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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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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
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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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Items 201–300 of 722
NP-hard but no longer hard to solve? Using quantum computing to tackle optimization problems
Au-Yeung, R., Chancellor, N., & Halffmann, P. (2023) · Frontiers in Quantum Science and Technology · doi:10.3389/frqst.2023.1128576 · Cited by 60
“Variational quantum eigensolvers (VQEs) [22, 81] are the best-known application of VQAs and were originally used to find the ground state energy of molecules [7, 66, 83].”
Quantum computing and chemistry
Weidman, J. D., Sajjan, M., Mikolas, C. A., Stewart, Z. J., Pollanen, J., Kais, S., & Wilson, A. K. (2024) · Cell Reports Physical Science · doi:10.1016/j.xcrp.2024.102105 · Cited by 51
“153 For variational dynamical simulations on closed or open quantum systems, additional measurements are necessary to retrieve elements of the propagator for constructing an equation of the motion of the parameters.”
BackgroundQuantum simulations of excited states with active-space downfolded Hamiltonians
Bauman, N. P., Low, G. H., & Kowalski, K. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5128103 · Cited by 45
Bao, S. L., Kleer, S., Wang, R., & Rahmani, A. (2018) · Physical Review A · doi:10.1103/physreva.97.062343 · Cited by 40
Gutzwiller hybrid quantum-classical computing approach for correlated materials
Yao, Y., Zhang, F., Wang, C.-Z., Ho, K.-M., & Orth, P. P. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.013184 · Cited by 54
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BackgroundMethodInfluentialLocalized Quantum Chemistry on Quantum Computers
Otten, M., Hermes, M. R., Pandharkar, R., Alexeev, Y., Gray, S. K., & Gagliardi, L. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00388 · Cited by 47
QDataSet, quantum datasets for machine learning
Perrier, E., Youssry, A., & Ferrie, C. (2022) · Scientific Data · doi:10.1038/s41597-022-01639-1 · Cited by 59
Exact and approximate symmetry projectors for the electronic structure problem on a quantum computer
Yen, T.-C., Lang, R. A., & Izmaylov, A. F. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5110682 · Cited by 40
Symmetry enhanced variational quantum spin eigensolver
Lyu, C., Xu, X., Yung, M., & Bayat, A. (2023) · Quantum · doi:10.22331/q-2023-01-19-899 · Cited by 43
“So far, several choices of the ansatz with different levels of complexity have been proposed [26, 49, 63, 76, 84, 93, 101].”
BackgroundQuantum computing for chemistry and physics applications from a Monte Carlo perspective
Mazzola, G. (2024) · The Journal of Chemical Physics · doi:10.1063/5.0173591 · Cited by 48
“8 On the other hand, such uncorrelated wave function collapses can have computational value if used as importance sampling in Monte Carlo.”
BackgroundInfluentialMaking trotters sprint: A variational imaginary time ansatz for quantum many-body systems
Beach, M. J. S., Melko, R. G., Grover, T., & Hsieh, T. H. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.100.094434 · Cited by 39
“This variational approach has been generalized for preparing both strongly correlated and highlyentangled states on near-term quantum devices [27–29].”
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Self-citationVariational quantum eigensolver for dynamic correlation functions
Chen, H., Nusspickel, M., Tilly, J., & Booth, G. H. (2021) · Physical Review A · doi:10.1103/physreva.104.032405 · Cited by 42
Solving hadron structures using the basis light-front quantization approach on quantum computers
Qian, W., Basili, R., Pal, S., Luecke, G. R., & Vary, J. P. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.043193 · Cited by 40
Quantum utility – definition and assessment of a practical quantum advantage
Herrmann, N., Arya, D., Doherty, M. W., Mingare, A., Pillay, J. C., Preis, F., & Prestel, S. (2023) · IEEE International Conference on Quantum Software (QSW) · doi:10.1109/qsw59989.2023.00028 · Cited by 53
Koridon, E., Yalouz, S., Senjean, B., Buda, F., O’Brien, T. E., & Visscher, L. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.033127 · Cited by 44
Variational quantum algorithms: fundamental concepts, applications and challenges
Qi, H., Xiao, S., Liu, Z., Gong, C., & Gani, A. (2024) · Quantum Information Processing · doi:10.1007/s11128-024-04438-2 · Cited by 51
“(3) Variational Hamiltonian ansatz Inspired by adiabatic state preparation, Wecker et al. [24] developed the Variational Hamiltonian Ansatz(VHA), which prepares a ground state for a given Hamiltonian H = (cid:10) i ˆ h i ( ˆ h i are Hermitian operators) by a Trotterized adiabatic state preparation…”
Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation
Sawaya, N. P. D., Smelyanskiy, M., McClean, J. R., & Aspuru‐Guzik, A. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00220 · Cited by 37
Sub-system quantum dynamics using coupled cluster downfolding techniques
Kowalski, K., & Bauman, N. P. (2020) · The Journal of Chemical Physics · doi:10.1063/5.0008436 · Cited by 37
Optimized Quantum Phase Estimation for Simulating Electronic States in Various Energy Regimes
Kang, C., Bauman, N. P., Krishnamoorthy, S., & Kowalski, K. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00577 · Cited by 41
Simulating large-size quantum spin chains on cloud-based superconducting quantum computers
Yu, H., Zhao, Y., & Wei, T.-C. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.013183 · Cited by 40
Sokolov, I. O., Dobrautz, W., Luo, H., Alavi, A., & Tavernelli, I. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023174 · Cited by 46
Algorithmic Error Mitigation Scheme for Current Quantum Processors
Suchsland, P., Tacchino, F., Fischer, M. H., Neupert, T., Barkoutsos, P. K., & Tavernelli, I. (2021) · Quantum · doi:10.22331/q-2021-07-01-492 · Cited by 36
Ryabinkin, I. G., Izmaylov, A. F., & Genin, S. N. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/abda8e · Cited by 39
“In view of these limitations, algorithms based on the variational quantum eigensolver (VQE) framework [3, 4], a hybrid quantum–classical variational scheme, show the most promise.”
Bauman, N. P., Chládek, J., Veis, L., Pittner, J., & Kowalski, K. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/abf602 · Cited by 38
Quantum Divide and Compute: Exploring the Effect of Different Noise Sources
Ayral, T., Régent, F.-M. L., Saleem, Z. H., Alexeev, Y., & Suchara, M. (2021) · SN Computer Science · doi:10.1007/s42979-021-00508-9 · Cited by 40
Gutzwiller hybrid quantum-classical computing approach for correlated materials
Yao, Y., Zhang, F., Wang, C., Ho, K., & Orth, P. P. (2021) · Iowa State University Digital Repository (Iowa State University) · Cited by 35
Barison, S., Moreno, J. R., & Motta, M. (2025) · Quantum Science and Technology · doi:10.1088/2058-9565/adb781 · Cited by 36
Mitarai, K., Yan, T., & Fujii, K. (2019) · Physical Review Applied · doi:10.1103/physrevapplied.11.044087 · Cited by 32
Fuchs, F. G., Falch, V., & Johnsen, C. (2020) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-020-00360-5 · Cited by 38
Ab initio molecular dynamics on quantum computers
Fedorov, D. A., Otten, M., Gray, S. K., & Alexeev, Y. (2021) · The Journal of Chemical Physics · doi:10.1063/5.0046930 · Cited by 35
A Generic Compilation Strategy for the Unitary Coupled Cluster AnsatzPreprint
Cowtan, A., Simmons, W., & Duncan, R. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2007.10515 · Cited by 49
“The Variational Quantum Eigensolver (VQE) is an archetypal hybrid quantum-classical algorithm, designed for the estimation of ground state energies of quantum systems on NISQ devices [51].”
Real-Time Krylov Theory for Quantum Computing Algorithms
Shen, Y., Klymko, K., Sud, J., Williams‐Young, D. B., de Jong, W. A., & Tubman, N. M. (2023) · Quantum · doi:10.22331/q-2023-07-25-1066 · Cited by 45
Quantum Algorithms and Applications for Open Quantum Systems
Delgado-Granados, L. H., Krogmeier, T. J., Sager-Smith, L. M., Avdic, I., Hu, Z., Sajjan, M., Abbasi, M., Smart, S. E., Narang, P., Kais, S., et al. (2025) · Chemical Reviews · doi:10.1021/acs.chemrev.4c00428 · Cited by 50
“Although a plethora of algorithms have been proposed, 27–33 most algorithms have focused on treating electronic structure in closed quantum systems.”
Ultrafast variational simulation of nontrivial quantum states with long-range interactions
Ho, W. W., Jonay, C., & Hsieh, T. H. (2019) · Physical Review A · doi:10.1103/physreva.99.052332 · Cited by 46
“[26] Dave Wecker, Matthew B.”
