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.
Decoded quantum interferometry requires structure
7 Pith papers cite this work. Polarity classification is still indexing.
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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.
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.
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.
The paper identifies four key hurdles in the transition from NISQ to FASQ quantum computers and argues that targeting them will accelerate progress toward useful quantum advantage.
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
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.
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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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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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Mind the gaps: The fraught road to quantum advantage
The paper identifies four key hurdles in the transition from NISQ to FASQ quantum computers and argues that targeting them will accelerate progress toward useful quantum advantage.