Single-shot error correction on toric codes with high-weight stabilizers
- URL: http://arxiv.org/abs/2310.16160v1
- Date: Tue, 24 Oct 2023 20:06:19 GMT
- Title: Single-shot error correction on toric codes with high-weight stabilizers
- Authors: Yingjia Lin, Shilin Huang, Kenneth R. Brown
- Abstract summary: Single-shot error correction allows for an error threshold with only one round of noisy syndrome measurements regardless of the code size.
The single-shot check operators result in a sustainable threshold at 5.62% for an error model with noisy measurements.
For this error model, the conventional check operators with multiple measurements yields a lower logical error rate.
- Score: 0.49109372384514843
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: For quantum error correction codes the required number of measurement rounds
typically increases with the code distance when measurements are faulty.
Single-shot error correction allows for an error threshold with only one round
of noisy syndrome measurements regardless of the code size. Here we implement
single-shot check operators for toric codes. The single-shot checks are
constructed by Gaussian elimination following Campbell [Campbell, 2019]. The
single-shot check operators result in a sustainable threshold at 5.62% for an
error model with noisy measurements, outperforming the conventional toric code
check operators with multiple rounds of noisy measurement. The cost of the
transformation is non-local high-weight stabilizer generators. We then consider
a gate-based error model that leads to increased measurement error with
stabilizer weight. Here we find no single-shot threshold behavior and instead
find the code family will have an optimal code size for a fixed error rate. For
this error model, the conventional check operators with multiple measurements
yields a lower logical error rate.
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