Dynamic local single-shot checks for toric codes

TL;DR

This paper introduces local single-shot checks with constraints on check weights and a dynamic measurement scheme to reduce measurement rounds, improving decoding performance for toric codes under circuit-level noise.

Contribution

It proposes a novel approach to single-shot error correction by imposing weight constraints and using dynamic measurements, reducing time overhead in fault-tolerant quantum computing.

Findings

Reduced measurement rounds by a factor related to check constraints

Improved decoding performance with sliding-window decoding

Numerical simulations demonstrate effectiveness under circuit-level noise

Abstract

Quantum error correction typically requires repeated syndrome extraction due to measurement noise, which results in substantial time overhead in fault-tolerant computation. Single-shot error correction aims to suppress errors using only one round of syndrome extraction. However, for most codes, it requires high-weight checks, which significantly degrade, and often eliminate, single-shot performance at the circuit level. In this work, we introduce local single-shot checks, where we impose constraints on check weights. Using a dynamic measurement scheme, we show that the number of required measurement rounds can be reduced by a factor determined by this constraint. As an example, we show through numerical simulation that our scheme can improve decoding performance compared to conventional checks when using sliding-window decoding with a reduced window size under circuit-level noise models for toric codes. Our work provides a new direction for constructing checks that can reduce time overhead in large-scale fault-tolerant quantum computation.