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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.
In the citing paper
“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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“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
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“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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Cites
The density-matrix renormalization group in the age of matrix product states
Schollwöck, U. (2011) · Annals of Physics · doi:10.1016/j.aop.2010.09.012 · Cited by 4,818
Powell, M. J. D. (1964) · The Computer Journal · doi:10.1093/comjnl/7.2.155 · Cited by 4,632
A variational eigenvalue solver on a photonic quantum processor
Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P. J., Aspuru-Guzik, A., & O’Brien, J. L. (2014) · Nature Communications · doi:10.1038/ncomms5213 · Cited by 4,552
Psi4: an open‐source ab initio electronic structure program
Turney, J. M., Simmonett, A. C., Parrish, R. M., Hohenstein, E. G., Evangelista, F. A., Fermann, J. T., Mintz, B. J., Burns, L. A., Wilke, J. J., Abrams, M. L., et al. (2011) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.93 · Cited by 1,089
Jaksch, D., & Zoller, P. (2005) · Annals of Physics · doi:10.1016/j.aop.2004.09.010 · Cited by 976
Class of Quantum Many-Body States That Can Be Efficiently Simulated
Vidal, G. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.110501 · Cited by 923
Competing States in the t - J Model: Uniform d -Wave State versus Stripe State
Corboz, P., Rice, T. M., & Troyer, M. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.046402 · Cited by 493
Self-citationSimulation of electronic structure Hamiltonians using quantum computers
Whitfield, J. D., Biamonte, J., & Aspuru-Guzik, A. (2011) · Molecular Physics · doi:10.1080/00268976.2011.552441 · Cited by 472
Simulating physical phenomena by quantum networks
Somma, R. D., Ortíz, G., Gubernatis, J. E., Knill, E. H., & Laflamme, R. (2002) · Physical Review A · doi:10.1103/physreva.65.042323 · Cited by 372
Computational complexity of projected entangled pair states
Schuch, N., Wolf, M. M., Verstraete, F., & Cirac, J. I. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.140506 · Cited by 313
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Asnaashari, K., Bondarenko, D., & Krems, R. V. (2026) · Physical Chemistry Chemical Physics · doi:10.1039/d5cp02860d · Cited by 7
Uvarov, A., Rabinovich, D., Lakhmanskaya, O., Lakhmanskiy, K., Biamonte, J., & Adhikary, S. (2024) · Physical Review A · doi:10.1103/physreva.110.012404 · Cited by 9
“[21] Dave Wecker, Matthew B Hastings, and Matthias Troyer.”
BackgroundExploring ground states of Fermi-Hubbard model on honeycomb lattices with counterdiabaticity
Tang, J., Xu, R., Ding, Y., Xu, X., Ban, Y., Yung, M., Pérez-Obiol, A., Platero, G., & Chen, X. (2024) · npj Quantum Materials · doi:10.1038/s41535-024-00697-5 · Cited by 7
“In VQA, the optimization of parameters is crucial and is accomplished by a classical computer aiming to minimize a cost function, thereby identifying the optimal set of parameters.”
Lan, Z., & Liang, W. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.4c00490 · Cited by 6
“The Ansatz we adopted is the Hamiltonian variational Ansatz (HVA), 58 and the number of layers l = 2 .”
Hamiltonian forging of a thermofield double
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“With these caveats in mind, we opt for a Hamiltonian Variational Ansatz (HVA) [34, 35] from which we can generate the vectors | f i ( θ ) = U ( θ ) b i ⟩ = L l s e − iθ s,l h s | b i ⟩ , directly from the elements of the computational basis, which are the eigenstates of H 2 .”
Quantum Computing for Chemical Applications: Variational Algorithms and Beyond
Kumar, S., Ghosh, K., Lee, S., & Yamijala, S. S. R. K. C. (2025) · Journal of the Indian Institute of Science · doi:10.1007/s41745-025-00488-2 · Cited by 7
“72,73 Apart from the circuit depth and qubit volume, one often also encounters the barren plateau 74–76 during the optimization due to the increased circuit parameters.”
