Question: Does a lower logical memory error rate demonstrate an arbitrary useful application running fault-tolerantly?
Open the worked answer
Claim: Under the reported Willow experimental conditions, logical memory errors decreased as the surface-code distance increased.
Locate the evidence: Read “A surface code memory below threshold,” especially the paragraph beginning “We characterize the logical performance,” and Figure 1c–d. The reported distance-7 result uses a neural-network decoder, with memory runs up to 250 error-correction cycles averaged across logical X and Z bases. Lower-distance results include multiple subgrids.
Keep the boundary: This experiment protects stored quantum information. It does not demonstrate arbitrary fault-tolerant applications. The distance-5 real-time decoder and the repetition-code study are distinct results in the same paper.
Reading note: The source supports a below-threshold surface-code memory result under its measured conditions. Logical computation, application workload and resource requirements need their own evidence. Sources checked .
Quantum source-provenance pilot · Version 1.0. These original annotations show how to keep a claim, source, check date and limitation together. A research result, a cryptographic standard and a software resource are different kinds of evidence. This English-language convenience selection supports reading exercises; it is not newly measured data, a comprehensive survey or a ranking.
Below-threshold surface-code memory
Google Quantum AI and collaborators reported Willow memory experiments with a logical-error suppression factor of 2.14 plus or minus 0.02 for each increase of two in surface-code distance.
Limit: This is a logical-memory result. It does not demonstrate arbitrary fault-tolerant applications or application-level advantage. The paper also discusses correlated errors, scale-up and decoding challenges.
Review note: The 28 April 2026 author correction fixes the repetition-code x-axis label and legend keys in Figure 3a. The publisher states that the HTML and PDF figure were amended.
NIST published FIPS 203 as a final standard on 13 August 2024, specifying ML-KEM for key encapsulation with three parameter sets.
Limit: A KEM establishes a shared key under stated conditions. A standard does not certify an implementation or prove migration. NIST’s 17 November 2025 Planning Note flags an issue for a future revision.
NIST published FIPS 204 as a final standard on 13 August 2024, specifying ML-DSA algorithms for generating and verifying digital signatures.
Limit: Digital signatures and key encapsulation serve different purposes. Publication does not certify deployment or implementation security. NIST’s 31 July 2026 Planning Note lists minor issues for correction in a future revision.
NIST published FIPS 205 as a final standard on 13 August 2024, specifying the stateless hash-based digital-signature algorithm SLH-DSA, based on SPHINCS+.
Limit: This is a digital-signature specification. It does not establish an organization’s migration, certify an implementation or provide a key-encapsulation algorithm.
Where to read: Date Published; Abstract; Document History
Review note: No Planning Note or errata link was displayed on the checked final record. This is a page-and-date observation, not a guarantee against future corrections.
IBM’s 12 August 2026 QOBLIB update describes ten shared optimization problem classes with metrics and classical baselines for comparing quantum and classical methods.
Limit: A benchmark library is not a solver result or proof of quantum advantage. A comparison must solve the same workload and required quality against strong classical methods.
The Python toolkit checks required fields, dates, links, duplicate IDs and review markers without network access or added dependencies. Passing the check verifies the format. It does not verify science, source accuracy or permission to reuse a source.
The text-only memory card keeps the takeaway, qualification, source links and check date together. It works without an embedded image, tracking code or a required link back to QubitWire.
The new worksheet, notes, card and original annotations use CC BY 4.0. The toolkit code uses the MIT License. These permissions apply only to this kit. Linked papers, standards, other QubitWire material and third-party media retain their own rights. Full reuse notes.