MethodZhang, F., Gomes, N., Berthusen, N., Orth, P. P., Wang, C.-Z., Ho, K.-M., & Yao, Y.-X. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.013039 · Cited by 34
“[5] D.”
MethodDecision Diagrams for Quantum Measurements with Shallow Circuits
Hillmich, S., Hadfield, C. F., Raymond, R., Mezzacapo, A., & Wille, R. (2021) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce52317.2021.00018 · Cited by 34
Gauge-invariant quantum circuits for U (1) and Yang-Mills lattice gauge theories
Mazzola, G., Mathis, S. V., Mazzola, G., & Tavernelli, I. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.043209 · Cited by 37
“Finally, note that since this set actually contains all terms appearing in the Hamiltonian of the system, it is reasonable to expect [71] that these pieces are sufficient to represent the whole physical Hilbert space of states for a particular choice of the variational parameters.”
BackgroundMethodLumia, L., Torta, P., Mbeng, G. B., Santoro, G. E., Ercolessi, E., Burrello, M., & Wauters, M. M. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.020320 · Cited by 36
Bosse, J. L., & Montanaro, A. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.105.094409 · Cited by 33
Non-trivial symmetries in quantum landscapes and their resilience to quantum noise
Fontana, E., Cerezo, M., Arrasmith, A., Rungger, I., & Coles, P. J. (2022) · Quantum · doi:10.22331/q-2022-09-15-804 · Cited by 52
“For the PQC ansatz we consider a subclass of the QAOA called Hamiltonian Variational Ansatz (HVA), first introduced in [61].”
MethodEffective calculation of the Green's function in the time domain on near-term quantum processors
Libbi, F., Rizzo, J., Tacchino, F., Marzari, N., & Tavernelli, I. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.043038 · Cited by 36
Quantum Pure State Tomography via Variational Hybrid Quantum-Classical Method
Xin, T., Nie, X., Kong, X., Wen, J., Lu, D., & Li, J. (2020) · Physical Review Applied · doi:10.1103/physrevapplied.13.024013 · Cited by 31
Quantum expectation-value estimation by computational basis sampling
Kohda, M., Imai, R., Kanno, K., Mitarai, K., Mizukami, W., & Nakagawa, Y. O. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.033173 · Cited by 36
“In such cases, the optimal numbers of measurements can be heuristically guessed by using expectation values for Haar random states [15, 22].”
MethodQuantum computation for periodic solids in second quantization
Ivanov, A. V., Sünderhauf, C., Holzmann, N., Ellaby, T., Kerber, R. N., Jones, G. A., & Camps, J. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.013200 · Cited by 39
Wiersema, R., Kökcü, E., Kemper, A. F., & Bakalov, B. (2024) · npj Quantum Information · doi:10.1038/s41534-024-00900-2 · Cited by 61
Quantum Computing: Codebreaking and Beyond
Roetteler, M., & Svore, K. M. (2018) · IEEE Security & Privacy · doi:10.1109/msp.2018.3761710 · Cited by 30
Accelerated Quantum Monte Carlo with Mitigated Error on Noisy Quantum Computer
Yang, Y., Lu, B.-N., & Li, Y. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.040361 · Cited by 32
“based on variational principles for solving ground-state energy [67, 68], real time simulation [69–73] and imaginary time simulation [74, 75].”
MethodVariational Quantum Simulators Based on Waveguide QED
Tabares, C., Heras, A. M. D. L., Tagliacozzo, L., Porras, D., & González-Tudela, A. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.073602 · Cited by 32
Quantum information scrambling: from holography to quantum simulators
Bhattacharyya, A., Joshi, L. K., & Sundar, B. (2022) · The European Physical Journal C · doi:10.1140/epjc/s10052-022-10377-y · Cited by 32
Bauman, N. P., & Kowalski, K. (2022) · Materials Theory · doi:10.1186/s41313-022-00046-8 · Cited by 31
Tamiya, S., & Yamasaki, H. (2022) · npj Quantum Information · doi:10.1038/s41534-022-00592-6 · Cited by 37
“(15) and (16), the initial point θ̂ ð0Þ to be updated according to Eq.”
