Learned-projector QAOA for hierarchical optimization
Abstract
Many optimization problems reveal inexpensive structural information before requiring costly final evaluation, whereas the conventional quantum approximate optimization algorithm (QAOA) applies a single aggregate objective throughout. We introduce the learned-projector quantum alternating operator ansatz (LP-QAOA), a multistage protocol that freezes optimized circuits and uses their output states to define later projector mixers. We prove a stability theorem for LP-QAOA that bounds the propagation of approximation errors through successive frozen stages. Our analysis also shows how learned-projector mixing avoids the high-order tunnelling suppression of local mixers. We conduct state-vector simulations on block-constrained spin tiling (BCST) instances, where LP-QAOA achieves higher probabilities of sampling the optimum, lower estimated logical-resource requirements, and better trainability than the tested baselines. A supporting stochastic block model experiment extends LP-QAOA to optimization problems with soft hierarchical structure. Our results highlight the potential of LP-QAOA to improve variational quantum optimization by exploiting hierarchical problem structure.
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BibTeX
@misc{zhou2026learnedprojector,
title = {{Learned-projector QAOA for hierarchical optimization}},
author = {Kangyun Zhou and Dong An and Jin-Peng Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28888},
eprint = {2609.28888},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28888},
}
RIS
TY - UNPB
TI - Learned-projector QAOA for hierarchical optimization
AU - Kangyun Zhou
AU - Dong An
AU - Jin-Peng Liu
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.28888
UR - https://arxiv.org/abs/2609.28888
AB - Many optimization problems reveal inexpensive structural information before requiring costly final evaluation, whereas the conventional quantum approximate optimization algorithm (QAOA) applies a single aggregate objective throughout. We introduce the learned-projector quantum alternating operator ansatz (LP-QAOA), a multistage protocol that freezes optimized circuits and uses their output states to define later projector mixers. We prove a stability theorem for LP-QAOA that bounds the propagation of approximation errors through successive frozen stages. Our analysis also shows how learned-projector mixing avoids the high-order tunnelling suppression of local mixers. We conduct state-vector simulations on block-constrained spin tiling (BCST) instances, where LP-QAOA achieves higher probabilities of sampling the optimum, lower estimated logical-resource requirements, and better trainability than the tested baselines. A supporting stochastic block model experiment extends LP-QAOA to optimization problems with soft hierarchical structure. Our results highlight the potential of LP-QAOA to improve variational quantum optimization by exploiting hierarchical problem structure.
ER -