Feasibility of performing quantum chemistry calculations on quantum computers
Louvet, T., Ayral, T., & Waintal, X. (2025) · Physical review. B./Physical review. B · doi:10.1103/hpt6-9tnk · Cited by 16
“The standard algorithms are VQE [10– 14] for noisy, intermediate scale quantum (NISQ) processors, or its fault-tolerant counterpart, the quantum phase estimation (QPE) algorithm [15–17].”
Bayesian Inference with Engineered Likelihood Functions for Robust Amplitude Estimation
Wang, G., Koh, D. E., Johnson, P. D., & Cao, Y. (2020) · Cited by 5
Quantum gradient evaluation through quantum non-demolition measurements
Solinas, P., Caletti, S., & Minuto, G. (2023) · The European Physical Journal D · doi:10.1140/epjd/s10053-023-00648-y · Cited by 5
“For example, in physical problems where we need to find the energy of the ground state of a Hamiltonian, the Pauli strings are usually the product of only four Pauli operators [20,29].”
BackgroundInfluentialExponential Hardness of Optimization from the Locality in Quantum Neural Networks
Zhang, H.-K., Zhu, C., Liu, G., & Wang, X. (2024) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v38i15.29614 · Cited by 6
“…devices have demonstrated the ability to achieve near-term quantum advantage for practical applications in key areas including many-body physics (Wecker, Hastings, and Troyer 2015; Uvarov, Biamonte, and Yudin 2020), chemistry (McArdle et al. 2020), finance (Egger et al. 2020), and machine…”
BackgroundSketching phase diagrams using low-depth variational quantum algorithms
Bosse, J. L., Santos, R. A., & Montanaro, A. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad4979 · Cited by 5
“In appendix D, we strengthen this result for translation-invariant non-interacting fermionic models and show that deep VQE circuits with the Hamiltonian Variational ansatz [9] are required to prepare ground states at or near criticality.”
BackgroundMethodInfluentialDeterministic Ansätze for the measurement-based variational quantum eigensolver
Schroeder, A. K., Heller, M., & Gachechiladze, M. (2024) · New Journal of Physics · doi:10.1088/1367-2630/ad51e5 · Cited by 8
Quantum annealer accelerates the variational quantum eigensolver in a triple-hybrid algorithm
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Hamiltonian-based graph-state ansatz for variational quantum algorithms
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Wang, Y., Avdic, I., & Mazziotti, D. A. (2025) · Physical Review A · doi:10.1103/1nml-xjqw · Cited by 5
“For example, the chemistry-inspired unitary coupled cluster ansatz [25–34] suffers from a large parameter space [35] while the hardware-efficient ansatz [17, 24] tailors the parametrization to the quantum device but is limited by the barren plateau phenomenon [36–38].”
Using gradient-based algorithms to determine ground-state energies on a quantum computer
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“Having opted for the VHA to provide the parametrized trial state, the parameter set is optimized such that the expectation value of the interacting Hamiltonian is minimized.”
BackgroundInfluentialIterative quantum optimization with an adaptive problem Hamiltonian for the shortest vector problem
Zhu, Y. R., Joseph, D., Ling, C., & Mintert, F. (2022) · Physical Review A · doi:10.1103/physreva.106.022435 · Cited by 5
Bang-bang algorithms for quantum many-body ground states: A tensor network exploration
Wang, R., Hsieh, T. H., & Vidal, G. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.106.195133 · Cited by 5
SpinQ Gemini: a desktop quantum computer for education and researchPreprint
Hou, S., Feng, G., Wu, Z., Zou, H., Shi, W., Zeng, J., Cao, C., Yü, S., Sheng, Z., Rao, X., et al. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2101.10017 · Cited by 5
“Hardware-efficient ansatz [72], unitary coupled clustered ansatz [80], and Hamiltonian variational ansatz [81, 82] are common choices for U(θ).”
