for Quantum Error Correction

    quant-ph 2026-08 conditional novelty 6.0 of 10

    Time-reversal-invariant logical qubits on an odd number of spins have automatically scalar even-weight Pauli errors, so single-qubit error detection implies correction and every such code has odd distance.

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