A recent preprint by Fernando Granha Jeronimo, Xiaojuan Ma, and Nikhil Shagrithaya describes a framework for constructing explicit quantum list-decodable codes. Its abstract says the authors obtain quantum low-density parity-check (qLDPC) constructions with optimal list sizes. The closest matching paper is “From Random Quantum Codes to Explicit qLDPC Codes via Local Properties”, submitted to arXiv on September 30, 2026. The title match is plausible, but not confirmed.
What quantum list decoding does
Quantum error-correcting codes encode quantum information so it can be recovered despite noise. In ordinary unique decoding, a decoder tries to identify one codeword consistent with the received data. List decoding addresses cases where the errors leave several plausible candidates: instead of returning one answer, a decoder can return a list of possible codewords.
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“Explicit” means the work gives a constructible family of codes rather than only showing that codes with the desired properties exist. The preprint’s abstract claims explicit constructions, but it does not, in the available description, provide details that would support claims about implementation or practical performance.
What the closest-matching preprint contributes
The authors’ paper, “From Random Quantum Codes to Explicit qLDPC Codes via Local Properties”, presents a framework for CSS quantum codes based on nested spaces. The abstract describes local constraints on physical representatives while measuring independence in the logical quotient. In broad terms, this lets the framework express different code properties through local witnesses and how they behave with respect to logical information.
The authors say the framework yields explicit quantum list-decodable and list-recoverable codes with optimal list sizes, as well as explicit quantum subspace-design codes. They also describe the constructions as qLDPC. These are the authors’ abstract-level claims; the abstract alone does not establish specific parameter values, decoding procedures, runtime guarantees, or practical benefits.
How this differs from a nearby decoding result
A separate preprint by William Gay, Fernando Granha Jeronimo, and Abhi Shukul is titled “Explicit Capacity-Achieving Quantum LDPC Codes List Decodable in Near-linear Time”. It emphasizes a different result: its abstract says the constructions approach the quantum Singleton bound with constant list sizes and provide near-linear-time list-decoding algorithms approaching capacity.
Rank #2
| Preprint | Emphasis stated in its abstract |
|---|---|
| From Random Quantum Codes to Explicit qLDPC Codes via Local Properties | A local-properties framework and explicit list-decodable, list-recoverable, and subspace-design constructions; the authors claim optimal list sizes. |
| Explicit Capacity-Achieving Quantum LDPC Codes List Decodable in Near-linear Time | Capacity and quantum Singleton-bound emphasis, with constant list sizes and near-linear-time decoding claims. |
These statements should not be merged into one result. In particular, the near-linear-time algorithm claim belongs to the second preprint; the available abstract for the first does not make that claim.
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- The closest matching record is an arXiv preprint submitted September 30, 2026, and its abstract states the framework and construction claims above.
- The available material does not establish that the preprint has been peer reviewed or published elsewhere.
- No numerical list-size parameters, theorem conditions, or implementation details are established by the abstracts summarized here, so “optimal” should be read as the authors’ characterization rather than a standalone quantitative guarantee.
- The record does not establish a hardware application, deployment path, or practical advantage for current quantum devices.
Accordingly, the result is best understood as a theoretical construction and framework claim. The nearby paper on capacity and runtime is a separate development, not evidence that the framework preprint offers the same decoding guarantees.
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