The XZZX Surface Code

TL;DR

The XZZX surface code is a novel quantum error-correcting code that achieves high error thresholds and practical decoding, outperforming previous codes especially under realistic noise conditions like qubit dephasing.

Contribution

This paper introduces the XZZX surface code, demonstrating its universal error threshold properties and practical advantages in fault-tolerant quantum computation under realistic noise models.

Findings

Error threshold matches hashing bounds for all single-qubit Pauli noise channels.

Exceeds hashing bounds for certain experimentally relevant noise parameters.

Maintains advantages under fault-tolerant quantum computation with unreliable syndrome measurements.

Abstract

Performing large calculations with a quantum computer will likely require a fault-tolerant architecture based on quantum error-correcting codes. The challenge is to design practical quantum error-correcting codes that perform well against realistic noise using modest resources. Here we show that a variant of the surface code -- the XZZX code -- offers remarkable performance for fault-tolerant quantum computation. The error threshold of this code matches what can be achieved with random codes (hashing) for every single-qubit Pauli noise channel; it is the first explicit code shown to have this universal property. We present numerical evidence that the threshold even exceeds this hashing bound for an experimentally relevant range of noise parameters. Focusing on the common situation where qubit dephasing is the dominant noise, we show that this code has a practical, high-performance decoder and surpasses all previously known thresholds in the realistic setting where syndrome measurements are unreliable. We go on to demonstrate the favourable sub-threshold resource scaling that can be obtained by specialising a code to exploit structure in the noise. We show that it is possible to maintain all of these advantages when we perform fault-tolerant quantum computation.