The Not-So-Secret Fourth Parameter of Quantum Codes
- URL: http://arxiv.org/abs/2310.17652v2
- Date: Sun, 7 Apr 2024 00:01:46 GMT
- Title: The Not-So-Secret Fourth Parameter of Quantum Codes
- Authors: Eric Kubischta, Ian Teixeira,
- Abstract summary: We show that non-additive codes can outperform stabilizer codes, and often byvariant margins.
We construct codes that implement a $ T gate $ using fewer qubits and with a better minimum distance than is possible with any stabilizer code.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The group of transversal gates is an invariant of quantum codes. With respect to this parameter, we demonstrate that non-additive codes can strictly outperform stabilizer codes, and often by large margins. We do this by constructing spin codes that corresponds to permutationally invariant multiqubit codes implementing generalized phase gates transversally. Of particular note, we construct codes that implement a transversal $ T $ gate using fewer qubits and with a better minimum distance than is possible with any stabilizer code.
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