Performance of hybrid quantum-classical variational heuristics for combinatorial optimization
Open accessAbstract
The recent literature on near-term applications for quantum computers contains several examples of the applications of hybrid quantum-classical variational approaches. This methodology can be applied to a variety of optimization problems, but its practical performance is not well studied yet. This paper moves some steps in the direction of characterizing the practical performance of the methodology, in the context of finding solutions to classical combinatorial optimization problems. Our study is based on numerical results obtained applying several classical nonlinear optimization algorithms to Hamiltonians for six combinatorial optimization problems; the experiments are conducted via noise-free classical simulation of the quantum circuits implemented in Qiskit. We empirically verify that: (1) finding the ground state is harder for Hamiltonians with many Pauli terms; (2) classical global optimization methods are more successful than local methods due to their ability of avoiding the numerous local optima; (3) there does not seem to be a clear advantage in introducing entanglement in the variational form.
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Investigations on the impact of different classical optimizers for parameter optimization in general advocate for gradient-free global optimizers when dealing with real quantum hardware.
“Investigations on the impact of different classical optimizers for parameter optimization in general advocate for gradient-free global optimizers when dealing with real quantum hardware [37, 47, 100, 121].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [100]
The paper reports that global classical optimizers were more successful than local methods in its noise-free simulations (opening summary, p. 1). It does not establish that gradient-free global optimizers are preferable on real quantum hardware: the Introduction (p. 1) explicitly says its conclusions might differ on noisy hardware, and the Conclusions (p. 14) suggest computing derivatives as a possible improvement. (LLM, conf=0.89)
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Optimizing Variational Circuits for Higher-Order Binary Optimization
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- Authors
- Nannicini, G.
- Affiliations
- IBM Research - Thomas J. Watson Research Center (US)
- Corresponding author
- Nannicini, Giacomo
- ORCID
- Nannicini, Giacomo
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2019-01-14
- Volume
- 99
- Issue
- 1
- Pages
- 013304-013304
- ISSN
- 2470-0045 (ISSN-L)
- 2470-0053
- OpenAlex
- W2805358412
- Cited by
- 138
- References
- 18
- Citations by year
- 2026: 10 · 2025: 22 · 2024: 25 · 2023: 26 · 2022: 20 · 2021: 18 · 2020: 12 · 2019: 5
- FWCI
- 6.35
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical review. E (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Air Force Research Laboratory (FA8750-C-18-0098)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- hybrid quantum-classical algorithms, variational quantum algorithms, combinatorial optimization, variational quantum eigensolver, Pauli term, entanglement, global optimization, local optimization, Qiskit
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