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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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Citations
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Steckmann, T., Keen, T., Kökcü, E., Kemper, A. F., Dumitrescu, E., & Wang, Y. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023198 · Cited by 24
“In the context of quantum computing, the Hubbard model has been recently investigated with the applications of VQE algorithms [38, 39] and as a benchmark for quantum simulations [5, 6, 40].”
MethodTraining variational quantum algorithms with random gate activation
Liu, S., Zhang, S., Jian, S.-K., & Yao, H. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.l032040 · Cited by 22
Kanno, S., Nakamura, H., Kobayashi, T., Gocho, S., Hatanaka, M., Yamamoto, N., & Gao, Q. (2024) · npj Quantum Information · doi:10.1038/s41534-024-00851-8 · Cited by 24
“There are several problem-inspired ansatze, such as the unitary coupled cluster ansatz 62 and Hamiltonian variational ansatz 63 .”
Effects of gate errors in digital quantum simulations of fermionic systems
Reiner, J.-M., Zanker, S., Schwenk, I., Leppäkangas, J., Wilhelm, F. K., Schön, G., & Marthaler, M. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aad5ba · Cited by 22
A diagrammatic approach to variational quantum ansatz construction
Herasymenko, Y., & O’Brien, T. E. (2021) · Quantum · doi:10.22331/q-2021-12-02-596 · Cited by 22
“By contrast, those founded on adiabatic principles (e.g. the variational Hamiltonian ansatz [24]) can be expected to perform best on systems with a large gap.”
BackgroundDiscontinuous Galerkin discretization for quantum simulation of chemistry
McClean, J. R., Faulstich, F. M., Zhu, Q., O’Gorman, B., Qiu, Y., White, S. R., Babbush, R., & Lin, L. (2020) · New Journal of Physics · doi:10.1088/1367-2630/ab9d9f · Cited by 24
“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].”
BackgroundSimulating noisy variational quantum eigensolver with local noise models
Zeng, J., Wu, Z., Cao, C., Zhang, C., Hou, S., Xu, P., & Zeng, B. (2021) · Quantum Engineering · doi:10.1002/que2.77 · Cited by 24
Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models
Mukherjee, A., Berthusen, N., Getelina, J. C., Orth, P. P., & Yao, Y. (2023) · Communications Physics · doi:10.1038/s42005-022-01089-6 · Cited by 25
Global sensitivity analyses prior to parameter calibration significantly improves prediction quality
Wang, C., Harrison, M. T., Brown, H., Qiao, Y., Yin, X., Yang, R., Zhang, Y., Zhou, M., & Liu, K. (2025) · Computers and Electronics in Agriculture · doi:10.1016/j.compag.2025.110750 · Cited by 20
Practical Verification of Quantum Properties in Quantum-Approximate-Optimization Runs
Alam, M. S., Wudarski, F., Reagor, M. J., Sud, J., Grabbe, S. R., Wang, Z., Hodson, M. J., Lott, P. A., Rieffel, E. G., & Venturelli, D. (2022) · Physical Review Applied · doi:10.1103/physrevapplied.17.024026 · Cited by 19
“variational quantum eigensolver (VQE) [37, 40], quantum machine learning [11, 25], or variational Hamiltonian ansatz [49, 50].”
BackgroundLötstedt, E., Yamanouchi, K., 土屋, 敬., & Tachikawa, Y. (2021) · Physical Review A · doi:10.1103/physreva.103.062609 · Cited by 20
Sampling, rates, and reaction currents through reverse stochastic quantization on quantum computers
Mazzola, G. (2021) · Physical Review A · doi:10.1103/physreva.104.022431 · Cited by 21
Liu, J., Matthews, D. A., & Cheng, L. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.1c01210 · Cited by 19
Spatial, spin, and charge symmetry projections for a Fermi-Hubbard model on a quantum computer
Seki, K., & Yunoki, S. (2022) · Physical Review A · doi:10.1103/physreva.105.032419 · Cited by 22
Haidar, M., Rančić, M. J., Ayral, T., Maday, Y., & Piquemal, J. (2023) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.1664 · Cited by 30
Computing the Many-Body Green’s Function with Adaptive Variational Quantum Dynamics
Gomes, N., Williams‐Young, D. B., & de Jong, W. A. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c00150 · Cited by 24
“For N = 2 with 8 layers and N = 4 with 16 layers of VHA [28] will, therefore, require about 150 two-qubit gates and 960 gates, respectively.”
MethodInfluentialMolecular Quantum Circuit Design: A Graph-Based Approach
Kottmann, J. S. (2023) · Quantum · doi:10.22331/q-2023-08-03-1073 · Cited by 25
“Pioneering physical motivated circuit designs in electronic structure [3, 13–15] relied on trotterized time evolutions leading to comparable deep circuits and the need for heuristics on the optimal ordering [16–18] of the primitive operations.”
Dual-frame optimization for informationally complete quantum measurements
Fischer, L. E., Dao, T. K. L., Tavernelli, I., & Tacchino, F. (2024) · Physical Review A · doi:10.1103/physreva.109.062415 · Cited by 19
Implementation of measurement reduction for the variational quantum eigensolver
Ralli, A., Love, P. J., Tranter, A., & Coveney, P. V. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.033195 · Cited by 22
“showed that to obtain energy estimates for HeH, BeH2 and H2O requires 10 8 − 10(9) samples to achieve an error of 1 mHa [14].”
BackgroundMethodOn-premises superconducting quantum computer for education and research
Rönkkö, J., Ahonen, O., Bergholm, V., Calzona, A., Geresdi, A., Heimonen, H., Heinsoo, J., Milchakov, V., Pogorzalek, S., Sarsby, M., et al. (2024) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-024-00243-z · Cited by 23
“Let H be the Hamiltonian that describes neutrinos.”
BackgroundTenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era
Li, W., Allcock, J., Cheng, L., Zhang, S., Chen, Y., Mailoa, J. P., Shuai, Z., & Zhang, S. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c00319 · Cited by 21
“The variational Hamiltonian ansatz [51, 52] and adaptive ansatz [53] are possible candidates for a universal solution for the quantum dynamics ansatz.”
MethodKashif, M., & Al-Kuwari, S. M. (2023) · International Journal of Parallel Emergent and Distributed Systems · doi:10.1080/17445760.2023.2231163 · Cited by 22
“Some frequently explored ansatzes in this regard are the Hamiltonian variational ansatz [48], coupled cluster ansatz [49–51], quantum alternating operator ansatz [10,52] and hardware-efficient ansatz [53].”
BackgroundOptimizing Shot Assignment in Variational Quantum Eigensolver Measurement
Zhu, L., Liang, S., Yang, C., & Li, X. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c01113 · Cited by 28
“21,35,36 40 These methods typically rely on prior knowledge of Hamiltonian terms, 22,35 often from classical simulations, to allocate measurement shots in a manner that minimizes the overall variance of energy estimation.”
MethodAssessing and advancing the potential of quantum computing: A NASA case study
Rieffel, E. G., Asanjan, A. A., Alam, M. S., Anand, N., Bernal, D. E., Block, S., Brady, L. T., Cotton, S., Izquierdo, Z. G., Grabbe, S. R., et al. (2024) · Future Generation Computer Systems · doi:10.1016/j.future.2024.06.012 · Cited by 25
“In the study [[81]], the team successfully prepared the ground state of the Kitaev honeycomb model using the Hamiltonian variational ansatz (HVA) [82].”
MethodFeedback-based quantum algorithms for ground state preparation
Larsen, J. B., Grace, M., Baczewski, A., & Magann, A. B. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.033336 · Cited by 24
“implement parameterized quantum circuits structured according to the Hamiltonian variational ansatz [40].”
MethodGyöngyösi, L., & Imre, S. (2025) · Quantum Information and Computation · doi:10.2478/qic-2025-0006 · Cited by 20
One-dimensional quantum computing with a ‘segmented chain’ is feasible with today’s gate fidelities
Li, Y., & Benjamin, S. C. (2018) · npj Quantum Information · doi:10.1038/s41534-018-0074-2 · Cited by 19
Variational quantum solver employing the PDS energy functional
Peng, B., & Kowalski, K. (2021) · Quantum · doi:10.22331/q-2021-06-10-473 · Cited by 18
“In this area, several quantum computing algorithms, including quantum phase estimator (QPE)?”
