The 2022 Google scaling experiment (Nature 614, 676-681) - the first demonstration that surface-code quantum error correction improves logical performance with increasing code size - closed with a five-part agenda for scalable fault tolerance: data-qubit leakage removal, roughly 20% component-error improvement to move below threshold, mitigation of correlated high-energy events, experimental validation of projections at larger code distances and durations, and real-time decoders with the required accuracy and throughput. Follow-up work resolved four of the five items: leakage removal was demonstrated and then adopted as a circuit element (Nature Physics 19, 1780-1786 (2023)), and the successor Willow processor operated distance-5 and distance-7 surface codes below threshold (error-suppression factor Λ=2.14±0.02\Lambda = 2.14 \pm 0.02, beyond break-even) with million-cycle stability and real-time decoding (Nature 638, 920-926 (2025)). What survives is the third item, sharpened by that same successor experiment: ionizing-radiation impacts still produce rare (approximately hourly) bursts of correlated errors that floor the logical error rate at about 10−1010^{-10} per cycle at the largest code distances, the mechanism is only partially identified (quasiparticle-induced qubit-frequency shifts causing correlated phase errors, plus residual impact-induced energy relaxation), and no demonstrated mitigation removes the floor. The open problem is to quantitatively attribute the floor to its physical mechanisms and radiation sources, and to demonstrate a hardware-, circuit-, or decoder-level mitigation that eliminates it, restoring exponential suppression of logical error with code distance in superconducting surface-code memories.

Background

A surface code is a quantum error-correcting code that encodes one logical qubit into a two-dimensional grid of physical qubits, with stabilizers - parity checks measured on neighboring qubits each cycle - whose outcomes flag errors; the code distance dd is the linear size of the grid, and larger dd means more physical errors must conspire to cause a logical fault. The theory predicts a threshold: if all physical operations err at rates below a critical value (of order one percent in standard circuit-level noise models), the logical error per error-correction cycle, εd\varepsilon_d, is exponentially suppressed as dd grows, conventionally quantified by an error-suppression factor Λ=εd/εd+2\Lambda = \varepsilon_d / \varepsilon_{d+2} greater than one (Fowler et al., Phys. Rev. A 86, 032324 (2012)). Whether a real device is below threshold can only be established by scaling experiments: running codes of several sizes on the same hardware and watching εd\varepsilon_d fall with dd.

The problem originates in the first such scaling experiment on superconducting qubits (Google Quantum AI and Collaborators, 'Suppressing quantum errors by scaling a surface code logical qubit', Nature 614, 676-681 (2023)). On the Sycamore processor, a distance-5 surface code modestly outperformed an ensemble of distance-3 codes (ε5=2.914%\varepsilon_5 = 2.914\% versus ε3=3.028%\varepsilon_3 = 3.028\% per cycle), placing the device in a finite-size crossover regime near threshold. A distance-25 repetition code (the bit-flip ancestor of the surface code, which corrects only one error type and can therefore reach much lower logical error rates) revealed a logical error floor of 1.7×10−61.7 \times 10^{-6} per round set by a single high-energy impact event. From its error budget, the paper derived five requirements for scalable fault tolerance: leakage removal on data qubits; at least 20% improvement in component performance to move below threshold; mitigation of rare, highly correlated high-energy events; experimental validation of the model projections at larger code sizes and longer durations; and real-time decoders combining accuracy with the throughput for continuous operation. (Leakage denotes quantum information escaping from the qubit's two computational levels into higher excited states of the transmon - the anharmonic superconducting oscillator serving as the qubit; a leaked qubit corrupts every stabilizer touching it, and leakage spreads through two-qubit gates.)

By 2025 most of this agenda had been discharged by the successor Willow processor ('Quantum error correction below the surface code threshold', Nature 638, 920-926 (2025)): distance-5 and distance-7 codes operating below threshold with Λ=2.14±0.02\Lambda = 2.14 \pm 0.02 and ε7=0.143%±0.003%\varepsilon_7 = 0.143\% \pm 0.003\% per cycle; beyond break-even, meaning the logical qubit's lifetime exceeded its best constituent physical qubit's by a factor of 2.4±0.32.4 \pm 0.3; data-qubit leakage removal implemented as a circuit element, raising Λ\Lambda by 35%; stable operation over up to 10610^6 cycles; and real-time decoding maintaining below-threshold performance at 63 microseconds average decoder latency. Ionizing-radiation impacts, however, remained the limiting mechanism. In distance-29 repetition codes, logical performance at d≥15d \geq 15 saturated at a floor near 10−1010^{-10} per cycle, set by rare (roughly once per hour) anisotropic bursts of correlated errors localized to neighborhoods of about 30 qubits and decaying over roughly 400 microseconds. Earlier, more frequent impact bursts had been strongly mitigated by gap engineering: fabricating the two sides of each Josephson junction (the superconducting tunnel junction at the heart of each transmon) with different superconducting energy gaps so that quasiparticles - unpaired electronic excitations created when impact-generated phonons break Cooper pairs throughout the chip substrate - cannot tunnel across the junction and relax the qubit. But the residual hourly bursts were reported as different from previously observed high-energy impact events, their cause was stated to be not yet understood, and mitigating them was called vital to building a fault-tolerant quantum computer.

