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.
Belief propagation with quantum messages for symmetric q-ary pure-state channels
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Optimal affine filtering measurements for group-covariant pure-state codewords reduce to an LP, and SPC-based affine-filtering+GE decoding can outperform symbol-wise USD and PGM on i.i.d. pure-state channels.
Locally-quantum decoding of LDPC codes under coherent bit-flip superpositions outperforms BP and sometimes Prange/SA on Gallager max-k-XORSAT, but an enhanced Prange algorithm ties it.
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.
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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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Affine Filtering Measurements and Their Applications to Quantum Decoding
Optimal affine filtering measurements for group-covariant pure-state codewords reduce to an LP, and SPC-based affine-filtering+GE decoding can outperform symbol-wise USD and PGM on i.i.d. pure-state channels.
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Optimization Using Locally-Quantum Decoders
Locally-quantum decoding of LDPC codes under coherent bit-flip superpositions outperforms BP and sometimes Prange/SA on Gallager max-k-XORSAT, but an enhanced Prange algorithm ties it.
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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.