Univariate bicycle codes give an explicit basis for logical operators and distance upper bounds in a restricted class of quantum LDPC codes while matching the performance of less constrained generalized and bivariate bicycle codes in simulations.
Existence and Characterisation of Bivariate Bicycle Codes
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Encoding quantum information in a quantum error correction (QEC) code offers protection against decoherence and enhances the fidelity of qubits and gate operations. One of the fundamental challenges of QEC is to construct codes with asymptotically good parameters, i.e. a non-vanishing rate and relative minimum distance. Such codes provide compact quantum memory with low overhead and enhanced error correcting capabilities, compared to state-of-the-art topological error correction codes such as the surface or colour codes. Recently, bivariate bicycle (BB) codes have emerged as a promising candidate for such compact memory, though the exact tradeoff of the code parameters $[[n,k,d]]$ remained unknown. In this Article, we explore these codes by leveraging their ring structure, and predict their dimension as well as conditions on their existence. Finally, we highlight asymptotic badness. Though this excludes this subclass of codes from the search towards practical good low-density parity check (LDPC) codes, it does not affect the utility of the moderately long codes that are known, which can already be used to experimentally demonstrate better QEC beyond the surface code.
verdicts
UNVERDICTED 3representative citing papers
Z_N bivariate-bicycle codes have essential topological properties determined by their Z_p prime-factor counterparts, enabling generalization of algebraic-geometric methods to anyon fusion rules and resolution of quasifractonic behavior via symmetry-enriched topological order.
BBS code dimension equals the algebraic multiplicity of finite nonzero common roots of the defining bivariate polynomials, enabling a root-based prescription for arbitrary boundary shapes that avoids corner corrections when edge conditions hold.
citing papers explorer
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Univariate Bicycle Quantum LDPC Codes: Explicit Logical Structure and Distance Bounds
Univariate bicycle codes give an explicit basis for logical operators and distance upper bounds in a restricted class of quantum LDPC codes while matching the performance of less constrained generalized and bivariate bicycle codes in simulations.
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Symmetry-enriched topological order and quasifractonic behavior in $\mathbb{Z}_N$ stabilizer codes
Z_N bivariate-bicycle codes have essential topological properties determined by their Z_p prime-factor counterparts, enabling generalization of algebraic-geometric methods to anyon fusion rules and resolution of quasifractonic behavior via symmetry-enriched topological order.
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Algebra of Bivariate-Bicycle Surface Codes
BBS code dimension equals the algebraic multiplicity of finite nonzero common roots of the defining bivariate polynomials, enabling a root-based prescription for arbitrary boundary shapes that avoids corner corrections when edge conditions hold.