Realizing repeated quantum error correction in a distance-three surface code

• Published in: Nature (London) 2022-05, Vol.605 (7911), p.669-674
• Main Authors: Krinner, Sebastian, Lacroix, Nathan, Remm, Ants, Di Paolo, Agustin, Genois, Elie, Leroux, Catherine, Hellings, Christoph, Lazar, Stefania, Swiadek, Francois, Herrmann, Johannes, Norris, Graham J., Andersen, Christian Kraglund, Müller, Markus, Blais, Alexandre, Eichler, Christopher, Wallraff, Andreas
• Format: Article
• Language: English
• Subjects: 142/126; 639/766/483/2802; 639/766/483/481; Algorithms; Circuits; Computer applications; Computers; Error correction; Error correction & detection; Error detection; Experiments; Fault tolerance; Humanities and Social Sciences; Mathematical models; Minimum weight; multidisciplinary; Numerical models; Parity; Quantum computers; Quantum computing; Quantum phenomena; Qubits (quantum computing); Science; Science & Technology - Other Topics; Science (multidisciplinary)
• ISSN: 0028-0836; 1476-4687
• DOI: 10.1038/s41586-022-04566-8

Quantum computers hold the promise of solving computational problems that are intractable using conventional methods 1 . For fault-tolerant operation, quantum computers must correct errors occurring owing to unavoidable decoherence and limited control accuracy 2 . Here we demonstrate quantum error correction using the surface code, which is known for its exceptionally high tolerance to errors 3 – 6 . Using 17 physical qubits in a superconducting circuit, we encode quantum information in a distance-three logical qubit, building on recent distance-two error-detection experiments 7 – 9 . In an error-correction cycle taking only 1.1 μs, we demonstrate the preservation of four cardinal states of the logical qubit. Repeatedly executing the cycle, we measure and decode both bit-flip and phase-flip error syndromes using a minimum-weight perfect-matching algorithm in an error-model-free approach and apply corrections in post-processing. We find a low logical error probability of 3% per cycle when rejecting experimental runs in which leakage is detected. The measured characteristics of our device agree well with a numerical model. Our demonstration of repeated, fast and high-performance quantum error-correction cycles, together with recent advances in ion traps 10 , support our understanding that fault-tolerant quantum computation will be practically realizable. By using 17 physical qubits in a superconducting circuit to encode quantum information in a surface-code logical qubit, fast (1.1 μs) and high-performance (logical error probability of 3%) quantum error-correction cycles are demonstrated.