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

Abstract

Quantum computers hold the promise of solving computational problems that are intractable using conventional methods¹. For fault-tolerant operation, quantum computers must correct errors occurring owing to unavoidable decoherence and limited control accuracy². 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 traps¹⁰, support our understanding that fault-tolerant quantum computation will be practically realizable.