Tailored XZZX codes for biased noise
- URL: http://arxiv.org/abs/2203.16486v1
- Date: Wed, 30 Mar 2022 17:26:31 GMT
- Title: Tailored XZZX codes for biased noise
- Authors: Qian Xu, Nam Mannucci, Alireza Seif, Aleksander Kubica, Steven T.
Flammia, Liang Jiang
- Abstract summary: We study a family of codes having XZZX-type stabilizer generators.
We show that these XZZX codes are highly qubit efficient if tailored to biased noise.
- Score: 60.12487959001671
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Quantum error correction (QEC) for generic errors is challenging due to the
demanding threshold and resource requirements. Interestingly, when physical
noise is biased, we can tailor our QEC schemes to the noise to improve
performance. Here we study a family of codes having XZZX-type stabilizer
generators, including a set of cyclic codes generalized from the five-qubit
code and a set of topological codes that we call generalized toric codes
(GTCs). We show that these XZZX codes are highly qubit efficient if tailored to
biased noise. To characterize the code performance, we use the notion of
effective distance, which generalizes code distance to the case of biased noise
and constitutes a proxy for the logical failure rate. We find that the XZZX
codes can achieve a favorable resource scaling by this metric under biased
noise. We also show that the XZZX codes have remarkably high thresholds that
reach what is achievable by random codes, and furthermore they can be
efficiently decoded using matching decoders. Finally, by adding only one flag
qubit, the XZZX codes can realize fault-tolerant QEC while preserving their
large effective distance. In combination, our results show that tailored XZZX
codes give a resource-efficient scheme for fault-tolerant QEC against biased
noise.
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