Within the Stochastic Rupture (SR) framework, the only channel through which an external influence could act on quantum measurement without violating the elimination theorem for the Born rule is the rate of decoherence Γ, never the individual outcomes. This makes a concrete, falsifiable prediction available to test on existing hardware: a narrow spectral line in the time series of detection-event rates of a quantum error-correction (QEC) memory experiment. We perform such a search on the publicly released data of Google’s 105-qubit Willow surface-code memory experiments (Zenodo 13273331), analysing the r = 250 slice: 28 experiments (18 × d=3, 8 × d=5, 2 × d=7), 5 × 104 shots each, 1.4 × 106 shots in total, covering 22–451 kHz. The result is null. No frequency exceeds the Bonferronicorrected threshold zcrit = 3.76 in any per-distance or global stack, and no frequency shows z > 2 in more than five of the 28 experiments. The pipeline is not insensitive: it recovers three expected structures in the same data — a broadband low-frequency red-noise ramp (z falling monotonically from 27.7 to 6.0 over five contiguous bins), a coloured background ∼1.7× above shot noise from the code’s round-to-round detector correlations, and long memory across shots (HDFA = 0.632 ± 0.097, 0.757 ± 0.024, 0.771 ± 0.026 for d = 3, 5, 7). Calibrating by injection into the real data, where the response is quadratic (∆z = c a2) with c rising steeply with code distance, we set what is to our knowledge the first upper limit of this kind: any narrowband periodic modulation of Γ in the band 22–451 kHz has fractional amplitude a < 0.99% at 99% confidence. The negative result and its limit are reported as the primary deliverable; the search is intended to be repeated on the remaining 392 experiments and replicated on an independent dataset.
Within the Stochastic Rupture (SR) framework, the only channel through which an external influence could act on quantum measurement without violating the elimination theorem for the Born rule is the rate of decoherence Γ, never the individual outcomes. This makes a concrete, falsifiable prediction available to test on existing hardware: a narrow spectral line in the time series of detection-event rates of a quantum error-correction (QEC) memory experiment. We perform such a search on the publicly released data of Google’s 105-qubit Willow surface-code memory experiments (Zenodo 13273331), analysing the r = 250 slice: 28 experiments (18 × d=3, 8 × d=5, 2 × d=7), 5 × 104 shots each, 1.4 × 106 shots in total, covering 22–451 kHz. The result is null. No frequency exceeds the Bonferronicorrected threshold zcrit = 3.76 in any per-distance or global stack, and no frequency shows z > 2 in more than five of the 28 experiments. The pipeline is not insensitive: it recovers three expected structures in the same data — a broadband low-frequency red-noise ramp (z falling monotonically from 27.7 to 6.0 over five contiguous bins), a coloured background ∼1.7× above shot noise from the code’s round-to-round detector correlations, and long memory across shots (HDFA = 0.632 ± 0.097, 0.757 ± 0.024, 0.771 ± 0.026 for d = 3, 5, 7). Calibrating by injection into the real data, where the response is quadratic (∆z = c a2) with c rising steeply with code distance, we set what is to our knowledge the first upper limit of this kind: any narrowband periodic modulation of Γ in the band 22–451 kHz has fractional amplitude a < 0.99% at 99% confidence. The negative result and its limit are reported as the primary deliverable; the search is intended to be repeated on the remaining 392 experiments and replicated on an independent dataset.
Quantum error correction [1, 2, 3, 4] 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. Here, we present two below-threshold surface code memories on our 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 our larger quantum memory is suppressed by a factor of Λ=2.14±0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% ± 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±0.3 . Our system maintains below-threshold performance when decoding in real time, achieving an average decoder latency of 63 μs at distance-5 up to a million cycles, with a cycle time of 1.1 μs. We also 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 3×109 cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms.
Quantum error-correction decoders are typically benchmarked against synthetic circuit-level noise, under the assumption that a decoder's ranking under such noise transfers to hardware and improves as the noise model becomes more realistic. The Willow processor, the first to operate below the surface-code threshold, allows us to test this assumption. We rank a panel of six decoders using a four-rung ladder of noise models with increasing fidelity, evaluated against real data across three code distances, two bases, and fifteen round counts. Rank agreement with hardware appears once the noise model gives each operation type its own error rate. Calibrating the model to the device improves absolute error rates but not rank agreement. We additionally provide the first independent evaluation of NVIDIA's Ising pre-decoder on hardware, at code distances below its training receptive field and via a mapping onto the lattice on which it was trained. Under these conditions, it holds no accuracy-latency advantage: another panel decoder matches or improves on it in both per-cycle error rate and decode latency in 278 of the 280 evaluations. We release the full pipeline and the per-shot outcome of every evaluation, so future decoders and devices can be compared.