BackgroundProbing many-body localization by excited-state variational quantum eigensolver
Liu, S., Zhang, S., Hsieh, C., Zhang, S., & Yao, H. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.024204 · Cited by 35
An invitation to distributed quantum neural networks
Pira, L., & Ferrie, C. (2023) · Quantum Machine Intelligence · doi:10.1007/s42484-023-00114-3 · Cited by 32
Quantum simulations employing connected moments expansions
Kowalski, K., & Peng, B. (2020) · The Journal of Chemical Physics · doi:10.1063/5.0030688 · Cited by 29
cQASM v1.0: Towards a Common Quantum Assembly LanguagePreprint
Khammassi, N., Guerreschi, G. G., Ashraf, I., Hogaboam, J., Almudéver, C. G., & Bertels, K. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1805.09607 · Cited by 29
Ding, Y., & Chong, F. T. (2020) · Synthesis lectures on computer architecture · doi:10.2200/s01014ed1v01y202005cac051 · Cited by 63
Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model
Li, A. C. Y., Alam, M. S., Iadecola, T., Jahin, A., Job, J., Kürkçüog̃lu, D. M., Li, R., Orth, P. P., Özgüler, A. B., Perdue, G., et al. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.033071 · Cited by 34
“One particular ansatz of interest is the Hamiltonian variational ansatz (HVA) [24].”
Meta-learning digitized-counterdiabatic quantum optimization
Chandarana, P., Vieites, P. S., Hegade, N. N., Solano, E., Ban, Y., & Chen, X. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/ace54a · Cited by 30
Classical simulations of noisy variational quantum circuits
Fontana, E., Rudolph, M. S., Duncan, R., Rungger, I., & Cîrstoiu, C. (2025) · npj Quantum Information · doi:10.1038/s41534-024-00955-1 · Cited by 81
“One may therefore wonder whether it extends to correlated parameter circuits, which are ubiquitous in quantum machine learning [38] as well as forming the basis of algorithms like the Quantum Approximate Optimisation Algorithm (QAOA) [39, 40] or the Hamiltonian Variational Ansatz (HVA) for chemistry problems [41, 42].”
Lie-algebraic classical simulations for quantum computing
Goh, M. L., Larocca, M., Cincio, Ł., Cerezo, M., & Sauvage, F. (2025) · Physical Review Research · doi:10.1103/3y65-f5w6 · Cited by 95
“…. depends entirely In cases where the relevant loss function on observables supported by the algebra of the circuit (e.g., VQE with Hamiltonian variational ansatz [66, 92–94] or QAOA), circuits overparametrizable in polynomial depth are exactly those that can be efficiently simulated with g -sim .”
Hybrid quantum-classical approach to enhanced quantum metrology
Yang, X., Chen, X., Li, J., Peng, X., & Laflamme, R. (2021) · Scientific Reports · doi:10.1038/s41598-020-80070-1 · Cited by 29
“[34] Wecker D, Hastings MB, Troyer M.”
Zhang, F., Gomes, N., Berthusen, N., Orth, P. P., Wang, C., Ho, K., & Yao, Y. (2021) · Iowa State University Digital Repository (Iowa State University) · Cited by 27
SpinQ Gemini: a desktop quantum computing platform for education and research
Hou, S., Feng, G., Wu, Z., Zou, H., Shi, W., Zeng, J., Cao, C., Yü, S., Sheng, Z., Rao, X., et al. (2021) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-021-00109-8 · Cited by 38
“Hardware-efficient ansatz [73], unitary coupled clustered ansatz [81], and Hamiltonian variational ansatz [82, 83] are common choices for U(θ ).”
BackgroundQuantum simulation of nuclear Hamiltonian with a generalized transformation for Gray code encoding
Siwach, P., & Arumugam, P. (2021) · Physical Review C · doi:10.1103/physrevc.104.034301 · Cited by 30
Preparing exact eigenstates of the open XXZ chain on a quantum computer
Dyke, J. S. V., Barnes, E., Economou, S. E., & Nepomechie, R. I. (2021) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ac4640 · Cited by 31
“On the other hand, obtaining quantum advantage for generic simulation problems on fault-tolerant quantum computers is believed to be enormously costly in terms of quantum resources [13–15].”
State preparation and evolution in quantum computing: A perspective from Hamiltonian moments
Aulicino, J. C., Keen, T., & Peng, B. (2021) · International Journal of Quantum Chemistry · doi:10.1002/qua.26853 · Cited by 30
Quantum algorithm for the simulation of open-system dynamics and thermalization
Su, H.-Y., & Li, Y. (2020) · Physical Review A · doi:10.1103/physreva.101.012328 · Cited by 27
“Variational quantum algorithms for solving the ground-state problem or simulating the real and imaginary time evolutions have been developed recently [34–37], which can avoid the enormous qubit cost and are suitable for the near-term quantum computation.”
