aiqbench analysis
This paper refines theoretical performance bounds for decoded quantum interferometry (DQI) by incorporating probability weights into failure rate calculations, offering tighter guarantees than previous uniform estimates. The analysis demonstrates that accounting for the correspondence between failure distributions and state probabilities prevents overestimating decoding errors in low-probability layers, particularly for binary linear constraint problems. These findings provide a more rigorous framework for evaluating DQI reliability in combinatorial optimization tasks using imperfect decoders like belief propagation.
Weighted performance bounds for decoded quantum interferometry with imperfect decoding
arXiv:2604.15025v3 Announce Type: replace Abstract: Decoded quantum interferometry (DQI) offers an approach to a class of combinatorial optimization problems by reducing quantum state preparation to a decoding task. However, the existing performance bound for imperfect decoding uses the maximum failure rate over error-weight layers to bound the performance loss uniformly, which may overestimate the effect of decoding failures in layers with low probability. Building on the existing analysis, we combine the failure rate of each layer with its probability weight in the chosen state to derive tighter performance lower bounds. For binary linear constraint problems with uniformly random target values, we obtain a finite-size lower bound on the average satisfaction ratio for fixed state parameters and a fixed decoder, and establish its improvement over the existing bound. In part of the parameter region where the existing bound falls to the random-assignment baseline, the weighted bound still provides a guarantee above that baseline. We further extend the analysis to general finite fields under a model of uniformly random translations of allowed sets of equal size. Trials in individual layers using a fixed belief propagation decoder illustrate the size of the improvement and provide confidence guarantees after accounting for sampling uncertainty. These results reveal the role of retaining the correspondence between the failure distribution and the state probabilities, and suggest directions for more refined performance analyses of other DQI constructions.
Abstract:Decoded quantum interferometry (DQI) offers an approach to a class of combinatorial optimization problems by reducing quantum state preparation to a decoding task. However, the existing performance bound for imperfect decoding uses the maximum failure rate over error-weight layers to bound the performance loss uniformly, which may overestimate the effect of decoding failures in layers with low probability. Building on the existing analysis, we combine the failure rate of each layer with its probability weight in the chosen state to derive tighter performance lower bounds. For binary linear constraint problems with uniformly random target values, we obtain a finite-size lower bound on the average satisfaction ratio for fixed state parameters and a fixed decoder, and establish its improvement over the existing bound. In part of the parameter region where the existing bound falls to the random-assignment baseline, the weighted bound still provides a guarantee above that baseline. We further extend the analysis to general finite fields under a model of uniformly random translations of allowed sets of equal size. Trials in individual layers using a fixed belief propagation decoder illustrate the size of the improvement and provide confidence guarantees after accounting for sampling uncertainty. These results reveal the role of retaining the correspondence between the failure distribution and the state probabilities, and suggest directions for more refined performance analyses of other DQI constructions.
arXiv:2604.15025 [quant-ph]
(or arXiv:2604.15025v3 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2604.15025 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 312 words
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