Quantum error correction below the surface code threshold

Quantum error correction 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. In this work, we present two surface code memories operating below this threshold: 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 \(\Lambda\) = 2.14 \(\pm\) 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% \(\pm\) 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 2.4 \(\pm\) 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 \(\mu\)s at distance-5 up to a million cycles, with a cycle time of 1.1 \(\mu\)s. To probe the limits of our error-correction performance, we 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 3 \(\times\) 10\(^9\) cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms.