Affine filtering measurements enable code-aware decoding of linear codes over pure-state quantum channels by identifying affine subspaces and outperform symbol-wise USD and pretty good measurement in LDPC code simulations.
Polar codes for cq channels: Decoding via belief-propagation with quantum messages
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2026 2verdicts
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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.
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Affine Filtering Measurements and Their Applications to Quantum Decoding
Affine filtering measurements enable code-aware decoding of linear codes over pure-state quantum channels by identifying affine subspaces and outperform symbol-wise USD and pretty good measurement in LDPC code 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.