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.
Low-density parity-check codes
4 Pith papers cite this work. Polarity classification is still indexing.
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A closed quantum belief-propagation framework is derived for factor graphs over arbitrary finite abelian groups by showing that group-covariant pure-state channels remain closed under check, equality, homomorphism, and marginalization factors.
MBBP-LD creates multiple cycle-free subtree decompositions of the Tanner graph to run parallel BP decodings on quantum LDPC codes, cutting error rates by up to 30% versus BP-OSD and 20% versus BPGD on tested bivariate bicycle codes with fewer total iterations.
A variational diffusion channel decoder fuses belief propagation with diffusion models to achieve the best reported decoding performance among neural methods while using significantly less computation and storage.
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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Quantum Message Passing for Factor Graphs over Finite Abelian Groups
A closed quantum belief-propagation framework is derived for factor graphs over arbitrary finite abelian groups by showing that group-covariant pure-state channels remain closed under check, equality, homomorphism, and marginalization factors.
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Multiple-Bases Belief Propagation List Decoding for Quantum LDPC Codes
MBBP-LD creates multiple cycle-free subtree decompositions of the Tanner graph to run parallel BP decodings on quantum LDPC codes, cutting error rates by up to 30% versus BP-OSD and 20% versus BPGD on tested bivariate bicycle codes with fewer total iterations.
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Variational Diffusion Channel Decoder
A variational diffusion channel decoder fuses belief propagation with diffusion models to achieve the best reported decoding performance among neural methods while using significantly less computation and storage.