BackgroundNonlinear Quantum Optimization Algorithms via Efficient Ising Model EncodingsPreprint
Patti, T. L., Kossaifi, J., Anandkumar, A., & Yelin, S. F. (2021) · Research Square · doi:10.21203/rs.3.rs-654802/v1 · Cited by 5
Tamiya, S., & Yamasaki, H. (2021) · arXiv (Cornell University) · Cited by 5
Quantum Computing for Photosensitizer Design in Photodynamic Therapy
Zehr, H., Baiardi, A., Tacchino, F., Gandon, A., Fischer, L. E., Xu, Y., DiFilippo, F. P., Guidoni, L., Haase, P. A. B., Talarico, N. W., et al. (2025) · Annual Review of Biomedical Data Science · doi:10.1146/annurev-biodatasci-103123-095644 · Cited by 8
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Cade, C., Folkertsma, M., Niesen, I., & Weggemans, J. R. (2023) · Quantum · doi:10.22331/q-2023-10-10-1133 · Cited by 19
“This is often the approach currently taken with heuristic quantum algorithms such as VQE [23, 11, 8] and QAOA [29, 24].”
MethodMurta, B., & Fernández-Rossier, J. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.035128 · Cited by 6
Solvent Distribution Effects on Quantum Chemical Calculations with Quantum Computers
Yoshida, Y., Mizukami, W., & Yoshida, N. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c01189 · Cited by 5
Classical Benchmarks for Variational Quantum Eigensolver Simulations of the Hubbard Model
Alvertis, A. M., Khan, A., Iadecola, T., Orth, P. P., & Tubman, N. M. (2025) · Quantum · doi:10.22331/q-2025-05-20-1748 · Cited by 11
“[41], for a 2D square-lattice sys-tem, a layer of the HVA applies a unitary operator of the form where t H o , t This generalized HVA introduces independent parameters for each term in the Hamiltonian, unlike the original HVA [63], which utilizes a single parameter for each class of terms, e.g. ,…”
Quantum Computer Simulation of Molecules in Optical Cavity
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Stabilizer configuration interaction: Finding molecular subspaces with error detection properties
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Variational quantum algorithms and geometry
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Dou, T., Wang, K., Zhou, Z., Yan, S., & Cui, W. (2021) · Chinese Control Conference (CCC) · doi:10.23919/ccc52363.2021.9549885 · Cited by 4
Kowalski, K., & Bauman, N. P. (2022) · Applied Sciences · doi:10.3390/app13010539 · Cited by 5
Quantum Bayesian inference for parameter estimation using quantum generative model
Ohno, H. (2023) · Quantum Information Processing · doi:10.1007/s11128-022-03809-x · Cited by 4
“Hybrid quantum-classical ML algorithms have been developed for many applications [2, 24, 27].”
BackgroundRyabinkin, I. G., Jena, A., & Genin, S. N. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c01155 · Cited by 8
A Variational Ansatz for Taylorized Imaginary Time Evolution
Koch, M., Schaudt, O., Mogk, G., Mrziglod, T., Berg, H., & Beck, M. E. (2023) · ACS Omega · doi:10.1021/acsomega.3c01060 · Cited by 6
Differential Privacy Preserving Quantum Computing via Projection Operator Measurements
Li, Y., Zhao, Y., Zhang, X., Zhong, H., Pan, M., & Zhang, C. (2024) · International Conference on Quantum Communications, Networking, and Computing (QCNC) · doi:10.1109/qcnc62729.2024.00045 · Cited by 11
“Regarding the discussion of shot noise, Wecker and Wandzura in [13] utilized the sampling theorem to model the measurement error in their work.”
MethodSun, R.-Y., Shirakawa, T., & Yunoki, S. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.085149 · Cited by 4
“Typically, for a given quantum circuit featuring repeating structural units, as observed in the cases of RQCs and PQCs considered in this study, a physical circuit layer is determined by a single type of re-peating unit.”
