Quantum error correction below the surface code threshold

Quantum error correction [1, 2, 3, 4] provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. Here, we present two below-threshold surface code memories on our newest generation of superconducting processors, Willow: a distance-7 code, and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% ± 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of . Our system maintains below-threshold performance when decoding in real time, achieving an average decoder latency of 63 μs at distance-5 up to a million cycles, with a cycle time of 1.1 μs. We also run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms.