Harnessing problem structure for end-to-end quantum speed-ups
Abstract
Quantum algorithms can offer substantial computational speed-ups, yet these advantages may disappear once the cost of structure-agnostic classical data encoding is taken into account. Real-world problem instances, however, often possess rich internal structure. This raises a fundamental question: can such structure be harnessed to make quantum speed-ups survive end-to-end cost accounting? Here we show that it can. We introduce a general framework for structure-aware quantum data encoding that compiles compact recursive descriptions of problem structure into efficient state-preparation circuits, translating structural information directly into reduced encoding complexity. For the uncapacitated facility-location problem, structure-agnostic encoding admits a classical dequantization that eliminates the quadratic quantum speed-up, whereas exploiting the underlying problem structure restores this advantage even when state-preparation costs are included. More broadly, the same framework prepares structured quantum states for combinatorial optimization that capture non-trivial relations among constraints, including group balance, conflicts and synergistic rewards, extending previously reported super-polynomial quantum advantages to broader classes of objectives. These results establish exploitable problem structure as a computational resource for quantum algorithms and provide a systematic route towards realizing quantum advantage in data-intensive problems.
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BibTeX
@misc{jiang2026harnessing,
title = {{Harnessing problem structure for end-to-end quantum speed-ups}},
author = {Qifan Jiang and Xiao-Ming Zhang and Debin Xiang and Xiao Yuan and Liqiang Lu and Jianwei Yin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.40105},
eprint = {2609.40105},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40105},
}
RIS
TY - UNPB
TI - Harnessing problem structure for end-to-end quantum speed-ups
AU - Qifan Jiang
AU - Xiao-Ming Zhang
AU - Debin Xiang
AU - Xiao Yuan
AU - Liqiang Lu
AU - Jianwei Yin
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2609.40105
UR - https://arxiv.org/abs/2609.40105
AB - Quantum algorithms can offer substantial computational speed-ups, yet these advantages may disappear once the cost of structure-agnostic classical data encoding is taken into account. Real-world problem instances, however, often possess rich internal structure. This raises a fundamental question: can such structure be harnessed to make quantum speed-ups survive end-to-end cost accounting? Here we show that it can. We introduce a general framework for structure-aware quantum data encoding that compiles compact recursive descriptions of problem structure into efficient state-preparation circuits, translating structural information directly into reduced encoding complexity. For the uncapacitated facility-location problem, structure-agnostic encoding admits a classical dequantization that eliminates the quadratic quantum speed-up, whereas exploiting the underlying problem structure restores this advantage even when state-preparation costs are included. More broadly, the same framework prepares structured quantum states for combinatorial optimization that capture non-trivial relations among constraints, including group balance, conflicts and synergistic rewards, extending previously reported super-polynomial quantum advantages to broader classes of objectives. These results establish exploitable problem structure as a computational resource for quantum algorithms and provide a systematic route towards realizing quantum advantage in data-intensive problems.
ER -