BackgroundDistribution-adaptive dynamic shot optimization for variational quantum algorithms
Kim, Y., Jang, E., Kim, H. J., Choi, S., Lee, C., Kim, D., Kyoung, W., Shin, K., & Ro, W. W. (2025) · Physical Review Research · doi:10.1103/vwhk-22b8 · Cited by 5
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Rastegin, A. E., & Shemet, A. M. (2023) · Modern Physics Letters A · doi:10.1142/s021773232350030x · Cited by 3
Variational quantum cloning machine on an integrated photonic interferometer
Hoch, F., Rodari, G., Caruccio, E., Polacchi, B., Carvacho, G., Giordani, T., Doosti, M., Nicolau, S., Pentangelo, C., Piacentini, S., et al. (2025) · Optica Quantum · doi:10.1364/opticaq.553762 · Cited by 5
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Kolotouros, I., Petrongonas, I., Prokop, M., & Wallden, P. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad80c0 · Cited by 3
“This type of ansatz family corresponds to many PQCs that appear in the literature like the hardware efficient ansatz [25], the quantum alternate operator ansatz [26], the variational Hamiltonian ansatz [27] or the quantum optimal control ansatz [28].”
BackgroundMethodA Review on Quantum Machine Learning and Quantum Cryptography
Solar, M. (2024) · Memoria Investigaciones en Ingeniería · doi:10.36561/ing.27.12 · Cited by 2
Classical and quantum algorithms for many-body problems
Ayral, T. (2025) · Comptes Rendus Physique · doi:10.5802/crphys.229 · Cited by 4
Exact closed-form unitary transformations of fermionic operators
Evangelista, F. A., & Magoulas, I. (2025) · Physical Review A · doi:10.1103/physreva.111.042825 · Cited by 4
Efficient Encoding of the Traveling Salesperson Problem on a Quantum Computer
Stenger, J., Crowe, S., Diaz, J., Rodriguez, R., Gunlycke, D., & Ptasinski, J. (2025) · Quantum Reports · doi:10.3390/quantum7030032 · Cited by 3
Singh, H., Bertels, L. W., Claudino, D., Economou, S. E., Barnes, E., Bauman, N. P., Kowalski, K., & Mayhall, N. J. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5c00896 · Cited by 6
“Recent strategies for reducing the shot count overhead of VQEs include efficient grouped measurement schemes, 13,18–27 state tomography via classical shadows, 28,29 positive operator-valued measurements, 30 variance minimization, 31–37 and machine learning.”
Supporting data for arXiv:2104.00569
García-Pérez, G., Rossi, M. A. C., Sokolov, B., Tacchino, F., Barkoutsos, P. K., Mazzola, G., Tavernelli, I., & Maniscalco, S. (2021) · Zenodo (CERN European Organization for Nuclear Research) · doi:10.5281/zenodo.5137227 · Cited by 2
Marécat, Q., Senjean, B., & Saubanère, M. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.155110 · Cited by 6
Optimized numerical gradient and Hessian estimation for variational quantum algorithms
Teo, Y. S. (2023) · Physical Review A · doi:10.1103/physreva.107.042421 · Cited by 6
Prasad, V. K., Cheng, F., Fekl, U., & Jacobsen, H. (2023) · Physical Chemistry Chemical Physics · doi:10.1039/d3cp03523a · Cited by 3
Preparing quantum statistical ensembles using mid-circuit measurements
Stenger, J., Hellberg, C. S., & Gunlycke, D. (2024) · Quantum Information Processing · doi:10.1007/s11128-024-04412-y · Cited by 3
“The number of shots required to achieve an accuracy of (cid:8) goes as [29].”
Distance-four quantum codes with combined postselection and error correction
Prabhu, P., & Reichardt, B. W. (2024) · Physical Review A · doi:10.1103/physreva.110.012419 · Cited by 5
“Noisy Intermediate-Scale Quantum (NISQ) algorithms for eigensolvers [PMS + 14, WHT15] and machine learning [BWP + 17] are growing as popular applications for state-of-the-art few-qubit quantum systems.”
BackgroundSemicoherent symmetric quantum processes: Theory and applications
Wang, Y., Chehade, S., & Dumitrescu, E. (2024) · AVS Quantum Science · doi:10.1116/5.0215919 · Cited by 3
“Note that 𝑀 ′ 𝑘 is obtained by exchanging all the primed and non-primed 𝑎 ’s.”
