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, and other gate-based approaches.
“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]
An efficient way for the oracle construction within Grover Adaptive Search that may allow it to be run on NISQ devices has been proposed.
“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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Amplitude Amplification for Optimization via Subdivided Phase Oracle
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A QUBO model of the RNA folding problem optimized by variational hybrid quantum annealing
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Hybrid Quantum-Classical Heuristic to Solve Large-Scale Integer Linear Programs
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Variational Amplitude Amplification for Solving QUBO Problems
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Quantum Algorithms for the Physical Layer: Potential Applications to Physical Layer Security
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Quantum Computing Approaches for Mission Covering Optimization
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Approaching Collateral Optimization for NISQ and Quantum-Inspired Computing (May 2023)
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Discrete-time quantum walk-based optimization algorithm
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ReLAQA: Reinforcement Learning-Based Autonomous Quantum Agent for Quantum Applications
Alomari, A., & Kumar, S. (2024) · IEEE Transactions on Artificial Intelligence · doi:10.1109/tai.2024.3437335 · Cited by 8 · see citing works
Analytical results for the quantum alternating operator ansatz with Grover mixer
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Monzón-Verona, J. M., García–Alonso, S., & Santana-Martín, F. J. (2025) · Sensors · doi:10.3390/s25041277 · Cited by 6 · see citing works
Efficient design of a quantum absolute-value circuit using Clifford+T gates
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Quantum Speedup for Multiuser Detection With Optimized Parameters in Grover Adaptive Search
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Coherence fraction in Grover's search algorithm
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Two-Step Quantum Search Algorithm for Solving Traveling Salesman Problems
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Hybrid quantum-classical multi-cut Benders approach with a power system application
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Quantum algorithm for smoothed particle hydrodynamics
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Model-Driven Optimization for Quantum Program Synthesis with MOMoT
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Industrial progress with quantum algorithms: an in-depth review
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The Quantum Optimization Benchmarking Library
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Self-citationA Predictive Approach for Selecting the Best Quantum Solver for an Optimization Problem
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Quantum search algorithm on weighted databases
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Multiple Query Optimization using a Hybrid Approach of Classical and Quantum ComputingPreprint
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Penalty-free approach to accelerating constrained quantum optimization
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Inductive Construction of Variational Quantum Circuit for Constrained Combinatorial Optimization
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Grover Adaptive Search With Fewer Queries
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Mixed Grover: A Hybrid Version to Improve Grover's Algorithm for Unstructured Database Search
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Grover’s search with learning oracle for constrained binary optimization problems
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Quantum optimization algorithm based on multistep quantum computation
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Canonical Construction of Quantum OraclesPreprint
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A Survey of Quantum Reinforcement Learning Approaches: Current Status and Future Research Directions
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Grover algorithm circuit optimization and noise analysis on integer factorization
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- 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 · 2020: 6
- 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 › Computer Science › Artificial Intelligence › 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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