The XZZX surface code

• Published in: Nature communications Vol. 12; no. 1; p. 2172
• Main Authors: Bonilla Ataides, J. Pablo, Tuckett, David K., Bartlett, Stephen D., Flammia, Steven T., Brown, Benjamin J.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 12-04-2021; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/483/2802; 639/766/483/481; Codes; Error correcting codes; Error correction; Error correction & detection; Fault tolerance; Humanities and Social Sciences; multidisciplinary; Noise; Quantum computers; Quantum computing; Qubits (quantum computing); Science; Science (multidisciplinary)
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-021-22274-1

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.
The surface code is a keystone in quantum error correction, but it does not generally perform well against structured noise and suffers from large overheads. Here, the authors demonstrate that a variant of it has better performance and requires fewer resources, without additional hardware demands.