Reducing measurement costs by recycling the Hessian in adaptive variational quantum algorithms
Ramôa, M., Santos, L. P., Mayhall, N. J., Barnes, E., & Economou, S. E. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad904e · Cited by 9
“Note that we can place a state-independent upper bound on the number of shots required for a given error [47].”
BackgroundLocal bottom-up effective theory of nonlocal electronic interactions
Lanatà, N. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.102.115115 · Cited by 3
Variational Quantum Simulation of Valence-Bond Solids
Huerga, D. (2022) · Quantum · doi:10.22331/q-2022-12-13-874 · Cited by 3
“used PQC-ansatze, which either admix symmetry sectors [39, 40] or require higher chip connectivities [11].”
MethodSuperconducting Qubits: Dephasing and Quantum Chemistry
O’Malley, P. J. J. (2016) · eScholarship (California Digital Library) · Cited by 5
Stair, N. H., & Evangelista, F. A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2108.04413 · Cited by 3
Lifetime of Strongly Correlated States on Near-Term Quantum Computers
Torres, L. I. P., Schouten, A. O., & Mazziotti, D. A. (2024) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.4c02665 · Cited by 2
Evolved quantum Boltzmann machines
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Yu, H., Zhang, Y., & Liu, J. (2025) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.5c01293 · Cited by 3
Extracting the spin excitation spectrum of a fermionic system using a quantum processor
Vilchez-Estevez, L., Santos, R. A., Wang, S. Y., & Gambetta, F. M. (2025) · Physical review. B./Physical review. B · doi:10.1103/ydfw-k83n · Cited by 8
“Consequently, the total circuit depth sums to 2 L + 12 N Trotter + 4 n layers + 3, and the number of two-qubit gates is L 2 + L (10 N Trotter + 2 n layers + 2) + (2 − 8 N Trotter − 2 n layers ).”
Quantum many-body simulations from a reinforcement-learned exponential Ansatz
Wang, Y., & Mazziotti, D. A. (2025) · Physical Review A · doi:10.1103/hrgr-klw3 · Cited by 2
“A challenge for VQEs lies in designing ansatz circuits that are both highly expressive to capture electron correlation accurately and sufficiently shallow to execute reliably on noisy quantum hardware, while also being capable of navigating complex optimization land-scapes [8–10].”
Jones, B. D. M., Mineh, L., & Montanaro, A. (2025) · Quantum Science and Technology · doi:10.1088/2058-9565/adfe15 · Cited by 2
“Much research has been done on understanding how to design good VQE cost functions (or ansätze) – i.e. which initial state to use, the precise form of the parametrised circuit, and how best to perform the energy measurements [3, 5–7].”
Jafarizadeh, A., Pollmann, F., & Gammon-Smith, A. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.043018 · Cited by 9
Tkachenko, N. V., Ren, H., Billings, W. M., Tomann, R., Whaley, K. B., & Head‐Gordon, M. (2025) · Chemical Science · doi:10.1039/d5sc03585f · Cited by 4
Tangent Space Excitation Ansatz for Quantum Circuits
Chen, J.-Y., Huang, B., Zhou, D. L., Schuch, N., Cao, C., & Yang, M. (2026) · Physical Review Letters · doi:10.1103/k2lc-v1hn · Cited by 3
“In this work we have used the Hamiltonian variational ansatz (HVA) for ground states [13, 18, 56], which has a linear depth D ∼ O ( N ) .”
Chi, Y., Shi, H., Zheng, W., Cai, H., Zhang, Y., Tan, X., Li, S., Wang, J., Cui, J., Yung, M., et al. (2025) · Science China Physics Mechanics and Astronomy · doi:10.1007/s11433-025-2779-x · Cited by 2
Mastorakis, E., Umer, M., Guevara-Bertsch, M., Ulmanis, J., Rohde, F., & Angelakis, D. G. (2026) · Quantum Science and Technology · doi:10.1088/2058-9565/ae3a13 · Cited by 2
Quantum computation of the electronic structure of some prototype solids
Khandelwal, N., Verma, N., Jamdagni, P., & Kumar, A. (2025) · Scientific Reports · doi:10.1038/s41598-025-27675-6 · Cited by 3
“Several strategies have been proposed to alleviate shot noise, including grouping of commuting Pauli terms 61 , adaptive shot allocation based on variance 62 , and classical shadow techniques 63 .”
