The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
Progress towards practical quantum variational algorithms
Open accessAbstract
The preparation of quantum states using short quantum circuits is one of the most promising near-term applications of small quantum computers, especially if the circuit is short enough and the fidelity of gates high enough that it can be executed without quantum error correction. Such quantum state preparation can be used in variational approaches, optimizing parameters in the circuit to minimize the energy of the constructed quantum state for a given problem Hamiltonian. For this purpose we propose a simple-to-implement class of quantum states motivated by adiabatic state preparation. We test its accuracy and determine the required circuit depth for a Hubbard model on ladders with up to 12 sites (24 spin orbitals), and for small molecules. We find that this ansatz converges faster than previously proposed schemes based on unitary coupled clusters. While the required number of measurements is astronomically large for quantum chemistry applications to molecules, applying the variational approach to the Hubbard model (and related models) is found to be far less demanding and potentially practical on small quantum computers. We also discuss another application of quantum state preparation using short quantum circuits, to prepare trial ground states of models faster than using adiabatic state preparation.
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“Several QML algorithms based on PQC have been proposed [21–27], demonstrating superior performance and computational abilities compared to conventional algorithms [28–31].”
From Medical image diagnosis based on adaptive Hybrid Quantum CNN (2023) · cites this paper as [21]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
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“Motivated by adiabatic state preparation, the Variational Hamiltonian Ansatz (VHA) was developed to reduce the number of parameters and accelerate the convergence (McClean et al. , 2016; Wecker et al. , 2015).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Wecker et al., 2015
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In the citing paper
“To this end, VQE (McClean et al. , 2016; Peruzzo et al. , 2014) has been proposed, to find the ground state of a Hamiltonian H in a manner that is suited for NISQ devices (Wecker et al. , 2015).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Wecker et al. , 2015
In the citing paper
“The AQC model has been shown to be computationally equivalent to the gate model 62 , meaning that algorithms written in either model can be translated to ones in the other model without incurring prohibitive computational overhead.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [62]
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Citations
Cites
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de Palhares, A. B., Varela, J. M., Duarte, D. H. G., & Chaves, R. (2026) · International Journal of Modern Physics C · doi:10.1142/s0129183126430059
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Wang, P., Li, C. Z., Shi, H., & Chen, P. (2026) · Chinese Physics B · doi:10.1088/1674-1056/ae6b33
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“The HVA [33] provides this balance by incorporating the problem structure directly into the circuit design.”
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Shen, L., Lin, M., Lin, C. Y.-Y., Xiao, D., & Cao, T. (2026) · Nature Communications · doi:10.1038/s41467-026-72769-y · Cited by 3
“Among the proposed approaches, HVA has emerged as a promising candidate [50].”
InfluentialHe, C., Li, Q., & Zhang, J. (2026) · Processes · doi:10.3390/pr14132095
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A review of variational quantum algorithms: Insights into fault-tolerant quantum computing
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“In quantum many-body systems, the Hamiltonian variational ansatz (HVA) lever-4 ages constituent terms of the Hamiltonian to construct layered circuits that approximate ground states with high expressibility, though compiling to native gates can require substantial depth and connectivity [27, 33].”
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Variational preparation and characterization of chiral spin liquids in quantum circuits
Zhang, Z.-Y., Kim, D.-H., & Chen, J.-Y. (2026) · Physical review. B./Physical review. B · doi:10.1103/s2ds-5n5k
“The circuit ansatz we used for searching ground states is a variant of the Hamiltonian Variational Ansatz (HVA) [57–59], with restriction of keeping only the two-body terms in the Hamiltonian.”
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Accuracy-cost trade-offs for reference VQE calculations of H 2 on IBM quantum hardware
Larrucea, J., Oliv, M., & Lorenz, J. M. (2026) · Quantum Science and Technology · doi:10.1088/2058-9565/aeb4e8
“It is therefore a canonical test case for experimental VQE implementations [1, 2, 5] and for studies of ansatz expressibility, optimization dynamics, and error mitigation”
Quantum Algorithms for Fixed Qubit Architectures
Farhi, E., Goldstone, J., Gutmann, S., & Neven, H. (2017) · arXiv · doi:10.48550/arxiv.1703.06199 · Cited by 93
“Recently there has been interest in using quantum computers for approximate combinatorial optimization [11, 12] and for simulating quantum systems [13, 14, 15, 16].”
Background
Metadata
- Authors
- Wecker, D., Hastings, M. B., & Troyer, M.
- Affiliations
- Microsoft (United States) (US)
- ETH Zurich (CH)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2015-10-02
- Volume
- 92
- Issue
- 4
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2254754114
- Cited by
- 716
- References
- 15
- Citations by year
- 2026: 48 · 2025: 108 · 2024: 101 · 2023: 97 · 2022: 100 · 2021: 110 · 2020: 69 · 2019: 40 · 2018: 21 · 2017: 11 · 2016: 11
- FWCI
- 14.03
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Microsoft Research
- National Science Foundation (PHY-1066293)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- quantum state preparation, adiabatic state preparation, variational ansatz, Hubbard model, unitary coupled cluster, quantum chemistry, circuit depth, NISQ devices
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