BackgroundMethodO’Brien, T. E., Ioffe, L. B., Su, Y., Fushman, D., Neven, H., Babbush, R., & Smelyanskiy, V. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.030345 · Cited by 25
Simulation of Condensed-Phase Spectroscopy with Near-Term Digital Quantum Computers
Lee, C., Hsieh, C., Zhang, S., & Shi, L. (2021) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.1c00849 · Cited by 17
Liu, J., & Cheng, L. (2021) · The Journal of Chemical Physics · doi:10.1063/5.0062090 · Cited by 18
Fermionic approach to variational quantum simulation of Kitaev spin models
Jahin, A., Li, A. C. Y., Iadecola, T., Orth, P. P., Perdue, G., Macridin, A., Alam, M. S., & Tubman, N. M. (2022) · Physical Review A · doi:10.1103/physreva.106.022434 · Cited by 16
Estimating Patterns of Classical and Quantum Skyrmion States
Mazurenko, V. V., Iakovlev, I. A., Sotnikov, O. M., & Katsnelson, M. I. (2023) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.92.081004 · Cited by 19
Fermionic quantum approximate optimization algorithm
Yoshioka, T., Sasada, K., Nakano, Y., & Fujii, K. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023071 · Cited by 18
“Another technique to deal with this has been proposed using fermionic fast fourier tansformation (FFFT) [10, 31, 32], which transform Ĥt into a diagonal representation and performs the computation efficiently.”
MethodTrainability and Expressivity of Hamming-Weight Preserving Quantum Circuits for Machine Learning
Monbroussou, L., Mamon, E. Z., Landman, J., Grilo, A. B., Kukla, R., & Kashefi, E. (2025) · Quantum · doi:10.22331/q-2025-05-15-1745 · Cited by 27
“Then we show how to achieve it efficiently using HW preserving gates and their subspace preserving properties.”
Iterative quantum algorithm for combinatorial optimization based on quantum gradient descent
Yi, X., Huo, J., Gao, Y., Fan, L., Zhang, R., & Cao, C. (2023) · Results in Physics · doi:10.1016/j.rinp.2023.107204 · Cited by 17
Dynamic adaptive quantum approximate optimization algorithm for shallow, noise-resilient circuits
Yanakiev, N., Mertig, N., Long, C. K., & Arvidsson-Shukur, D. R. M. (2024) · Physical Review A · doi:10.1103/physreva.109.032420 · Cited by 26
Unitary-coupled restricted Boltzmann machine ansatz for quantum simulations
Hsieh, C., Sun, Q., Zhang, S., & Lee, C. (2021) · npj Quantum Information · doi:10.1038/s41534-020-00347-1 · Cited by 21
Efficient two-electron ansatz for benchmarking quantum chemistry on a quantum computer
Smart, S. E., & Mazziotti, D. A. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.023048 · Cited by 17
Exploiting fermion number in factorized decompositions of the electronic structure Hamiltonian
McArdle, S., Campbell, E. T., & Su, Y. (2022) · Physical Review A · doi:10.1103/physreva.105.012403 · Cited by 23
Certification of quantum states with hidden structure of their bitstrings
Sotnikov, O. M., Iakovlev, I. A., Iliasov, A. A., Katsnelson, M. I., Bagrov, A. A., & Mazurenko, V. V. (2022) · npj Quantum Information · doi:10.1038/s41534-022-00559-7 · Cited by 16
“For instance, one can use variational approaches 67 – 69 and adiabatic algorithms 70 – 72 to approximate the target state on a quantum device.”
MethodMitigating algorithmic errors in quantum optimization through energy extrapolation
Cao, C., Yu, Y., Wu, Z., Shannon, N., Zeng, B., & Joynt, R. (2022) · Quantum Science and Technology · doi:10.1088/2058-9565/ac969c · Cited by 21
“A well-studied one is the Hamiltonian variational ansatz [55, 56], where the parameterized gates are determined by the target Hamiltonian.”
