A logical memory bench
The Error That Shrinks
Operate a faithful fitted model of Google Quantum AI's Willow surface-code memory result: move measured detection probability through the reported crossover and watch larger codes change from worse to better, then inspect the real-time decoder queue and the rare correlated bursts that stop a simple exponential story.
Adding qubits is not automatically protection. On one side of a threshold, a larger code creates more places to fail. On the other, the extra checks suppress logical failure. Move the noise proxy. The ordering must reverse.
Layer one: threshold ordering
Computing
Computing the ordering.
The live text alternative will describe the plotted ordering.
Apparatus boundary. The analytic view is a faithful fitted model built from the paper's rounded relation 1/Lambda = 3.4 p_det + 0.29. It is not a Willow simulator and it does not run a decoder. The published-fit replay reconstructs three points on the reported regression line from the published distance-7 value and suppression factor. It is not a fresh reduction of the 5.7 GB Zenodo archive.
Layer twoThe queue that must not grow
A final decoder latency can be longer than one correction cycle while the system still works in real time. The condition is throughput: streamed work must leave at least as fast as it arrives. This schematic replay uses ten-cycle packets, following the paper's block description. Its service time is an openly chosen visual convention, not a measured Willow latency trace.
Streaming queue replay
Ready
Choose a run length, then run the stream.
Honesty trapdoor: one error channel
Computing
Computing the ideal extrapolation.
The teal number is an ideal independent-error extrapolation normalized by the page to meet the published apparent floor at distance 15. That normalization is a free visual choice. The floor, six bursts, run length, and fitted suppression factor are published results. A repetition code protects one error channel, not the full surface-code memory.
The live text alternative will report the burst count and rate.
The check: rebuilt in this browser
Every row below starts empty and is filled by the same runtime engine that drives the controls. Published constants are labeled as published. Derived values are recomputed.
- Published fit replay
- Computing
- Error conversion
- Computing
- Distance-7 qubits
- Computing
- Rounded crossover
- Computing
- Lifetime ratio
- Computing
- Million-cycle time
- Computing
- Rare-burst rate
- Computing
Uncertainties, approximations, conventions, and free choices
- Decoder choice matters. The displayed published replay uses the offline neural-network result. The same experiment gave a different suppression factor with ensembled matching synthesis. The real-time result used sparse blossom on a separate 72-qubit processor.
- Only three hardware distances enter the headline fit. Distance-3 averages nine subgrids, distance-5 averages four, and distance-7 is one code. Surface codes through distance 11 in the paper are simulations, not additional hardware runs.
- Detection probability is a proxy. It is the rate of disagreeing weight-4 stabilizer comparisons, not a universal physical gate-error probability. The fitted coefficients are rounded, so the derived crossing is approximate.
- The analytic curve is an anchored stand-in, not a decoder simulation. It is pinned to the paper's published distance-5 point, 0.306 percent at a detection probability of 8.5 percent, carries its shared noise dependence as the paper's own power law in the detection probability, and takes its distance dependence from the fitted suppression factor. Every curve therefore rises with noise, which is the physical behaviour; it is plotted only over the range the paper fits.
- The published fit replay is reconstructed. Its distance-3 and distance-5 points are generated on the line fixed by the published distance-7 error and published suppression factor. The raw 5.7 GB archive was not downloaded or independently decoded here.
- Lifetime comparison uses a defined average. Physical and logical noise differ. The paper compares uniform-state-average lifetimes, not a simple substitution for a physical qubit's T1.
- The queue is schematic. The chosen 9.5 microsecond service time per ten-cycle visual packet is not reported hardware data. It only demonstrates how bounded streaming can coexist with a longer final-result latency.
- The repetition-code curve is not surface-code performance. Its anchor at the apparent floor is a declared visual normalization. Correlated noise violates the independent-error extrapolation.
- Units and indexing. Probabilities are fractions internally and percentages at the controls. Code distances are odd integers. Times are converted from microseconds to seconds with one million microseconds per second.
- Landing date. The supplied spec contained no landing date, so this entry uses the build date, 29 July 2026.
Still open
This experiment did not demonstrate logical gates, state injection, multiple logical qubits, a useful algorithm, implemented feedback, or a complete fault-tolerant computer. Surface-code scaling beyond distance 7 was not measured on this hardware. Real-time decoding was demonstrated at distance 5, not distance 7. The cause of the rare repetition-code bursts was unknown, and their effect on larger surface codes was not established. Whether this hardware and classical stack scale economically to long computations remains unresolved.
Primary sources
- 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. Peer-reviewed article, published online 9 December 2024, version of record 29 January 2025, issue date 27 February 2025.
- arXiv:2408.13687, the preprint and author manuscript. It independently exposes the headline summary values but is not itself peer reviewed.
- Google Quantum AI, Data for "Quantum error correction below the surface code threshold," Zenodo record 13273331, version 1.0.0, published 26 August 2024. Public research dataset, not a peer-reviewed article.
- Google Quantum AI and Collaborators, Author Correction, Nature 653, E5 (2026), DOI 10.1038/s41586-026-10559-8, published 28 April 2026. This is a journal correction whose peer-review status is not separately stated on its record. It corrects labels in Figure 3a. The load-bearing values used here were not changed.
- Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill, "Topological quantum memory," Journal of Mathematical Physics 43, 4452-4505 (2002), DOI 10.1063/1.1499754. Peer-reviewed theoretical source for the surface-code threshold framework.
Offline check:
node research/the-error-that-shrinks/verify-the-error-that-shrinks.mjs.