Photonic variational quantum eigensolver for NISQ-compatible quantum technology
Hu, K.-M., Namkung, M., & Lim, H. (2025) · Nano Convergence · doi:10.1186/s40580-025-00525-x · Cited by 2
All you need is spin: SU(2) equivariant variational quantum circuits based on spin networks
East, R. D. P., Alonso-Linaje, G., & Park, C.-Y. (2026) · Quantum Science and Technology · doi:10.1088/2058-9565/ae4cff · Cited by 9
“Nevertheless, since we focus on local Hamiltonians, the existence of local gate constructions capable of preparing the ground state is ensured by the adiabatic theorem [27, 28].”
Benchmarking Adaptive Quantum Circuit Optimization Algorithms for Quantum Chemistry
Saib, W., Bonet-Monroig, X., Dunjko, V., Tavernelli, I., Bäck, T., & Wang, H. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.10188 · Cited by 2
“Physically motivated PQCs leverage knowledge from classical quantum chemistry methods such as coupled-cluster or variational hamiltonian ansatze [3], [4], [9].”
BackgroundQuantum simulation of the one-dimensional Fermi-Hubbard model as a Z2 lattice-gauge theory
Khodaeva, U. E., Kovrizhin, D. L., & Knolle, J. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.013032 · Cited by 2
Hybrid GRU-CNN bilinear parameters initialization for quantum approximate optimization algorithm
Xu, Z., Cai, P., Shen, K., Yang, T., Hu, Y., Gong, M., Zhu, Y., Wu, Z., Dai, Y., & Yang, F. (2024) · Physica Scripta · doi:10.1088/1402-4896/ad5a50 · Cited by 2
Huang, X., Niu, L., Chen, J., Li, L., Hayat, K., & Liu, W. (2024) · Critical Reviews in Environmental Science and Technology · doi:10.1080/10643389.2024.2365907 · Cited by 2
“…two algorithms can be implemented is restricted due to the small to moderate number of available qubits, and many studies also attach importance to the barren plateau problem (McClean et al., 2018; Wecker et al., 2015): the exponential disappearance of VQE parameter gradients for larger systems.”
Performance and scaling analysis of variational quantum simulation
Ponce-Martinez, M., Cope, T., de Vega, I., & Leib, M. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad8eee · Cited by 2
Learning density functionals from noisy quantum data
Koridon, E., Frohnert, F., Prehn, E., van Nieuwenburg, E., Tura, J., & Polla, S. (2025) · Machine Learning Science and Technology · doi:10.1088/2632-2153/adcb89 · Cited by 3
“We will consider two ansätze in this work: the well-known variational Hamiltonian ansatz (VHA) [7] and the number preserving fabric (NPF) [40] ansatz, which combine the advantages of both categories.”
InfluentialLi, J., Li, W., Xiao, X., Liu, L., Li, Z., Ren, J., & Fang, W. (2025) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.5c00739 · Cited by 3
A novel approach to reduce derivative costs in variational quantum algorithms
Minuto, G., Melegari, D., Caletti, S., & Solinas, P. (2025) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/adcf62 · Cited by 3
Kattemölle, J., & Hariharan, S. (2025) · ACM Transactions on Quantum Computing · doi:10.1145/3733842 · Cited by 7
“…introducing variable parameters for the per-term evolution times, these circuits are transformed to circuits that prepare ansatz states for the variational quantum eigensolver ( VQE ) [57], designed to variationally find the ground state of the quantum-mechanical system (static quantum simulation).”
