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Grover Adaptive Search for Constrained Polynomial Binary Optimization
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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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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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