Problem Statement

The problem, which survives from the open issues of the 2022 surface-code scaling experiment (the other four issues having been resolved by the 2023-2025 lineage documented in Background), is to eliminate ionizing-radiation-impact-induced correlated error bursts as a limiting mechanism in superconducting surface-code quantum error correction. Concretely: (i) quantitatively attribute the logical-error floor observed at the highest code distances in gap-engineered superconducting processors (approximately 10−1010^{-10} per cycle at distances 15 and above in repetition codes) to specific physical mechanisms and radiation sources - discriminating among quasiparticle-induced qubit-frequency shifts and their correlated phase errors, residual impact-induced energy relaxation, transient two-level-system defects (material defects that switch randomly between two configurations and intermittently absorb or release energy near the qubit frequency), and non-radiation sources such as cryostat vibration to identify the dominant mechanism(s) - with predictions for event rates, deposited-energy spectra, spatial burst extent, and recovery dynamics that match the measurements reported in the cited experiments; and (ii) demonstrate a mitigation strategy - hardware-level (quasiparticle or phonon traps, junction gap profiles, materials, shielding, packaging and radon-progeny control), circuit-level (dynamical-decoupling sequences - inserted refocusing pulse sequences that average out slowly varying errors - robust to MHz-scale quasi-static frequency shifts that compose with surface-code schedules), and/or decoder-level (treatment of correlated, non-Pauli error structures within real-time throughput budgets) - that removes this floor, meaning that under the mitigation the logical error rate at the largest implementable code distances is no longer set by impact-induced bursts and exponential suppression of logical error with code distance extends below the currently floored levels. The two components are jointly required, and neither alone resolves the problem: identification is what makes a targeted mitigation checkable, and the disappearance of the floor in large-distance code operation is the experimental acceptance test that the identification and mitigation are correct and complete. Because the floor is observed specifically in the repetition-code experiments, which floor for d≥15d \geq 15, the operative test is the repetition-code regime: a demonstration at the floored distances (d≥15d \geq 15, up to the largest repetition code reported, d=29d = 29) that the impact-burst contribution no longer sets the logical error rate is necessary and sufficient, and the same mitigation is expected to extend to superconducting surface-code memories once their distances reach the floored regime. A mitigation is demonstrated when it is shown, by device measurement at those code distances or by a quantitative error-budget or circuit-level noise-model analysis showing that the impact-burst contribution no longer sets the logical error rate there, to remove the floor; a mitigation whose floor removal is only asserted does not resolve the problem.

References

  1. Rajeev Acharya et al. (Google Quantum AI and Collaborators), 'Suppressing quantum errors by scaling a surface code logical qubit', Nature 614, 676-681 (2023). DOI: 10.1038/s41586-022-05434-1; arXiv:2207.06431. https://arxiv.org/abs/2207.06431
  2. Rajeev Acharya 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; arXiv:2408.13687. https://arxiv.org/abs/2408.13687
  3. Kevin C. Miao, Matt McEwen, Juan Atalaya, Dvir Kafri, et al., 'Overcoming leakage in quantum error correction', Nature Physics 19, 1780-1786 (2023). DOI: 10.1038/s41567-023-02226-w; arXiv:2211.04728. https://arxiv.org/abs/2211.04728
  4. Matt McEwen et al., 'Resisting high-energy impact events through gap engineering in superconducting qubit arrays', Physical Review Letters 133, 240601 (2024). DOI: 10.1103/PhysRevLett.133.240601; arXiv:2402.15644. https://arxiv.org/abs/2402.15644
  5. Vladislav D. Kurilovich et al., 'Correlated Error Bursts in a Gap-Engineered Superconducting Qubit Array', arXiv:2506.18228 (2025). https://arxiv.org/abs/2506.18228
  6. Patrick M. Harrington et al., 'Synchronous Detection of Cosmic Rays and Correlated Errors in Superconducting Qubit Arrays', arXiv:2402.03208 (2024). https://arxiv.org/abs/2402.03208
  7. H. Douglas Pinckney et al., 'Characterization of Radiation-Induced Errors in Superconducting Qubits Protected with Various Gap-Engineering Strategies', arXiv:2603.13460 (2026). https://arxiv.org/abs/2603.13460
  8. Hannah P. Binney et al., 'Distinguishing types of correlated errors in superconducting qubits', arXiv:2603.16494 (2026). https://arxiv.org/abs/2603.16494
  9. Jihee Yang et al., 'High-Temporal-Resolution Measurements of the Impacts of Ionizing Radiation on Superconducting Qubits', arXiv:2602.23544 (2026). https://arxiv.org/abs/2602.23544
  10. E. Celi et al., 'Measuring quasiparticle dynamics for particle impact reconstruction in a superconducting qubit chip', arXiv:2604.13176 (2026). https://arxiv.org/abs/2604.13176
  11. Sagar S. Poudel et al., 'Accelerating Surface Radiation Content to Investigate the Impact of Radon Progeny on Superconducting Qubits', arXiv:2606.00473 (2026). https://arxiv.org/abs/2606.00473
  12. Ambra Mariani et al., 'A Cryogenic Muon Tagging System Based on Kinetic Inductance Detectors for Superconducting Quantum Processors', arXiv:2512.10679 (2025). https://arxiv.org/abs/2512.10679
  13. Daniel Gaytan-Villarreal et al., 'Real-Time Detection of Charge Jumps in Superconducting Qubits with a Convolutional Neural Network', arXiv:2607.14293 (2026). https://arxiv.org/abs/2607.14293
  14. Austin G. Fowler, Matteo Mariantoni, John M. Martinis, Andrew N. Cleland, 'Surface codes: Towards practical large-scale quantum computation', Physical Review A 86, 032324 (2012). DOI: 10.1103/PhysRevA.86.032324; arXiv:1208.0928. https://arxiv.org/abs/1208.0928