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Quantum Low-Density Parity-Check Codes

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arxiv 2103.06309 v2 pith:7R4MJZ3S submitted 2021-03-10 quant-ph

Nikolas P. Breuckmann , Jens Niklas Eberhardt This is my paper
classification quant-ph
keywords quantumcodesdiscussldpclow-densityparity-checkparticularadvances
verification ladder T0 review T1 audit T2 compute T3 formal
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Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of quantum codes called low-density parity-check (LDPC) quantum codes. The codes we discuss are alternatives to the surface code, which is the currently leading candidate to implement quantum fault-tolerance. We introduce the zoo of LDPC quantum codes and discuss their potential for making quantum computers robust against noise. In particular, we explain recent advances in the theory of LDPC quantum codes related to certain product constructions and discuss open problems in the field.

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Cited by 2 Pith papers

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

  1. 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...

  2. 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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