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Asymptotically Good Quantum and Locally Testable Classical LDPC Codes

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arxiv 2111.03654 v2 pith:DNK5ELLH submitted 2021-11-05 cs.IT math.ITquant-ph

Pavel Panteleev , Gleb Kalachev This is my paper
classification cs.ITmath.ITquant-ph
keywords codesldpcasymptoticallyclassicalgoodlocallyquantumtestable
verification ladder T0 review T1 audit T2 compute T3 formal
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We study classical and quantum LDPC codes of constant rate obtained by the lifted product construction over non-abelian groups. We show that the obtained families of quantum LDPC codes are asymptotically good, which proves the qLDPC conjecture. Moreover, we show that the produced classical LDPC codes are also asymptotically good and locally testable with constant query and soundness parameters, which proves a well-known conjecture in the field of locally testable codes.

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Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Logical computation with canonical lifted product codes

    quant-ph 2026-07 conditional novelty 7.0 of 10

    Canonical lifted-product qLDPC codes admit a row/column cyclic logical basis that enables constant-seed modular surgery, compact extractors, and parallel Clifford and magic primitives.

  2. Logical Spectroscopy: Lifted-Product Codes with Addressable Bases

    quant-ph 2026-07 accept novelty 7.0 of 10

    Logical spectroscopy decomposes Abelian lifted-product codes into Frobenius packets, builds a complete addressable conjugate logical basis by finite-field algebra plus idempotent lifts, and supplies design diagnostics...

  3. (2,2)-GB Codes: Classification and Comparison with weight-4 Surface Codes

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    Three new families of (2,2)-generalized bicycle codes reach optimal parameters, including the first optimal even-distance family [[4r^2,2,2r]].

  4. OmniQEC: discovering practical quantum error-correcting codes by an AI scientist

    quant-ph 2026-07 conditional novelty 6.0 of 10

    OmniQEC discovers qLDPC codes whose simulated circuit-level logical error rates beat the BB [[72,12,6]] and [[144,12,12]] baselines at 98- and 240-qubit budgets.

  5. CSS-$T$ codes over Binary Extension Fields and their Physical Foundations

    quant-ph 2025-07 reject novelty 6.0 of 10

    A new trace-based definition of CSS-T codes over F_{2^s} is claimed to yield asymptotically good LDPC CSS-T code families over every binary extension field.

  6. Transversal Gates for Highly Asymmetric qLDPC Codes

    quant-ph 2025-06 conditional novelty 6.0 of 10

    First qLDPC code constructions with transversal non-Clifford phase gates, obtained by embedding a local code with the desired transversal gate into a Tanner-based hypergraph or balanced product code, at the cost of O(...

  7. Multivariate Multicycle Codes for Complete Single-Shot Decoding

    quant-ph 2026-01 conditional novelty 5.0 of 10

    Koszul complexes built from four polynomial generators over cyclic group rings yield CSS codes with both X and Z metachecks, giving small, high-confinement, single-shot-decodable quantum codes.

  8. Native Non-Clifford Gates in Quantum LDPC Codes: Conditions, Synthesis, and Scaling Limits

    quant-ph 2026-01 reject novelty 4.0 of 10

    The main theorem claiming constant-depth logical CCZ gates exist from many 'magic-friendly triples' has mutually inconsistent hypotheses, and its key local-implementation step is unproved.

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