Permutation-Invariant Quantum Codes with Transversal Generalized Phase Gates

• URL: http://arxiv.org/abs/2310.17652v3
• Date: Fri, 04 Oct 2024 19:31:13 GMT
• Title: Permutation-Invariant Quantum Codes with Transversal Generalized Phase Gates
• Authors: Eric Kubischta, Ian Teixeira,
• Abstract summary: We demonstrate that non-additive codes can outperform stabilizer codes. We construct permutation-invariant quantum codes that implement a $T$ gate using fewer qubits.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: With respect to the transversal gate group (an invariant of quantum codes), we demonstrate that non-additive codes can outperform stabilizer codes. We do this by constructing spin codes that correspond to permutation-invariant multiqubit codes that can implement generalized phase gates transversally. Of particular note, we construct permutation-invariant quantum codes that implement a transversal $T$ gate using fewer qubits and with a better minimum distance than is possible with the best known stabilizer codes.

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