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Cited by 51Quantum Computing Algorithms and ArchitectureMetaheuristic Optimization Algorithms ResearchQuantum many-body systems

Quantum Approximate Optimization with Hard and Soft Constraints

Hadfield, Stuart, Wang, Zhihui, Rieffel, Eleanor G., O'Gorman, Bryan, Venturelli, Davide, Biswas, Rupak·2017·Proceedings of the Second International Workshop on Post Moores Era Supercomputing
DOI 10.1145/3149526.3149530
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Abstract

Challenging computational problems arising in the practical world are frequently tackled by heuristic algorithms. Small universal quantum computers will emerge in the next year or two, enabling a substantial broadening of the types of quantum heuristics that can be investigated beyond quantum annealing. The immediate question is: what experiments should we prioritize that will give us insight into quantum heuristics? One leading candidate is the quantum approximate optimization algorithm (QAOA) metaheuristic. In this work, we provide a framework for designing QAOA circuits for a variety of combinatorial optimization problems with both hard constraints that must be met and soft constraints whose violation we wish to minimize. We work through a number of examples, and discuss design principles.

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  • Encoding hard constraints directly into the mixing Hamiltonian restricts the state evolution to the feasible subspace where no hard constraints are violated.

    “Building on previous work in quantum annealing (Hen and Sarandy, 2016; Hen and Spedalieri, 2016), it was proposed to encode the hard constraints directly into the mixing Hamiltonian (Hadfield et al. , 2017). This approach yields the main advantage of restricting the state evolution to the feasible subspace where no hard constraints are violated.”

    From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Hadfield et al., 2017

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Authors
Hadfield, S., Wang, Z., Rieffel, E. G., O'Gorman, B., Venturelli, D., & Biswas, R.
Affiliations
  • Columbia University (US)
  • Ames Research Center (US)
  • Quantum Artificial Intelligence Lab., NASA Ames Research Center, Moffett Field, CA and Stinger Ghaffarian Technologies, Inc., Greenbelt, MD
ORCID
Venue
Proceedings of the Second International Workshop on Post Moores Era Supercomputing
Publisher
ACM
Published
2017-11-12
Pages
15-21
DOI
10.1145/3149526.3149530
OpenAlex
W2766078569
Cited by
51
References
3
Citations by year
2026: 5 · 2025: 7 · 2024: 3 · 2023: 9 · 2022: 10 · 2021: 7 · 2020: 5 · 2019: 3 · 2018: 2
FWCI
1.25
Type
conference paper
Language
en
Open access
closed
Licence
www.acm.org/publications/policies/copyright_policy#Background (vor)
Funders
  • Universities Space Research Association
  • Advanced Exploration Systems
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
quantum approximate optimization algorithm, hard constraints, soft constraints, combinatorial optimization, constraint violation minimization, quantum optimization

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