The DOI matches its Crossref record; 47 of the 47 references it cites were found in a registry or an index.
Grover Adaptive Search for Constrained Polynomial Binary Optimization
Open accessAbstract
In this paper we discuss Grover Adaptive Search (GAS) for Constrained Polynomial Binary Optimization (CPBO) problems, and in particular, Quadratic Unconstrained Binary Optimization (QUBO) problems, as a special case. GAS can provide a quadratic speed-up for combinatorial optimization problems compared to brute force search. However, this requires the development of efficient oracles to represent problems and flag states that satisfy certain search criteria. In general, this can be achieved using quantum arithmetic, however, this is expensive in terms of Toffoli gates as well as required ancilla qubits, which can be prohibitive in the near-term. Within this work, we develop a way to construct efficient oracles to solve CPBO problems using GAS algorithms. We demonstrate this approach and the potential speed-up for the portfolio optimization problem, i.e. a QUBO, using simulation and experimental results obtained on real quantum hardware. However, our approach applies to higher-degree polynomial objective functions as well as constrained optimization problems.
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“Within the gate-model domain, a further distinction can be made between VQAs, Grover-based approaches [52, 118], and other gate-based approaches that have been mentioned above, e.g., References [15, 16, 24, 94].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [52]
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“An efficient way for the oracle construction within this algorithm that may allow it to be run on NISQ devices has been proposed [52].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [52]
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Cites
A fast quantum mechanical algorithm for database search
Grover, L. K. (1996) · Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96 · doi:10.1145/237814.237866 · Cited by 8,830
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539795293172 · Cited by 8,472
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A variational eigenvalue solver on a photonic quantum processor
Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P. J., Aspuru-Guzik, A., & O’Brien, J. L. (2014) · Nature Communications · doi:10.1038/ncomms5213 · Cited by 4,552
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Harrow, A. W., Hassidim, A., & Lloyd, S. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.150502 · Cited by 3,325
Quantum Computation and Quantum Information: 10th Anniversary Edition
Nielsen, M. A., & Chuang, I. L. (2011) · Cited by 2,724
Quantum annealing with manufactured spins
Johnson, M. W., Amin, M. H. S., Gildert, S., Lanting, T., Hamze, F., Dickson, N., Harris, R., Berkley, A. J., Johansson, J., Bunyk, P., et al. (2011) · Nature · doi:10.1038/nature10012 · Cited by 1,891
A Quantum Approximate Optimization Algorithm
Farhi, E., Goldstone, J., & Gutmann, S. (2014) · arXiv · doi:10.48550/arxiv.1411.4028 · Cited by 1,789
Quantum amplitude amplification and estimation
Brassard, G., Høyer, P., Mosca, M., & Tapp, A. (2002) · Contemporary Mathematics · doi:10.1090/conm/305/05215 · Cited by 1,680
Qiskit: An Open-source Framework for Quantum Computing
Aleksandrowicz, G., Alexander, T., Barkoutsos, P. K., Bello, L., Ben-Haim, Y., Bucher, D., Cabrera-Hernández, F. J., Carballo-Franquis, J., Chen, A., Chen, C.-F., et al. (2019) · Zenodo (CERN European Organization for Nuclear Research) · doi:10.5281/zenodo.2562110 · Cited by 1,454
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Quantum Computing for Finance: State-of-the-Art and Future Prospects
Egger, D. J., Gambella, C., Marecek, J., McFaddin, S., Mevissen, M., Raymond, R., Simonetto, A., Woerner, S., & Yndurain, E. (2020) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2020.3030314 · Cited by 466
Self-citationHerman, D., Googin, C., Liu, X., Sun, Y., Galda, A., Safro, I., Pistoia, M., & Alexeev, Y. (2023) · Nature Reviews Physics · doi:10.1038/s42254-023-00603-1 · Cited by 361
Challenges and opportunities in quantum optimization
Abbas, A., Ambainis, A., Augustino, B., Bärtschi, A., Buhrman, H., Coffrin, C., Cortiana, G., Dunjko, V., Egger, D. J., Elmegreen, B. G., et al. (2024) · Nature Reviews Physics · doi:10.1038/s42254-024-00770-9 · Cited by 201
“As in unconstrained discrete optimization, Grover search can be leveraged to achieve a quadratic speedup over brute-force search 77 .”
Self-citationFormulating and Solving Routing Problems on Quantum Computers
Harwood, S., Gambella, C., Trenev, D., Simonetto, A., Bernal Neira, D., & Greenberg, D. (2021) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2021.3049230 · Cited by 145
Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information
Gacon, J., Zoufal, C., Carleo, G., & Woerner, S. (2021) · Quantum · doi:10.22331/q-2021-10-20-567 · Cited by 113
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Metadata
- Authors
- Gilliam, A., Woerner, S., & Gonciulea, C.
- Affiliations
- JPMorgan Chase & Co (United States) (US)
- IBM Research - Zurich (CH)
- Venue
- Quantum
- Published
- 2021-04-08
- Volume
- 5
- Pages
- 428
- ISSN
- 2521-327X (ISSN-L)
- OpenAlex
- W2992763160
- Cited by
- 153
- References
- 44
- Citations by year
- 2026: 22 · 2025: 40 · 2024: 33 · 2023: 23 · 2022: 15 · 2021: 14
- FWCI
- 7.48
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Quantum (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University) (cc-by)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
- Keywords
- QUBO, quantum oracle, quantum arithmetic, Toffoli gate, portfolio optimization, combinatorial optimization, quantum advantage, quantum computing hardware
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