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Quantum "hyperbicycle" low-density parity check codes with finite rate

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arxiv 1212.6703 v2 pith:5ECKEJKK submitted 2012-12-30 quant-ph

classification quant-ph
keywords codeshyperbicycleratecheckfinitegeneralizedhypergraph-productlow-density
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We introduce a "hyperbicycle" ansatz for quantum codes which gives the hypergraph-product (generalized toric) codes by Tillich and Z\'emor and generalized bicycle codes by MacKay et al. as limiting cases. The construction allows for both the lower and the upper bounds on the minimum distance; they scale as a square root of the block length. Many of thus defined codes have finite rate and a limited-weight stabilizer generators, an analog of classical low-density parity check (LDPC) codes. Compared to the hypergraph-product codes, hyperbicycle codes generally have wider range of parameters; in particular, they can have higher rate while preserving the (estimated) error threshold.

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Cited by 4 Pith papers

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

  1. The Pangaea Architecture: Fault-Tolerant Heterogeneous Topological Codes via a Quantum Bus

    quant-ph 2026-08 conditional novelty 7.0 of 10

    A quantum bus connects many logical qubits through a gauge-code strip, with a claimed factor O(d) reduction in qubit overhead for long-range logical interactions.

  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. The Pinnacle Architecture: Reducing the cost of breaking RSA-2048 to 100 000 physical qubits using quantum LDPC codes

    quant-ph 2026-02 unverdicted novelty 7.0 of 10

    Pinnacle Architecture using QLDPC codes reduces physical qubits needed to factor RSA-2048 to under 100,000 at 10^{-3} error rate.

  4. Quantum Bicycle LDPC Codes with High $kd^2/n$ from Divisor-Driven Search

    cs.IT 2026-08 conditional novelty 6.0 of 10

    A polynomial-gcd reformulation of bicycle quantum LDPC codes enables an exact-distance search that finds [[66,20,7]] with kd^2/n=14.85 and proves an n=48 exclusion result.

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