BackgroundImproving the accuracy and efficiency of quantum connected moments expansions *
Claudino, D., Peng, B., Bauman, N. P., Kowalski, K., & Humble, T. S. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/ac0292 · Cited by 25
Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers
Kirmani, A. A., Bull, K., Hou, C.-Y., Saravanan, V., Saeed, S. M., Papić, Z., Rahmani, A., & Ghaemi, P. (2022) · Physical Review Letters · doi:10.1103/physrevlett.129.056801 · Cited by 31
Quench dynamics of the Schwinger model via variational quantum algorithms
Nagano, L., Bapat, A., & Bauer, C. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.034501 · Cited by 31
Kanno, K., Kohda, M., Imai, R., Koh, S., Mitarai, K., Mizukami, W., & Nakagawa, Y. O. (2026) · Physical Review Research · doi:10.1103/dmn4-snfx · Cited by 162
“The total shot is distributed to each of the groups with the shot allocation optimized for the exact ground state 14 [101, 102].”
Accelerated variational algorithms for digital quantum simulation of many-body ground states
Lyu, C., Montenegro, V., & Bayat, A. (2020) · Quantum · doi:10.22331/q-2020-09-16-324 · Cited by 27
“oth the system size and the depth of the circuit. To overcome these obstacles, the VQE method, a hybrid combination of a quantum circuit and a classical optimizer, has been theoretically investigated [4, 52,53,55,65,82,83,88] and experimentally implemented on various NISQ simulators, including photonic chips [61], ion…”
MethodUnitary block optimization for variational quantum algorithms
Slattery, L., Villalonga, B., & Clark, B. K. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.023072 · Cited by 28
Bauman, N. P., & Kowalski, K. (2022) · The Journal of Chemical Physics · doi:10.1063/5.0076260 · Cited by 28
Quantum algorithms for electronic structures: basis sets and boundary conditions
Liu, J., Fan, Y., Li, Z., & Yang, J. (2022) · Chemical Society Reviews · doi:10.1039/d1cs01184g · Cited by 27
The barren plateaus of quantum neural networks: review, taxonomy and trends
Qi, H., Wang, L., Zhu, H., Gani, A., & Gong, C. (2023) · Quantum Information Processing · doi:10.1007/s11128-023-04188-7 · Cited by 31
“HVA [62] is a QAOA [8] and adiabatic calculations based on [62].”
Assessing three closed-loop learning algorithms by searching for high-quality quantum control pulses
Yang, X., Arenz, C., Pelczer, I., Chen, Q., Wu, R.-B., Peng, X., & RABITZ, H. A. (2020) · Physical Review A · doi:10.1103/physreva.102.062605 · Cited by 25
Variational Quantum Simulation of Chemical Dynamics with Quantum Computers
Lee, C., Hsieh, C., Zhang, S., & Shi, L. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.1c01176 · Cited by 28
“VI, we use a Hamiltonian variational ansatz (HVA) of two layers[17] and only include one-and two-qubits rotations.”
MethodEvolving objective function for improved variational quantum optimization
Kolotouros, I., & Wallden, P. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.023225 · Cited by 24
“Other problems use different ansatz families, like the unitary coupled cluster, which is widely used in chemistry to obtain the ground state of a molecule [42], or the variational Hamiltonian ansatz, which encodes the problem’s Hamiltonian [43].”
BackgroundAccelerating the variational quantum eigensolver using parallelism
Mineh, L., & Montanaro, A. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/acd0d2 · Cited by 28
“We make use of the Hamiltonian variational (HV) ansatz [13] which has previously been shown to be effective for solving the Hubbard model in simulation [12–14] and in experiment [7, 8].”
MethodEffects of noise on the overparametrization of quantum neural networks
García-Martín, D., Larocca, M., & Cerezo, M. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.013295 · Cited by 32
“Here, the red, blue and green curves correspond to the trajectories that the state follows when changing the parameters along the directions given by the three eigenvectors of the QFIM with associated non-zero eigenvalue.”
ResultInfluentialApplication of Pontryagin's minimum principle to Grover's quantum search problem
Lin, C., Wang, Y., Kolesov, G., & Kalabic, U. V. (2019) · Physical Review A · doi:10.1103/physreva.100.022327 · Cited by 22
“More recently, there are quantum algorithms based on the variational principle, notably the Variational Quantum Eigensolver (VQE) [25–27] and the Quantum Approximate Optimization Algorithm (QAOA) [28–30].”