InfluentialExploring new variational quantum circuit ansatzes for solving SU(2) matrix models
Dao, H. L. (2025) · The European Physical Journal C · doi:10.1140/epjc/s10052-025-14322-7 · Cited by 4
Double-bracket quantum algorithms for high-fidelity ground-state preparation
Robbiati, M., Pedicillo, E., Pasquale, A., Xiaoyue, L., Kiss, O., Wright, A. L., Farias, R. M. S., Giang, K. U., Son, J., Knörzer, J., et al. (2026) · Physical Review Research · doi:10.1103/jz88-32rb · Cited by 5
“…and there exist many potential candidates depending on the problem, including: parametrized circuits [26], the Hamiltonian variational ansatz [27–29], Hartree-Fock circuits [30], tensor networks [31, 32], quantum imaginary-a We propose a two-stage ground state preparation protocol: first, apply…”
Noise tailoring for robust amplitude estimation
Dalal, A., & Katabarwa, A. (2023) · New Journal of Physics · doi:10.1088/1367-2630/acb5bc · Cited by 6
Practical limitations of quantum data propagation on noisy quantum processors
Saxena, G., Shalabi, A., & Kyaw, T. H. (2024) · Physical Review Applied · doi:10.1103/physrevapplied.21.054014 · Cited by 3
“One such important class of algorithms are variational quantum algorithms (VQAs) [12–14].”
BackgroundHybrid Quantum-Classical Eigensolver without Variation or Parametric Gates
Jouzdani, P., & Bringuier, S. A. (2021) · Quantum Reports · doi:10.3390/quantum3010008 · Cited by 2
“Ideally, the implementation of UCC ansatz should be constructed such that the number of gates is minimized so that the circuit depth does not exhaust the current coherence times of NISQ devices.”
MethodInfluentialOptimization of VQE-UCC Algorithm Based on Spin State Symmetry
Guo, Q., & Chen, P. (2021) · Frontiers in Physics · doi:10.3389/fphy.2021.735321 · Cited by 2
Discontinuous Galerkin discretization for quantum simulation of chemistryPreprint
McClean, J. R., Faulstich, F. M., Zhu, Q., O’Gorman, B., Qiu, Y., White, S. R., Babbush, R., & Lin, L. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1909.00028 · Cited by 2
“Such Trotter steps can be repeated to perform time-evolution for modeling dynamics or for preparing eigen-states via the phase estimation algorithm [60, 61], but they can also serve as an ansatz for composing quantum variational algorithms [15, 62].”
BackgroundMontanaro, A., & Bosse, J. L. (2021) · arXiv (Cornell University) · doi:10.5523/bris.25sbud0vk99lz2ohjch1cm1vwg · Cited by 2
“[17] D.”
BackgroundMethodInfluentialWada, K., Raymond, R., Sato, Y., & Watanabe, H. C. (2022) · arXiv (Cornell University) · doi:10.48550/arxiv.2209.08535 · Cited by 2
“[20] Dave Wecker, Matthew B Hastings, and Matthias Troyer.”
BackgroundAlgorithm-Aware Qubit MappingPreprint
Ji, Y., & Polian, I. (2022) · doi:10.36227/techrxiv.21786146 · Cited by 1
Le, D.-T., Nguyen, V.-L., Nguyen, H. C., Nguyen, H. Q., & Nguyen, V.-D. (2025) · Research Square · doi:10.21203/rs.3.rs-6497487/v1 · Cited by 2
Mineh, L., & Montanaro, A. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.105.125117 · Cited by 22
Quantum computing for partial differential equations in practice
Neumann, N. M. P., Verbree, J., & Hoek, C. R. (2024) · SPIE Quantum Technologies for Defence and Security · doi:10.1117/12.3033212 · Cited by 1
He, Z., Re, L. D., Kemper, A. F., & Freericks, J. K. (2025) · Physical review. B./Physical review. B · doi:10.1103/p1mq-8xbg · Cited by 1
Sheng, Z., Li, W., & Shuai, Z. (2025) · Chinese Science Bulletin (Chinese Version) · doi:10.1360/tb-2024-1150 · Cited by 1
Neutral atom quantum computers for the applications in condensed matter physics
Shweta, Kaur, I., Singh, N., Kanjilal, S., & Santra, B. (2025) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/adbb9b · Cited by 2
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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