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.
Belief propagation with quantum messages for symmetric q-ary pure-state channels
4 Pith papers cite this work. Polarity classification is still indexing.
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quant-ph 4years
2026 4verdicts
UNVERDICTED 4representative citing papers
A quantum decoder for LDPC codes with coherent errors outperforms belief propagation on average-case D-regular max-k-XORSAT for several k and D, matching an enhanced version of Prange's algorithm.
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.
Extends NP-hardness of exceeding r/q + O(1/sqrt(D)) for bounded-degree max-Ek-LINSAT(q,r) over F_q and shows quantum decoding is required for DQI to achieve the hardness-optimal 1/sqrt(D) scaling.
citing papers explorer
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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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Optimization Using Locally-Quantum Decoders
A quantum decoder for LDPC codes with coherent errors outperforms belief propagation on average-case D-regular max-k-XORSAT for several k and D, matching an enhanced version of Prange's algorithm.
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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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Approximability limits for bounded-degree max-LINSAT and implications for decoded quantum interferometry
Extends NP-hardness of exceeding r/q + O(1/sqrt(D)) for bounded-degree max-Ek-LINSAT(q,r) over F_q and shows quantum decoding is required for DQI to achieve the hardness-optimal 1/sqrt(D) scaling.