MethodVariationally scheduled quantum simulation
Matsuura, S., Buck, S., Senicourt, V., & Zaribafiyan, A. (2021) · Physical Review A · doi:10.1103/physreva.103.052435 · Cited by 27
“One example is Hamiltonian variational approach [41].”
Quantum inverse iteration algorithm for programmable quantum simulators
Kyriienko, O. (2025) · Figshare · Cited by 27
Simulating Static and Dynamic Properties of Magnetic Molecules with Prototype Quantum Computers
Crippa, L., Tacchino, F., Chizzini, M., Aita, A., Grossi, M., Chiesa, A., Santini, P. M., Tavernelli, I., & Carretta, S. (2021) · Magnetochemistry · doi:10.3390/magnetochemistry7080117 · Cited by 24
Schrödinger-Heisenberg Variational Quantum Algorithms
Shang, Z.-X., Chen, M.-C., Yuan, X., Lu, C., & Pan, J.-W. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.060406 · Cited by 30
“To make SH-VQA trainable, a good trainability Schrödinger circuit is a prerequisite such as the Unitary Coupled Cluster [15] and the Hamiltonian Variational Ansatz [13].”
BackgroundMethodInfluentialQuantum chemistry and charge transport in biomolecules with superconducting circuits
García-Álvarez, L., Heras, U. L., Mezzacapo, A., Sanz, M., Solano, E., & Lamata, L. (2016) · Scientific Reports · doi:10.1038/srep27836 · Cited by 23
Error-resilient Monte Carlo quantum simulation of imaginary time
Huo, M., & Li, Y. (2023) · Quantum · doi:10.22331/q-2023-02-09-916 · Cited by 29
Efficient quantum feature extraction for CNN-based learning
Dou, T., Zhang, G., & Cui, W. (2023) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2023.06.003 · Cited by 26
Using Differential Evolution to avoid local minima in Variational Quantum Algorithms
Faílde, D., Viqueira, J. D., Juane, M. M., & Gómez, A. (2023) · Scientific Reports · doi:10.1038/s41598-023-43404-3 · Cited by 22
“By contrast, we use a Hamiltonian Variational Ansatz (HVA) that is adequate to model a wide range of condensed matter systems [39, 40, 54].”
MethodGroup-theoretic error mitigation enabled by classical shadows and symmetries
Zhao, A., & Miyake, A. (2024) · npj Quantum Information · doi:10.1038/s41534-024-00854-5 · Cited by 34
“The number of repetitions required can be immense, both to suppress shot noise and to handle the measurement of noncommuting observables [49, 50].”
Practical Quantum Advantage on Partially Fault-Tolerant Quantum Computer
Toshio, R., Akahoshi, Y., Fujisaki, J., Oshima, H., Sato, S., & Fujii, K. (2025) · Physical Review X · doi:10.1103/physrevx.15.021057 · Cited by 49
Quantum simulation of bosons with the contracted quantum eigensolver
Wang, Y., Sager-Smith, L. M., & Mazziotti, D. A. (2023) · New Journal of Physics · doi:10.1088/1367-2630/acf9c3 · Cited by 24
Variational Quantum Simulation of Lindblad Dynamics via Quantum State Diffusion
Luo, J., Lin, K., & Gao, X. B. (2024) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.4c00576 · Cited by 20
Quantum algorithms for scientific computing
Au-Yeung, R., Camino, B., Rathore, O., & Kendon, V. M. (2024) · Reports on Progress in Physics · doi:10.1088/1361-6633/ad85f0 · Cited by 37
Martin, B. A., Simon, P., & Rančić, M. J. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.023190 · Cited by 25
“We investigated the Variational Hamiltonian Ansatz (VHA) [17] through the example of the one-dimensional Hubbard model.”
MethodStair, N. H., & Evangelista, F. A. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.1c01155 · Cited by 31
Variational quantum optimization with multibasis encodings
Patti, T. L., Kossaifi, J., Anandkumar, A., & Yelin, S. F. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.033142 · Cited by 21
Automated Quantum Circuit Design With Nested Monte Carlo Tree Search
Wang, P., Usman, M., Parampalli, U., Hollenberg, L. C. L., & Myers, C. R. (2023) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2023.3265709 · Cited by 25
“Recently, there has been a lot of progress made in finding the ground state energy of simple molecules on near-term quantum computers with the variational circuit, both on the theoretical [39], [40], [41] and experimental [1], [7], [42], [43], [44], [45] front.”
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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