Abstract Quantum error-correction decoders must convert noisy syndrome records into logical decisions while operating under strict latency and reliability constraints. Minimum-weight perfect matching (MWPM) remains a strong baseline for surface-code decoding because it is fast, interpretable, and exact for its graphlike optimization problem [1–8]. However, the graphlike independent-error approximation can become mismatched when syndrome records contain temporal drift, measurement corruption, crosstalk, bursts, or mixtures of mechanisms [9–18]. We introduce SAGE-QEC, a failure-aware selective decoder that retains nominal PyMatching as its default decision and learns when an observable syndrome structure warrants an alternative candidate. SAGE-QEC uses train-frozen structure thresholds, a candidate ranker, validation-only policy selection, and a paired blind evaluation. Across 45 simulator conditions, SAGE-QEC reduced the aggregate logical error rate from 27.1285% for PyMatching to 24.8320%, corresponding to an 8.47% relative reduction. The campaign used rotated surface-code memory circuits at distances 3, 5, and 7, nominal circuit parameters 0.002, 0.003, and 0.005, five seeds, and four test regimes withheld from training: Burst-3, Temporal Drift, Crosstalk, and Mixed Noise. The test set contained 81,000 paired shots. All twelve distance-by-regime aggregate comparisons favored SAGE-QEC in the executed campaign, with paired bootstrap intervals below zero for SAGE-QEC minus PyMatching. The result is evidence of a reproducible simulator-level improvement, not a claim of universal decoder superiority. SAGE-QEC currently uses logical-output proxy candidates rather than a complete physical correction search, and its intervention rate remains high under distribution shift. It has not yet been compared with a fully calibrated correlated-noise space-time PyMatching baseline or hardware calibration data. We therefore characterize SAGE-QEC as a strong qualification-stage prototype and release a complete audit protocol for the next industrial validation stage.
Quantum error correction can suppress logical errors exponentially with code distance when physical noise is below threshold. Realizing this on hardware requires tight coordination among quantum gates, mid-circuit measurements, and qubit coherence. Device variation, noise asymmetry, and correlations across space and time complicate the translation of these capabilities into logical error suppression. Here, we study rotated surface-code memory on an IBM Nighthawk r2 processor. Performance varies across tested processor placements, which we attribute to differences in qubit quality. We optimize the code by combining short readout, fused measurement and reset, and an XX echo on data qubits during ancilla readout. Compared with standard readout without reset or echo, the optimized syndrome extraction circuit reduces the median per-round logical error rate by factors of 3.8 in the X basis and 1.4 in the Z basis. In memory experiments of up to 150 rounds, the distance advantage weakens, alongside long-lived correlations that may reflect a persistent error component. Under our optimization recipe, increasing the protected distance from 3 to 6 while holding the other distance fixed reduces the per-round logical error rate from 0.53% to 0.24% in Z memory and from 0.52% to 0.22% in X memory. The corresponding error-suppression factors under maximum-likelihood decoding are 1.68 and 1.85. These results connect circuit compilation and optimization to surface-code memory performance and limitations, and motivate QPU and QEC circuit codesign for fault-tolerant quantum computing primitives on current cloud hardware.
We analyse Google's publicly released Willow 72-qubit repetition code dataset (d=29, 200 samples, 20billion measurements) through the lens of the Quantum Ocean framework. By mapping the empiricalfindings to the mathematical equations established in Parts 58 and 77, we derive three quantitativeresults:1. Cross-basis spectral correlation r = 0.982 maps directly to the basis-independence of the oceanHamiltonian Hocean, which couples through the scalar field ϕ(x0) — a term that,by construction, carries no Pauli-basis preference. The measured correlation provides the firstempirical constraint on the ocean spectral density: Jocean(ω)≈JX(ω)≈JZ(ω) to within 1.8%.2. Universal frequency peak at f = 0.001 (SNR = 55.4× in X, 37.2× in Z, detected in 20/20samples) maps to a discrete mode in the ocean spectrum $J(\omega) = \sumi |gi|^2 \delta(\omega -\omega_i)$, corresponding to a single vacuum oscillation at period T=1002 QEC cycles.3. X > Z asymmetry (p = 0.063) maps to the superposition-dependent coupling gef =g0+g1⋅S, where X-basis preparations (which are superpositions in the computational basis)have S=1 while Z-basis preparations have S=0.Combined with the IBM Heron results from Part 78, the Quantum Ocean framework now has crossplatform empirical support from two independent quantum architectures (superconductingtransmon), consistent with a universal ocean coupling that is hardware-independent — exactly as theframework predicts. 🌌 Interactive Space Research Assistant: Explore and ask questions about this research interactively with the Quantum Ocean Framework Ai Chat (or talk directly with the Quantum Ocean Framework Ai voice conversation).
The pursuit of scalable quantum computing is intrinsically limited by qubit decoherence, making robust quantum error correction (QEC) techniques crucial. As a leading solution, the topological surface code offers inherent protection against local noise. This study presents the first comprehensive implementation and quantitative characterization of a full surface code pipeline, which includes encompassing lattice construction, multi-round syndrome extraction, and MWPM decoding, using the high-level Qrisp programming framework. The entire pipeline was executed on IQM superconducting quantum processors to provide an empirical assessment under current noisy intermediate-scale quantum (NISQ) conditions. Our experimental data definitively show that the system operates significantly below the fault-tolerance threshold. Crucially, a quantitative resource analysis isolates and establishes the lack of native qubit reset on the hardware as the dominant architectural bottleneck. This constraint forces the physical qubit count to scale as d2+(d2−1)T, effectively preventing scaling to larger code distances (d) and execution times (T) on current devices. The work confirms Qrisp’s capability to support advanced QEC protocols, demonstrating that high-level abstraction can reduce implementation complexity by simplifying scheduling and mapping, thereby facilitating deeper experimental analysis of hardware limitations.