The DOI matches its Crossref record; 97 of the 101 references it cites were found in a registry or an index.
VQE method: a short survey and recent developments
Open accessAbstract
The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation (QPE) because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schrödinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by the choice of the variational ansatz used to represent the trial wave function. Hence, the construction of an efficient ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatzes for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing efficient ansatzes that fall into two categories—chemistry–inspired and hardware–efficient—that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.
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“Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer.”
From On Circuit-Based Hybrid Quantum Neural Networks for Remote Sensing Imagery Classification (2022) · cites this paper as [15]
In the citing paper
“Within the Noisy Intermediate-Scale Quantum (NISQ) era, Variational Quantum Eigensolvers (VQEs) [5] have emerged as one of the most promising algorithms for quantum chemistry applications. [6,7]”
From Limitations of Quantum Hardware for Molecular Energy Estimation Using VQE (2026) · cites this paper as [7]
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Method
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Cited by
Sorted by citations
The Variational Quantum Eigensolver: A review of methods and best practices
Tilly, J., Chen, H., Cao, S., Picozzi, D., Setia, K., Li, Y., Grant, E., Wossnig, L., Rungger, I., Booth, G. H., et al. (2022) · Physics Reports · doi:10.1016/j.physrep.2022.08.003 · Cited by 1,031
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
On Circuit-Based Hybrid Quantum Neural Networks for Remote Sensing Imagery Classification
Sebastianelli, A., Zaidenberg, D. A., Spiller, D., Le Saux, B., & Ullo, S. (2022) · IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing · doi:10.1109/jstars.2021.3134785 · Cited by 162
Quantum Machine Learning—An Overview
Tychola, K. A., Kalampokas, Τ., & Papakostas, G. A. (2023) · Electronics · doi:10.3390/electronics12112379 · Cited by 143
Recent Advances for Quantum Neural Networks in Generative Learning
Tian, J., Sun, X., Du, Y., Zhao, S., Liu, Q., Zhang, K., Yi, W., Huang, W., Wang, C., Wu, X., et al. (2023) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2023.3272029 · Cited by 147
Metadata
- Authors
- Fedorov, D. A., Peng, B., Govind, N., & Alexeev, Y.
- Affiliations
- Oak Ridge Associated Universities (US)
- Pacific Northwest National Laboratory (US)
- Argonne National Laboratory (US)
- Corresponding author
- Fedorov, Dmitry A.
- Peng, Bo
- Govind, Niranjan
- Alexeev, Yuri
- Venue
- Materials Theory
- Published
- 2022-01-06
- Volume
- 6
- Issue
- 1
- ISSN
- 2509-8012 (ISSN-L)
- OpenAlex
- W4206745400
- Cited by
- 224
- References
- 101
- Citations by year
- 2026: 28 · 2025: 64 · 2024: 52 · 2023: 53 · 2022: 24
- FWCI
- 15.87
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Materials Theory (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Office of Science (DE-SC002024, DE-AC02-06CH11357)
- 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 › Advanced Chemical Physics Studies
- Keywords
- variational quantum eigensolver, variational ansatz, hybrid quantum-classical algorithms, hardware-efficient ansatz, electronic Schrödinger equation, molecular quantum chemistry, variational quantum algorithms, quantum chemistry on quantum computers
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