aiqbench analysis
This research demonstrates that exploiting the internal structure of real-world problems can restore quantum speed-ups even when accounting for state-preparation costs, which often negate advantages in structure-agnostic approaches. By compiling compact recursive descriptions into efficient circuits, the proposed framework extends super-polynomial benefits to broader combinatorial optimization tasks like facility location. These findings establish problem structure as a critical computational resource for achieving practical quantum advantage in data-intensive applications.
Harnessing problem structure for end-to-end quantum speed-ups
arXiv:2609.40105v1 Announce Type: new 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.
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.
arXiv:2609.40105 [quant-ph]
(or arXiv:2609.40105v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.40105 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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