Application of Quantum Annealing to Nurse Scheduling Problem
Open accessAbstract
Quantum annealing is a promising heuristic method to solve combinatorial optimization problems, and efforts to quantify performance on real-world problems provide insights into how this approach may be best used in practice. We investigate the empirical performance of quantum annealing to solve the Nurse Scheduling Problem (NSP) with hard constraints using the D-Wave 2000Q quantum annealing device. NSP seeks the optimal assignment for a set of nurses to shifts under an accompanying set of constraints on schedule and personnel. After reducing NSP to a novel Ising-type Hamiltonian, we evaluate the solution quality obtained from the D-Wave 2000Q against the constraint requirements as well as the diversity of solutions. For the test problems explored here, our results indicate that quantum annealing recovers satisfying solutions for NSP and suggests the heuristic method is potentially achievable for practical use. Moreover, we observe that solution quality can be greatly improved through the use of reverse annealing, in which it is possible to refine returned results by using the annealing process a second time. We compare the performance of NSP using both forward and reverse annealing methods and describe how this approach might be used in practice.
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Forward and reverse annealing have been applied to the nurse scheduling problem and portfolio optimization.
“When it comes to more advanced quantum annealing methods, forward as well as reverse annealing have been applied to the nurse scheduling problem [69] and portfolio optimization [140].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [69]
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Maximizing gerrymandering through ising model optimization
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Yoshida, A., Miki, T., Shimada, M., Yoneda, Y., & Shirakashi, J. (2022) · Applied Physics Express · doi:10.35848/1882-0786/ac6b84 · Cited by 4 · see citing works
A Quantum Approach to the Problem of Charging Electric Cars on a Motorway
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Topological aspects of matters and Langlands program
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Self-citationA Hybrid Framework Using a QUBO Solver For Permutation-Based Combinatorial OptimizationPreprint
Goh, S. T., Gopalakrishnan, S., Bo, J., & Lau, H. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2009.12767 · Cited by 9 · see citing works
Traffic signal optimization using quantum annealing on real mapPreprint
Shikanai, R., Ohzeki, M., & Tanaka, K. (2023) · Research Square · doi:10.21203/rs.3.rs-3302709/v1 · Cited by 4 · see citing works
Intelligent Clinic Nurse Scheduling Considering Nurses Paired with Doctors and Preference of Nurses
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Incorporating external fields in analog Ising machines
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Quang, T. N., Matsuyama, K., Shimizu, K., Sugano, H., Kurimoto, E., Miki, M., Suzuki, J., Chen, Z., Waidyasooriya, H. M., Hariyama, M., et al. (2025) · Scientific Reports · doi:10.1038/s41598-025-28481-w · Cited by 6 · see citing works
Minor embedding for quantum annealing with reinforcement learning
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Kakuda, K., Sakaguchi, S., & Okuno, Y. (2025) · MRS Advances · doi:10.1557/s43580-025-01309-5 · Cited by 3 · see citing works
Deleplanque, S., Armas, L. F. P., & Creemers, S. (2025) · Journal of Heuristics · doi:10.1007/s10732-025-09564-3 · Cited by 3 · see citing works
Suksmono, A. B., & Minato, Y. (2022) · Scientific Reports · doi:10.1038/s41598-021-03586-0 · Cited by 4 · see citing works
An experimental study on binary optimization using quantum annealing in D-Wave
Singh, N. B., Krishna, G., Roy, A., Pachuau, J. L., & Saha, A. K. (2022) · International Conference on Informatics and Computing (ICIC) · doi:10.1109/icic56845.2022.10007004 · Cited by 3 · see citing works
Task Scheduling Optimization in the Cloud using Quantum Annealing
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QUBO Formulation for a Nurse Scheduling Problem: An Application for Sales Force Scheduling
Palma, B., Gatti, L., & Sotelo, R. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.10254 · Cited by 3 · see citing works
Reverse Quantum Annealing Assisted by Forward Annealing
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Applying analog quantum computing to solve optimisation problems: case studies on Max-Cut and CVRP
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The U Q Platform: A Unifed Approach To Q uantum Annealing
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Inverse Reticle Optimization With Quantum Annealing and Hybrid Solvers
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Solving the Resource-Constrained Project Scheduling Problem (RCPSP) with Quantum AnnealingPreprint
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Yoneda, Y., Shimada, M., Yoshida, A., & Shirakashi, J.-I. (2023) · Applied Physics Express · doi:10.35848/1882-0786/accc6d · Cited by 2 · see citing works
Input Data Format for Sparse Matrix in Quantum Annealing Emulator
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Quantum annealing for nearest neighbour compliance problem
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OPTIMIZATION OF THE TRANSPORTATION PLAN OF DESIGNATED WASTE USING QUANTUM ANNEALING
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A New Mathematical Model for Staff Scheduling in the Operating Room Based on their Preferences
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Okonogi, D., Jimbo, S., Ando, K., Chu, T. V., Yu, J., Motomura, M., & Kawamura, K. (2023) · IEICE Transactions on Information and Systems · doi:10.1587/transinf.2023pap0003 · Cited by 2 · see citing works
- Authors
- Ikeda, K., Nakamura, Y., & Humble, T. S.
- Affiliations
- The University of Osaka (JP)
- University of Tennessee at Knoxville (US)
- Oak Ridge National Laboratory (US)
- Corresponding author
- Ikeda, Kazuki
- Venue
- Scientific Reports
- Published
- 2019-09-06
- Volume
- 9
- Issue
- 1
- Pages
- 12837-12837
- ISSN
- 2045-2322 (ISSN-L)
- PMC
- PMC6731278
- OpenAlex
- W2972088227
- Cited by
- 139
- References
- 26
- Citations by year
- 2026: 9 · 2025: 21 · 2024: 25 · 2023: 28 · 2022: 29 · 2021: 13 · 2020: 13 · 2019: 1
- FWCI
- 6.39
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Scientific Reports (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy (AC05-00OR22725, DE-AC05?, 00OR22725)
- Battelle (DE-AC05- 00OR22725, AC05-00OR22725, DE-AC05)
- UT-Battelle (DE-AC05, DEAC05-00OR22725, AC05-00OR22725)
- Ministry of Education, Culture, Sports, Science and Technology
- Ministry of Science, ICT and Future Planning
- National Research Foundation of Korea
- Office of Science (DEAC05- 00OR22725, AC05-00OR22725)
- Japan Society for the Promotion of Science (19J11073)
- Oak Ridge National Laboratory (AC05-00OR22725)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Social Sciences › Decision Sciences › Management Science and Operations Research › Scheduling and Timetabling Solutions
- Physical Sciences › Computer Science › Computer Networks and Communications › Constraint Satisfaction and Optimization
- Keywords
- quantum annealing, nurse scheduling, D-Wave 2000Q, Ising Hamiltonian, reverse annealing, combinatorial optimization, hard constraints, solution quality, solution diversity, shift assignment
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