Towards Exponential Quantum Improvements in Solving Cardinality-Constrained Binary Optimization
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908887918051328 |
|---|---|
| author | Yuan, Haomu Wu, Hanqing Chen, Kuan-Cheng Cheng, Bin Barnes, Crispin H. W. |
| author_facet | Yuan, Haomu Wu, Hanqing Chen, Kuan-Cheng Cheng, Bin Barnes, Crispin H. W. |
| contents | Cardinality-constrained binary optimization is a fundamental computational primitive with broad applications in machine learning, finance, and scientific computing. In this work, we introduce a Grover-based quantum algorithm that exploits the structure of the fixed-cardinality feasible subspace under a natural promise on solution existence. For quadratic objectives, our approach achieves ${O}\left(\sqrt{\frac{\binom{n}{k}}{M}}\right)$ Grover rotations for any fixed cardinality $k$ and degeneracy of the optima $M$, yielding an exponential reduction in the number of Grover iterations compared with unstructured search over $\{0,1\}^n$. Building on this result, we develop a hybrid classical--quantum framework based on the alternating direction method of multipliers (ADMM) algorithm. The proposed framework is guaranteed to output an $ε$-approximate solution with a consistency tolerance $ε+ δ$ using at most $ {O}\left(\sqrt{\binom{n}{k}}\frac{n^{6}k^{3/2} }{ \sqrt{M}ε^2 δ}\right)$ queries to a quadratic oracle, together with ${O}\left(\frac{n^{6}k^{3/2}}{ε^2δ}\right)$ classical overhead. Overall, our method suggests a practical use of quantum resources and demonstrates an exponential improvements over existing Grover-based approaches in certain parameter regimes, thereby paving the way toward quantum advantage in constrained binary optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14744 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Towards Exponential Quantum Improvements in Solving Cardinality-Constrained Binary Optimization Yuan, Haomu Wu, Hanqing Chen, Kuan-Cheng Cheng, Bin Barnes, Crispin H. W. Quantum Physics Computational Complexity Optimization and Control Statistics Theory Cardinality-constrained binary optimization is a fundamental computational primitive with broad applications in machine learning, finance, and scientific computing. In this work, we introduce a Grover-based quantum algorithm that exploits the structure of the fixed-cardinality feasible subspace under a natural promise on solution existence. For quadratic objectives, our approach achieves ${O}\left(\sqrt{\frac{\binom{n}{k}}{M}}\right)$ Grover rotations for any fixed cardinality $k$ and degeneracy of the optima $M$, yielding an exponential reduction in the number of Grover iterations compared with unstructured search over $\{0,1\}^n$. Building on this result, we develop a hybrid classical--quantum framework based on the alternating direction method of multipliers (ADMM) algorithm. The proposed framework is guaranteed to output an $ε$-approximate solution with a consistency tolerance $ε+ δ$ using at most $ {O}\left(\sqrt{\binom{n}{k}}\frac{n^{6}k^{3/2} }{ \sqrt{M}ε^2 δ}\right)$ queries to a quadratic oracle, together with ${O}\left(\frac{n^{6}k^{3/2}}{ε^2δ}\right)$ classical overhead. Overall, our method suggests a practical use of quantum resources and demonstrates an exponential improvements over existing Grover-based approaches in certain parameter regimes, thereby paving the way toward quantum advantage in constrained binary optimization. |
| title | Towards Exponential Quantum Improvements in Solving Cardinality-Constrained Binary Optimization |
| topic | Quantum Physics Computational Complexity Optimization and Control Statistics Theory |
| url | https://arxiv.org/abs/2603.14744 |