Quantum Computation of Hydrogen Bond Dynamics and Vibrational Spectra
Richerme, P., Revelle, M., Yale, C. G., Lobser, D., Burch, A. D., Clark, S., Saha, D., Lopez-Ruiz, M. A., Dwivedi, A., Smith, J. M., et al. (2023) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.3c01601 · Cited by 23
“[25] Dave Wecker, Matthew B Hastings, and Matthias Troyer, “Progress towards practical quantum variational algorithms,” Physical Review A 92, 042303 (2015).”
BackgroundSimulating Energy Transfer in Molecular Systems with Digital Quantum Computers
Lee, C., Lau, J. W. Z., Shi, L., & Kwek, L. C. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.1c01296 · Cited by 20
“We use a wavefunction ansatz with only three variational parameters ∣∣ψ(~ θ) 〉 = e3 1 xσ 2 xe2 2 xe1 1 z |ψ0〉, corresponding to the popular Hamiltonian ansatz [45].”
MethodQuantum variational approach to lattice gauge theory at nonzero density
Yamamoto, A. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.104.014506 · Cited by 16
Extending the reach of quantum computing for materials science with machine learning potentials
Schuhmacher, J., Mazzola, G., Tacchino, F., Dmitriyeva, O., Bui, T., Huang, S., & Tavernelli, I. (2022) · AIP Advances · doi:10.1063/5.0099469 · Cited by 18
Optimizing the information extracted by a single qubit measurement
Polla, S., Anselmetti, G.-L., & O’Brien, T. E. (2023) · Physical Review A · doi:10.1103/physreva.108.012403 · Cited by 17
“[32] Dave Wecker, Matthew B Hastings, and Matthias Troyer, “Progress towards practical quantum variational algorithms,” Physical Review A 92, 042303 (2015).”
BackgroundAmsler, M., Deglmann, P., Degroote, M., Kaicher, M., Kiser, M., Kühn, M., Kumar, C., Maier, A., Samsonidze, G. G., Schroeder, A. K., et al. (2023) · The Journal of Chemical Physics · doi:10.1063/5.0146934 · Cited by 27
Low-depth simulations of fermionic systems on square-grid quantum hardware
Algaba, M. G., Sriluckshmy, P. V., Leib, M., & Šimkovic, F. (2024) · Quantum · doi:10.22331/q-2024-04-30-1327 · Cited by 23
Grimsley, H. R., & Evangelista, F. A. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad9fa2 · Cited by 20
Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping
Gresch, A., & Kliesch, M. (2025) · Nature Communications · doi:10.1038/s41467-024-54859-x · Cited by 20
Survey on Hybrid Classical-Quantum Machine Learning Models
Metawei, M. A., Said, H., Taher, M., Eldeib, H. E. S., & Nassar, S. M. (2020) · International Conference on Communications, Computing, Cybersecurity, and Informatics (CCCI) · doi:10.1109/ccci49893.2020.9256649 · Cited by 17
“Recent research work [20], [21] proved the quantum advantage over classical variational methods.”
BackgroundQuantum simulation of molecules without fermionic encoding of the wave function
Mazziotti, D. A., Smart, S. E., & Mazziotti, A. (2021) · New Journal of Physics · doi:10.1088/1367-2630/ac3573 · Cited by 14
Improved quantum computing with higher-order Trotter decomposition
Yang, X., Nie, X., Ji, Y., Xin, T., Lu, D., & Li, J. (2022) · Physical Review A · doi:10.1103/physreva.106.042401 · Cited by 17
“[46], and recent works [47, 48] also provide insights into informing VQA on quantum optimal control perspective.”
BackgroundClassically optimized variational quantum eigensolver with applications to topological phases
Okada, K. N., Osaki, K., Mitarai, K., & Fujii, K. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.043217 · Cited by 23
Quantum simulation of two-dimensional quantum chemistry in optical lattices
Argüello-Luengo, J., González-Tudela, A., Shi, T., Zoller, P., & Cirac, J. I. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.042013 · Cited by 16
“[18] Dave Wecker, Matthew B.”
BackgroundPerrier, E. (2021) · Proceedings of the AAAI/ACM Conference on AI Ethics and Society · doi:10.1145/3461702.3462611 · Cited by 15
“Examples might include a typical hybrid model of quantum algorithmic learning using quantum variational eigensolvers, for example see [27].”
Hong, C.-L., Tsai, T., Chou, J., Chen, P.-J., Tsai, P.-K., Chen, Y.-C., Kuo, E.-J., Srolovitz, D. J., Hu, A., Cheng, Y., et al. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.020360 · Cited by 18
Weaving, T., Ralli, A., Kirby, W. M., Tranter, A., Love, P. J., & Coveney, P. V. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00910 · Cited by 15
“This is more often a symptom of ‘hardware efficient’ ansätze 1,8–12 , which aim to access the largest possible region of Hilbert space for the fewest number of native quantum gates.”
BackgroundMethodDíez-Valle, P., Luis-Hita, J., Hernández-Santana, S., Martínez-García, F., Díaz-Fernández, Á., Andrés, E., García‐Ripoll, J. J., Sánchez-Martínez, E., & Porras, D. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/ace474 · Cited by 17
“Although some problem-dependent or problem-inspired ansätze for VQE has been proposed to solve problems in quantum chemistry [43, 44, 45], in this algorithm the variational ansatz (1) is free, in the sense that it does not need to be determined by the Hamiltonian of the problem as in QAOA.”
BackgroundMitigated barren plateaus in the time-nonlocal optimization of analog quantum-algorithm protocols
Broers, L., & Mathey, L. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.013076 · Cited by 17
Xiao, X., Zhao, H., Ren, J., Fang, W., & Li, Z. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c00966 · Cited by 21
“28 35–38 Another type of physics-inspired ansatz is the Hamiltonian variational ansatz (HVA), 39,40 which is problem specific and widely used for model systems.”
BackgroundFitzek, D., Jonsson, R., Dobrautz, W., & Schäfer, C. (2024) · Quantum · doi:10.22331/q-2024-04-09-1313 · Cited by 20
“In order to combat those challenges, mixed quantum-classical algorithms, labeled variational quantum algorithms (VQAs) [1, 9, 10, 11, 12, 2, 3], have been devised.”
MethodEfficient two-electron ansatz for benchmarking quantum chemistry on a quantum computer
Smart, S. E., & Mazziotti, D. A. (2020) · University of Chicago · doi:10.6082/2cxwm-y5012 · Cited by 16
Assessment of the Variational Quantum Eigensolver: Application to the Heisenberg Model
Jattana, M. S., Jin, F., Raedt, H. A. D., & Michielsen, K. F. L. (2022) · Frontiers in Physics · doi:10.3389/fphy.2022.907160 · Cited by 15
Quantum Information and Computation for Chemistry
Olson, J., Cao, Y., Romero, J., Johnson, P., Dallaire-Demers, P.-L., Sawaya, N., Narang, P., Kivlichan, I., Wasielewski, M., & Aspuru-Guzik, A. (2017) · arXiv · doi:10.48550/arxiv.1706.05413 · Cited by 15
“Two representative HQC algorithms are the variational quantum eigensolver (VQE) (Peruzzo et al., 2013; Wecker et al., 2015; McClean et al., 2016; O’Malley et al., 2016; Santagati et al., 2016; Guerreschi and Smelyanskiy, 2017; McClean et al., 2017; Romero et al., 2017; Shen et al., 2017) and the…”
BackgroundMethodProgress toward practical quantum cryptanalysis by variational quantum cloning
Coyle, B., Doosti, M., Kashefi, E., & Kumar, N. (2022) · Physical Review A · doi:10.1103/physreva.105.042604 · Cited by 19
Toward density functional theory on quantum computers?
Senjean, B., Yalouz, S., & Saubanère, M. (2023) · SciPost Physics · doi:10.21468/scipostphys.14.3.055 · Cited by 18
“[67], the number of measurements to achieve a given accuracy ε in estimating the energy scales with the square of the one-norm of the Hamiltonian.”
BackgroundBlueprint for a digital-analog variational quantum eigensolver using Rydberg atom arrays
Michel, A., Grijalva, S., Henriet, L., Domain, C., & Browaeys, A. (2023) · Physical Review A · doi:10.1103/physreva.107.042602 · Cited by 14
“Previous studies [14] have quantified the demanding resource requirements for practical VQE applications.”
