Quantum computers hold the promise of solving computational problems which
are intractable using conventional methods. For fault-tolerant operation
quantum computers must correct errors occurring due to unavoidable decoherence
and limited control accuracy. Here, we demonstrate quantum error correction
using the surface code, which is known for its exceptionally high tolerance to
errors. Using 17 physical qubits in a superconducting circuit we encode quantum
information in a distance-three logical qubit building up on recent
distance-two error detection experiments. In an error correction cycle taking
only $1.1\,\mu$s, we demonstrate the preservation of four cardinal states of
the logical qubit. Repeatedly executing the cycle, we measure and decode both
bit- and phase-flip error syndromes using a minimum-weight perfect-matching
algorithm in an error-model-free approach and apply corrections in
postprocessing. We find a low 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, support our understanding
that fault-tolerant quantum computation will be practically realizable.

本文研究使用 17 个物理量子位于一个超导电路中，使量子信息编码在距离为 3 的逻辑量子位上。通过量子纠错重复实验，作者在消除纠缠、控制精度受限等因素干扰时，测量和解码比特和相位翻转错误综合使用最小权完美匹配算法并进行后处理修正，以实现高性能、快速和重复的量子纠错周期，证明了量子纠错的可行性和表现良好。