Geometric-resource bounds and permutation-averaged success probabilities for the WZP algorithm
Abstract
Solving linear systems of equations is a fundamental task in machine learning and optimization. In this work, we extend the original WZP algorithm from real symmetric linear systems to complex Hermitian linear systems. We then study the success probability of the modified WZP algorithm from a resource-theoretic perspective. By expressing the postselection success probability as the expectation value of a positive operator, we derive upper and lower bounds of the maximal success probability over separable, incoherent, and real pure states. These bounds further establish connections between the maximal success probability and geometric entanglement, coherence, and imaginarity. We further show that, under permutation averaging, the averaged success probability is an affine function of the coherence fraction, with its dependence determined by the alignment between the success operator and the equal-superposition state. We also investigate the preprocessed WZP algorithm under subgroup-constrained preprocessing. For the two-level family, the optimal success probability is determined by the maximal projection weight onto the orbit of the target projector. Our results provide a unified perspective on the WZP success probability under different operational constraints.
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BibTeX
@misc{ye2026geometricresource,
title = {{Geometric-resource bounds and permutation-averaged success probabilities for the WZP algorithm}},
author = {Linlin Ye and Linmao Wang and Zhaoqi Wu and Shao-Ming Fei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20198},
eprint = {2610.20198},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20198},
}
RIS
TY - UNPB
TI - Geometric-resource bounds and permutation-averaged success probabilities for the WZP algorithm
AU - Linlin Ye
AU - Linmao Wang
AU - Zhaoqi Wu
AU - Shao-Ming Fei
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20198
UR - https://arxiv.org/abs/2610.20198
AB - Solving linear systems of equations is a fundamental task in machine learning and optimization. In this work, we extend the original WZP algorithm from real symmetric linear systems to complex Hermitian linear systems. We then study the success probability of the modified WZP algorithm from a resource-theoretic perspective. By expressing the postselection success probability as the expectation value of a positive operator, we derive upper and lower bounds of the maximal success probability over separable, incoherent, and real pure states. These bounds further establish connections between the maximal success probability and geometric entanglement, coherence, and imaginarity. We further show that, under permutation averaging, the averaged success probability is an affine function of the coherence fraction, with its dependence determined by the alignment between the success operator and the equal-superposition state. We also investigate the preprocessed WZP algorithm under subgroup-constrained preprocessing. For the two-level family, the optimal success probability is determined by the maximal projection weight onto the orbit of the target projector. Our results provide a unified perspective on the WZP success probability under different operational constraints.
ER -