Multivariate DQI uses N-variable polynomials for weighted Max-LINSAT, derives closed-form asymptotics for expectation and concentration, provides a single-decoder preparation circuit, and shows outperformance over weighted Prange for some OPI cases while extending to Hamiltonian DQI.
No quantum advantage in decoded quantum interferometry for maxcut
8 Pith papers cite this work. Polarity classification is still indexing.
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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.
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.
Decoded quantum interferometry is generalized to translation association schemes, reducing analysis to tridiagonal eigenvalue problems, with a finite-field matrix rank-difference protocol that produces constant-probability residual-rank bounds but no additive optimality guarantee.
DQI-Kit automates encoding of objectives and constraints into Max-LINSAT instances and estimates expected DQI performance on the resulting problems.
Large qLDPC blocks in distributed quantum computing enable Pauli-based computation to run up to 10x faster than surface codes for optimization algorithms by using spare nodes to bypass serialization bottlenecks.
A Master Theorem gives a strictly tighter lower bound on quantum advantage in DQI by replacing the worst-case error penalty with an eigenvector-weighted Rayleigh quotient penalty.
A review describing the Decoded Quantum Interferometry algorithm for quantum speedups in max-LINSAT optimization, with claimed superpolynomial advantage in the OPI problem.
citing papers explorer
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Multivariate Decoded Quantum Interferometry for Weighted Optimization
Multivariate DQI uses N-variable polynomials for weighted Max-LINSAT, derives closed-form asymptotics for expectation and concentration, provides a single-decoder preparation circuit, and shows outperformance over weighted Prange for some OPI cases while extending to Hamiltonian DQI.
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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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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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Decoded Quantum Interferometry Beyond Hamming: Rank-Metric and Translation Association Schemes
Decoded quantum interferometry is generalized to translation association schemes, reducing analysis to tridiagonal eigenvalue problems, with a finite-field matrix rank-difference protocol that produces constant-probability residual-rank bounds but no additive optimality guarantee.
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From Constraint to Code: DQI-Kit -- A Software Framework for Decoded Quantum Interferometry
DQI-Kit automates encoding of objectives and constraints into Max-LINSAT instances and estimates expected DQI performance on the resulting problems.
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Space-Time Tradeoffs of Pauli-Based Computation in Distributed qLDPC Architectures
Large qLDPC blocks in distributed quantum computing enable Pauli-based computation to run up to 10x faster than surface codes for optimization algorithms by using spare nodes to bypass serialization bottlenecks.
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Hidden Quantum Advantage near the Decoding Threshold of Decoded Quantum Interferometry
A Master Theorem gives a strictly tighter lower bound on quantum advantage in DQI by replacing the worst-case error penalty with an eigenvector-weighted Rayleigh quotient penalty.
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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.