BackgroundEfficient quantum simulation of electron-phonon systems by variational basis state encoder
Li, W., Ren, J., Huai, S., Cai, T., Shuai, Z., & Zhang, S. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023046 · Cited by 14
“The variational Hamiltonian ansatz [35] with 3 layers is used if not otherwise specified.”
MethodQuantum-Social Network Analysis for Community Detection: A Comprehensive Review
Muhuri, S., & Singh, S. S. (2024) · IEEE Transactions on Computational Social Systems · doi:10.1109/tcss.2024.3397967 · Cited by 16
“Forcommunity discovery in SN, quantum-inspired optimization techniques, including quantum annealing [13] and variational algorithms [21], have been investigated.”
MethodMao, R., Tian, G., & Sun, X. (2024) · Communications Physics · doi:10.1038/s42005-024-01798-0 · Cited by 19
“The ans¨atzes employed in VQEs can be broadly categorized into three types [20, 21]: chemically inspired ans¨atze [3], hardware-efficient ans¨atze (HEA [4]), and Hamiltonian variational ans¨atze (HVA [22]).”
MethodWeaving, T., Ralli, A., Love, P. J., Succi, S., & Coveney, P. V. (2025) · npj Quantum Information · doi:10.1038/s41534-024-00952-4 · Cited by 25
“This has implications on the sampling overhead required in VQE, which scales asymptotically as O (Λ 2 ϵ − 2 ) to achieve a desired error ϵ > 0 [30, 31].”
Computationally Efficient Quantum Expectation with Extended Bell Measurements
Kondo, R., Sato, Y., Koide, S., Kajita, S., & Takamatsu, H. (2022) · Quantum · doi:10.22331/q-2022-04-13-688 · Cited by 15
“The bottleneck of a VQA relates to the computational cost of calculating the expectation value [19].”
BackgroundKöhn, A., & Olsen, J. (2022) · The Journal of Chemical Physics · doi:10.1063/5.0104815 · Cited by 14
Muñoz-Moller, A. D., Pereira, L., Zambrano, L., Cortés-Vega, J., & Delgado, A. (2022) · Physical Review Applied · doi:10.1103/physrevapplied.18.024048 · Cited by 14
Dynamical mean-field theory for the Hubbard-Holstein model on a quantum device
Backes, S., Murakami, Y., 酒井, 志., & Arita, R. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.165155 · Cited by 19
Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation
Seki, K., Otsuka, Y., & Yunoki, S. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.105.155119 · Cited by 15
Error mitigation by training with fermionic linear opticsPreprint
Montanaro, A., & Stanisic, S. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2102.02120 · Cited by 37
“[16] D. Wecker, M. B. Hastings, and M. Troyer.”
MethodInfluentialOnline quantum time series processing with random oscillator networks
Nokkala, J. (2023) · Scientific Reports · doi:10.1038/s41598-023-34811-7 · Cited by 16
Measurement-induced entanglement phase transitions in variational quantum circuits
Wiersema, R., Zhou, C., Carrasquilla, J., & Kim, Y. B. (2023) · SciPost Physics · doi:10.21468/scipostphys.14.6.147 · Cited by 20
“From these data, we find similar critical measurement rates pc ≈ 0.25 and pc ≈ 0.5 for the XXZ-HVA and HEA, respectively.”
MethodInfluentialSorella, S. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.115133 · Cited by 13
Quantum computing Floquet energy spectra
Fauseweh, B., & Zhu, J. (2023) · Quantum · doi:10.22331/q-2023-07-20-1063 · Cited by 22
“We use a variational Hamiltonian approach [54] to effectively reach the target states,”
MethodHalder, S., Shrikhande, C., & Maitra, R. (2023) · The Journal of Chemical Physics · doi:10.1063/5.0166433 · Cited by 13
Phenomenological theory of variational quantum ground-state preparation
Astrakhantsev, N., Mazzola, G., Tavernelli, I., & Carleo, G. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.033225 · Cited by 22
Deep Neural Network Assisted Quantum Chemistry Calculations on Quantum Computers
Ghosh, K., Kumar, S., Nirmal, M. R., & Yamijala, S. S. R. K. C. (2023) · ACS Omega · doi:10.1021/acsomega.3c07364 · Cited by 13
Zeng, X., Fan, Y., Liu, J., Li, Z., & Yang, J. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c00527 · Cited by 15
Sequential optimal selections of single-qubit gates in parameterized quantum circuits
Wada, K., Raymond, R., Sato, Y., & Watanabe, H. C. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad4583 · Cited by 23
“[20] Dave Wecker, Matthew B Hastings, and Matthias Troyer.”
