Scaling a surface-code logical qubit is the leading route to fault-tolerant quantum computing on superconducting hardware, but it only pays off when physical error rates lie below a critical threshold and when rare correlated error events do not set a logical-error floor. Google's 2023 distance-3/5/7 scaling experiment identified exactly these as the outstanding obstacles: component errors needing at least a 20% reduction to reach below-threshold operation, leakage and stray interactions, cosmic-ray-like high-energy events, validation of threshold projections at larger code sizes, and scalable decoders. The 2024/2025 Willow-generation result resolved the first obstacle (distance-7 below-threshold operation with real-time decoding and data-qubit leakage removal) but exposed a sharper, still-open core: unexplained correlated error bursts occurring roughly once per hour now set a ~10^-10 logical error floor in high-distance repetition codes, and below-threshold suppression has not been validated at code distances beyond 7. The open problem is to identify the physical origin of these rare correlated events, mitigate them at scale, and experimentally confirm that below-threshold surface-code scaling extends to larger two-dimensional codes over long durations with decoders that keep pace, on the path to algorithmically relevant logical error rates.

Background

The surface code is a quantum error-correcting code in which information is stored in the joint parities ('stabilizers') of a two-dimensional grid of data qubits, with ancillary measure qubits reading out those parities every cycle; its code distance dd (the linear grid size) sets how many independent physical errors are needed to cause a logical error, and the record of stabilizer outcomes is called the syndrome. Quantum error correction only helps when physical error rates are below a threshold: in that regime the logical error rate per cycle εd\varepsilon_d falls roughly exponentially with dd, conventionally quantified by the error-suppression factor Λ=εd/εd+2\Lambda=\varepsilon_d/\varepsilon_{d+2}. A logical qubit is 'beyond break-even' when it preserves quantum information longer than the best isolated physical qubit, and minimum-weight perfect matching (MWPM) is the standard algorithm that infers which errors occurred from the pattern of flipped stabilizers ('detection events'). In Google Quantum AI's 2023 experiment (Nature 614, 676–681), distance-3, 5, and 7 surface codes on superconducting transmon qubits (a transmon is an anharmonic-oscillator superconducting circuit whose two lowest levels encode the qubit) sat in a 'crossover' regime where finite-size effects initially mask threshold behaviour: distance 5 modestly beat distance 3 (logical error per cycle 2.914%±0.016%2.914\%\pm0.016\% versus 3.028%±0.023%3.028\%\pm0.023\%), and the extracted error budget indicated that component performance, dominated by CZ (controlled-Z, two-qubit) gate error and data-qubit decoherence during measurement and reset, needed to improve by at least 20% to move below threshold. Two damaging rare-error mechanisms were characterized: leakage, the population of non-computational excited states of the transmons, together with stray unwanted interactions, which generate detection events correlated over long distances and times that decoders misread as multiple independent errors; and high-energy particle impacts (cosmic-ray-like events), which the same collaboration had previously shown to produce chip-wide bursts of correlated errors (Nature Physics 18, 107–111 (2022)). A distance-25 one-dimensional repetition code (the bit-flip-only limit of the surface code) exhibited a 1.7×10−61.7\times10^{-6} logical error per round floor set by a single such high-energy event. The paper's closing outlook states that its error-model projections — simulations in which physical faults are idealized as random Pauli (bit-flip and phase-flip) operators, with the 'Pauli+' variant adding leakage states to that model — must be validated experimentally by testing larger code sizes with longer durations, and that finding and mitigating highly correlated errors such as cosmic ray impacts 'will be an important area of research moving forward'. The 2024/2025 follow-up (Nature 638, 920–926) then realized distance-5 and distance-7 surface codes below threshold on 72- and 105-qubit processors (Λ=2.14±0.02\Lambda=2.14\pm0.02, 0.143%±0.003%0.143\%\pm0.003\% logical error per cycle at distance 7, beyond break-even by a factor of 2.4±0.32.4\pm0.3), maintained below-threshold operation with a real-time streaming decoder (63 μ\mus latency at distance 5 for up to a million cycles), and implemented data-qubit leakage removal (DQLR, swapping leaked excitations to measure qubits each cycle, worth a 35% increase in Λ\Lambda at distance 5) plus gap-engineered Josephson junctions — Josephson junctions are the superconducting tunnel junctions at the heart of each transmon, and gap engineering shapes the superconducting energy-gap profile around the junction to block tunnelling by quasiparticles (unpaired electron-like excitations in the superconductor) — which are credited with breaking the earlier once-per-ten-seconds radiation-induced error floor. However, distance-29 repetition codes on the same hardware deviate from exponential suppression for d≥15d\geq15, culminating in an apparent logical error floor near 10−1010^{-10} caused by rare correlated error events occurring roughly once per hour whose 'origins are not yet understood' — one type presenting as spatially grouped detection-probability bursts with a sharp rise and a 400–700 μ\mus exponential decay, the other as a single detector turning persistently noisy for 1–2 ms — and these events account for all observed distance-27 logical errors. The authors state that identifying and mitigating this error mechanism 'will be integral to running larger quantum algorithms', and that the demonstrated processor performance 'can scale in principle, but which we must now scale in practice', noting for example that a 10−610^{-6} logical error rate would already require distance 27, i.e. 1457 physical qubits, with syndrome data per cycle growing quadratically in dd. A follow-up study from the same collaboration (arXiv:2506.18228) has since characterized a further impact-induced correlated-error mechanism that survives gap engineering — systematically negative qubit-frequency shifts of up to 3 MHz lasting about 1 ms, attributed to quasiparticle–qubit interactions in the junction region, producing correlated phase errors — but it does not identify the once-per-hour burst events of the below-threshold experiment, nor remove the logical-error floor.

