The DOI matches its Crossref record; 21 of the 21 references it cites were found in a registry or an index.
Grover Mixers for QAOA: Shifting Complexity from Mixer Design to State Preparation
Open accessAbstract
We propose GM-QAOA, a variation of the Quantum Alternating Operator Ansatz (QAOA) that uses Grover-like selective phase shift mixing operators. GM-QAOA works on any NP optimization problem for which it is possible to efficiently prepare an equal superposition of all feasible solutions; it is designed to perform particularly well for constraint optimization problems, where not all possible variable assignments are feasible solutions. GM-QAOA has the following features: (i) It is not susceptible to Hamiltonian Simulation error (such as Trotterization errors) as its operators can be implemented exactly using standard gate sets and (ii) Solutions with the same objective value are always sampled with the same amplitude. We illustrate the potential of GM-QAOA on several optimization problem classes: for permutation-based optimization problems such as the Traveling Salesperson Problem, we present an efficient algorithm to prepare a superposition of all possible permutations of$n$numbers, defined on O (n2) qubits; for the hard constraint k-Vertex-Cover problem, and for an application to Discrete Portfolio Rebalancing, we show that GM-QAOA outperforms existing QAOA approaches.
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“Besides the mentioned ansatz search, as the driving force behind ansatz adaptation, there is also the possibility of having these adaptations as a byproduct, like it happens, e.g., within the Quantum Alternating Operator Ansatz where the primary goal is to find a mixing Hamiltonian that ensures to stay in the feasible subspace [11, 58, 95, 112, 116, 117, 120, 127].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [11]
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“Another possibility is to shift the complexity to the generation of the initial state [11], where the idea is to further utilize the state preparation circuit, which creates an equal superposition of all feasible states, for the design of the mixing Hamiltonian.”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [11]
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Cites
A fast quantum mechanical algorithm for database search
Grover, L. K. (1996) · Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96 · doi:10.1145/237814.237866 · Cited by 8,830
Lloyd, S. (1996) · Science · doi:10.1126/science.273.5278.1073 · Cited by 3,088 · cited 5×
“It follows as a benefit that GM-QAOA does not suffer from numerical errors that Hamiltonian simulation methods, such as Trotterization [10], Local Combination of Unitaries [11], or Quantum Walk based simulation [12], introduce.”
MethodInfluentialAssignment Problems and the Location of Economic Activities
Koopmans, T., & Beckmann, M. (1957) · Econometrica · doi:10.2307/1907742 · Cited by 2,567
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
Hadfield, S., Wang, Z., O’Gorman, B., Rieffel, E. G., Venturelli, D., & Biswas, R. (2019) · Algorithms · doi:10.3390/a12020034 · Cited by 772
Simulating Hamiltonian Dynamics with a Truncated Taylor Series
Berry, D. W., Childs, A. M., Cleve, R., Kothari, R., & Somma, R. D. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.090502 · Cited by 742
Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
Kivlichan, I. D., McClean, J., Wiebe, N., Gidney, C., Aspuru-Guzik, A., Chan, G. K.-L., & Babbush, R. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.110501 · Cited by 431
Hamiltonian Simulation with Nearly Optimal Dependence on all Parameters
Berry, D. W., Childs, A. M., & Kothari, R. (2015) · 2015 IEEE 56th Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2015.54 · Cited by 372
Average-Case Complexity Versus Approximate Simulation of Commuting Quantum Computations
Bremner, M. J., Montanaro, A., & Shepherd, D. J. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.080501 · Cited by 299
Fixed-Point Quantum Search with an Optimal Number of Queries
Yoder, T. J., Low, G. H., & Chuang, I. L. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.210501 · Cited by 267
Grover, L. K. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.150501 · Cited by 209
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A review on Quantum Approximate Optimization Algorithm and its variants
Blekos, K., Brand, D., Ceschini, A., Chou, C.-H., Li, R.-H., Pandya, K., & Summer, A. (2024) · Physics Reports · doi:10.1016/j.physrep.2024.03.002 · Cited by 563
Warm-starting quantum optimization
Egger, D. J., Mareček, J., & Woerner, S. (2021) · Quantum · doi:10.22331/q-2021-06-17-479 · Cited by 269
Barren plateaus in variational quantum computing
Larocca, M., Thanasilp, S., Wang, S., Sharma, K., Biamonte, J., Coles, P. J., Cincio, Ł., McClean, J. R., Holmes, Z., & Cerezo, M. (2025) · Nature Reviews Physics · doi:10.1038/s42254-025-00813-9 · Cited by 523
Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
Larocca, M., Czarnik, P., Sharma, K., Muraleedharan, G., Coles, P. J., & Cerezo, M. (2022) · Quantum · doi:10.22331/q-2022-09-29-824 · Cited by 272
Challenges and opportunities in quantum optimization
Abbas, A., Ambainis, A., Augustino, B., Bärtschi, A., Buhrman, H., Coffrin, C., Cortiana, G., Dunjko, V., Egger, D. J., Elmegreen, B. G., et al. (2024) · Nature Reviews Physics · doi:10.1038/s42254-024-00770-9 · Cited by 201
“Alternatively, one can also directly replace the mixing Hamiltonian H X in equation (2), for example, for Hamming-weight constraints by an XY -model Hamiltonian 81,82 , or by a Grover-based 83,84 Hamiltonian.”
Metadata
- Authors
- Bartschi, A., & Eidenbenz, S.
- Affiliations
- Los Alamos National Laboratory (US)
- ORCID
- Eidenbenz, Stephan
- Venue
- 2020 IEEE International Conference on Quantum Computing and Engineering (QCE)
- Publisher
- IEEE
- Published
- 2020-10
- Pages
- 72-82
- OpenAlex
- W3029819693
- Cited by
- 122
- References
- 21
- Citations by year
- 2026: 11 · 2025: 27 · 2024: 25 · 2023: 29 · 2022: 17 · 2021: 10 · 2020: 3
- FWCI
- 5.55
- Type
- conference paper
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- IEEE International Conference on Quantum Computing and Engineering (QCE) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- 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 Alternating Operator Ansatz, mixer design, quantum state preparation, constraint optimization, traveling salesman problem
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