BackgroundUnveiling quantum phase transitions from traps in variational quantum algorithms
Cao, C., Gambetta, F. M., Montanaro, A., & Santos, R. A. (2025) · npj Quantum Information · doi:10.1038/s41534-025-01038-5 · Cited by 18
“Our approach employs the Hamiltonian variational ansatz, as detailed in Refs.”
Uttarkar, A., & Niranjan, V. (2024) · International Journal of Biological Macromolecules · doi:10.1016/j.ijbiomac.2024.133033 · Cited by 14
Fixing detailed balance in ancilla-based dissipative state engineering
Lambert, N., Cirio, M., Lin, J.-D., Menczel, P., Liang, P., & Nori, F. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.043229 · Cited by 13
Solving an industrially relevant quantum chemistry problem on quantum hardware
Nützel, L., Gresch, A., Hehn, L., Marti, L., Freund, R., Steiner, A., Marciniak, C. D., Eckstein, T., Stockinger, N., Wolf, S., et al. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad9ed3 · Cited by 18
Effects of cosine tapering window on quantum phase estimation
Rendon, G., Izubuchi, T., & Kikuchi, Y. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.034503 · Cited by 14
Hybrid Auxiliary Field Quantum Monte Carlo for Molecular Systems
Chen, Y., Zhang, L., Weinan, E., & Car, R. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c00038 · Cited by 13
“Approaches of this kind have been developed for multiple applications, including the simulation of quantum model on a lattice[29, 30, 31, 32] and preparation of quantum states for quantum computing applications[33, 34, 35].”
MethodFLIP: A flexible initializer for arbitrarily-sized parametrized quantum circuitsPreprint
Sauvage, F., Sim, S., Kunitsa, A. A., Simon, W., Mauri, M., & Perdomo‐Ortiz, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.08572 · Cited by 32
“For instance, it could be the expectation value C ( | ψ (cid:105) ) = (cid:104) ψ |O| ψ (cid:105) of a Hermitian operator O as it is often the case in VQAs [18, 19] or a distance to a target probability distribution [20, 21].”
BackgroundAdaptive variational preparation of the Fermi-Hubbard eigenstates
Gyawali, G., & Lawler, M. J. (2022) · Physical Review A · doi:10.1103/physreva.105.012413 · Cited by 18
“The ADAPT-VQE ansatz is built one operator at a time as opposed to the non-adaptive ansatzs such as Hamiltonian variational ansatz and number preserving ansatz in which the operators are fixed, and only optimization performed is for the variational parameters [19, 20].”
MethodScaling adaptive quantum simulation algorithms via operator pool tiling
Dyke, J. S. V., Shirali, K., Barron, G. S., Mayhall, N. J., Barnes, E., & Economou, S. E. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.l012030 · Cited by 20
Dissipative Variational Quantum Algorithms for Gibbs State Preparation
Ilin, Y., & Arad, I. (2024) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2024.3511419 · Cited by 22
“These algorithms may leverage approaches similar to non-variational algorithms, such as thermalization [26, 82], imaginary time evolution [26, 83], or Monte Carlo style methods [84], among others [3, 85].”
Avoiding barren plateaus with entanglement
Yao, Y., & Hasegawa, Y. (2025) · Physical Review A · doi:10.1103/physreva.111.022426 · Cited by 12
Algorithm-oriented qubit mapping for variational quantum algorithms
Ji, Y., Chen, X., Polian, I., & Ban, Y. (2025) · Physical Review Applied · doi:10.1103/physrevapplied.23.034022 · Cited by 19
“Three common categories of ansatz circuits are chemically inspired [54], hardware-efficient ansatz (HEA) [34], and Hamiltonian variational [55].”
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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