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Lowering Connectivity Requirements For Bivariate Bicycle Codes Using Morphing Circuits

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arxiv 2407.16336 v3 pith:PAGKO3I4 submitted 2024-07-23 quant-ph

Mackenzie H. Shaw , Barbara M. Terhal This is my paper · ORCID
classification quant-ph
keywords codescircuitsmorphingbicyclebivariatebravyicodeconnectivity
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In Ref. [1], Bravyi et al. found examples of Bivariate Bicycle (BB) codes with similar logical performance to the surface code but with an improved encoding rate. In this work, we generalize a novel parity-check circuit design principle called morphing circuits and apply it to BB codes. We define a new family of BB codes whose parity check circuits require a qubit connectivity of degree five instead of six while maintaining their numerical performance. Logical input/output to an ancillary surface code is also possible in a biplanar layout. Finally, we develop a general framework for designing morphing circuits and present a sufficient condition for its applicability to two-block group algebra codes [1] S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, Nature 627, 778 (2024).

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Cited by 3 Pith papers

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

  1. Transversal Logical Clifford gates on rotated surface codes with reconfigurable neutral atom arrays

    quant-ph 2024-12 conditional novelty 7.0 of 10

    The authors complete a transversal Clifford gate set on rotated surface codes by embedding a fold-transversal S gate inside a syndrome extraction round, with detector construction and numerical support.

  2. 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.

  3. Diamond Circuits for Surface Codes

    quant-ph 2025-02 conditional novelty 6.0 of 10

    Diamond circuits implement a surface code on a Heavy-Square lattice using about 25% fewer qubits and 40% fewer control lines than the standard circuit, at the cost of a roughly 3x lower threshold and longer detecting regions.

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