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.
& Tillich, J.-P
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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.
A review describing the Decoded Quantum Interferometry algorithm for quantum speedups in max-LINSAT optimization, with claimed superpolynomial advantage in the OPI problem.
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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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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.
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Quantum Decoding Algorithms: Quantum Speedups in Optimization
A review describing the Decoded Quantum Interferometry algorithm for quantum speedups in max-LINSAT optimization, with claimed superpolynomial advantage in the OPI problem.