Single-shot quantum error correction with the three-dimensional subsystem toric code

TL;DR

This paper introduces the 3D subsystem toric code, a new topological quantum code enabling single-shot quantum error correction with local measurements, achieving a high error threshold suitable for fault-tolerant quantum computing.

Contribution

The paper presents the first implementation of single-shot QEC with a 3D topological code using local parity checks, demonstrating its high error threshold and practical advantages.

Findings

Achieves a storage threshold of approximately 1.045% against various errors.

Proposes an efficient single-shot QEC strategy for the 3D STC.

Shows the 3D STC's suitability for fault-tolerant quantum computing.

Abstract

We introduce a new topological quantum code, the three-dimensional subsystem toric code (3D STC), which is a generalization of the stabilizer toric code. The 3D STC can be realized by measuring geometrically-local parity checks of weight at most three on the cubic lattice with open boundary conditions. We prove that single-shot quantum error correction (QEC) is possible with the 3D STC, i.e., one round of local parity-check measurements suffices to perform reliable QEC even in the presence of measurement errors. We also propose an efficient single-shot QEC strategy for the 3D STC and investigate its performance. In particular, we numerically estimate the resulting storage threshold against independent bit-flip, phase-flip and measurement errors to be $p_\text{STC} \approx 1.045\%$. Such a high threshold together with local parity-check measurements of small weight make the 3D STC particularly appealing for realizing fault-tolerant quantum computing.