Problem Statement

After the demonstration of below-threshold distance-7 surface-code operation with real-time decoding and data-qubit leakage removal, determine whether superconducting surface-code logical qubits can be scaled in practice to algorithmically relevant logical error rates. This splits into two linked open targets, both stated as unresolved in the primary literature: (1) identify the physical origin of the rare correlated error events — occurring roughly once per hour, presenting either as spatially grouped detection-probability bursts with a 400–700 μs exponential decay or as a single detector that turns persistently noisy for 1–2 ms — that set the apparent ~10^-10 logical-error floor in high-distance repetition codes and account for all observed distance-27 logical errors, with measured signatures that distinguish the mechanism from known quasiparticle/radiation bursts and from the already-characterized impact-induced qubit-frequency-shift mechanism of gap-engineered arrays, and demonstrate a hardware, control, materials, or decoder-level mitigation that removes this floor or renders it tolerable for large fault-tolerant circuits, together with the resulting change in the logical-error floor and in distance-scaling behaviour; and (2) experimentally validate that the below-threshold exponential suppression of logical error with code distance, previously established only up to distance 7, extends to larger two-dimensional surface codes operated for long durations with decoders and control that keep pace with syndrome generation, establishing the code distances, durations, and error rates achieved, so that the simulated threshold and scaling projections derived from Pauli and Pauli+ error models are confirmed rather than masked by finite-size or correlated-error effects. A negative determination is equally acceptable: an answer that establishes with measured evidence that the rare events cannot be attributed to a mechanism distinct from the known quasiparticle/radiation processes, or that below-threshold suppression does not extend to larger two-dimensional surface codes, must state what that determination resolves and what remains open.

References

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  2. Acharya, R. et al. (Google Quantum AI and Collaborators). Quantum error correction below the surface code threshold. Nature 638, 920–926 (2025). DOI 10.1038/s41586-024-08449-y, https://doi.org/10.1038/s41586-024-08449-y; arXiv:2408.13687, https://arxiv.org/abs/2408.13687
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