Surface code memories below threshold on the Willow processor

Short answer: A 2024 Nature paper from Google's team reports surface code memories on its Willow superconducting processor that operate below the error threshold. The authors report that the logical error rate falls by a factor of 2.14 when the code distance goes up by 2, and that a distance-7 memory outlives its best physical qubit by a factor of 2.4. This is a company-authored experiment on one device. The authors say that if scaled, the performance could meet requirements for large-scale fault-tolerant algorithms.

Why a threshold matters

The authors describe quantum error correction as combining several physical qubits into a logical qubit whose logical error rate is suppressed exponentially as more qubits are added. They say this suppression only occurs if the physical error rate is below a critical threshold. The paper's introduction notes that code distance d implies 2d squared minus 1 physical qubits per logical qubit.

What was reported

The paper presents two below-threshold surface code memories on Willow, which the authors call their newest generation of superconducting processors: 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 plus or minus 0.02 when increasing the code distance by 2. The distance-7 code reaches 0.143% plus or minus 0.003% error per cycle of error correction. The authors say this memory is also beyond breakeven, exceeding the lifetime of its best physical qubit by a factor of 2.4 plus or minus 0.3.

Real-time decoding

The authors 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, and a cycle time of 1.1 microseconds.

Repetition codes and rare events

To probe limits, they 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 about 3 times 10 to the 9 cycles.

Limits

This is a result reported by the group that built the processor, in a single paper. The final sentence of the abstract is conditional: the authors say the results indicate device performance that, if scaled, could realize the operational requirements of large-scale fault-tolerant quantum algorithms. The paper's own introduction notes that many-qubit platforms have only recently shown 99.9% entangling gates, far short of the error rates below 10 to the minus 10 needed for many applications. The rare correlated errors are a stated limit on the repetition code results.

FAQ

What does below threshold mean?

Per the authors, the physical error rate is low enough that the logical error rate is suppressed as more qubits are added.

How much did the logical error fall with code distance?

By a factor of 2.14 plus or minus 0.02 for each increase of 2 in distance, in the larger memory.

Did the logical qubit beat its best physical qubit?

The authors say the distance-7 memory exceeded its best physical qubit's lifetime by a factor of 2.4 plus or minus 0.3.

Was decoding done in real time?

For the distance-5 code, with average decoder latency of 63 microseconds up to a million cycles and a cycle time of 1.1 microseconds.

What limited the repetition codes?

Rare correlated error events about once an hour, according to the authors.