Short answer: Quantum error correction only helps if the physical error rate is below a threshold, so that adding qubits to a code makes the logical qubit better. A 2024 Nature paper reports surface-code memories on its Willow processor in which the logical error rate falls by a factor of about 2.14 each time the code distance goes up by 2. A separate Physical Review Letters paper reports below-threshold operation using leakage suppression. These are reports by the hardware team itself.
What "below threshold" means
The 2024 paper explains the idea: error correction combines many physical qubits into one logical qubit whose error rate should be suppressed exponentially as more qubits are added, but that only happens if the physical error rate is below a critical threshold. Showing that scaling on real hardware is therefore a central experimental milestone.
The Willow experiment
The authors present two below-threshold surface code memories on their 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 the larger memory is suppressed by a factor of 2.14 +/- 0.02 for each increase of the code distance by 2. The distance-7 code uses 101 qubits and reaches 0.143% +/- 0.003% error per cycle of error correction. The authors also report the memory is beyond breakeven, exceeding the lifetime of its best physical qubit by a factor of 2.4 +/- 0.3.
They report that below-threshold performance is maintained with real-time decoding, with an average decoder latency of 63 microseconds at distance 5 for up to a million cycles, with a cycle time of 1.1 microseconds. They also run repetition codes up to distance 29.
Leakage suppression
A Physical Review Letters paper titled as experimental error correction below the surface code threshold via all-microwave leakage suppression says leakage from the computational subspace is a critical challenge for scalable error correction, because it creates long-lived, correlated errors spreading across space and time. The authors implement an all-microwave leakage suppression architecture on a distance-7 surface code, integrating a hardware-efficient leakage reduction unit for data qubits with a fast unconditional reset for ancilla qubits. They report that this reverses the above-threshold scaling that unmitigated leakage had caused. The exact suppression factor is in the paper and not repeated here.
What this does not show
These are memory experiments: they preserve a logical state and do not run logic operations. The numbers come from the authors' own devices and decoders, and a distance-7 memory is far smaller than the codes that fault-tolerant algorithms are expected to need.
FAQ
What is the error suppression factor?
The ratio by which the logical error rate falls when the code distance increases by 2. The Willow paper reports 2.14 +/- 0.02.
What is breakeven?
When the logical qubit outlasts the best physical qubit in the device. The paper reports a factor of 2.4 +/- 0.3 beyond it.
Did decoding keep up in real time?
At distance 5, the authors report an average decoder latency of 63 microseconds.
Why is leakage important?
It creates correlated errors that can stop the threshold behaviour, per the Physical Review Letters paper.
Does this mean fault-tolerant computing is solved?
No. These are small memories and do not include logic.
All field notes