The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
Progress towards practical quantum variational algorithms
Open accessAbstract
The preparation of quantum states using short quantum circuits is one of the most promising near-term applications of small quantum computers, especially if the circuit is short enough and the fidelity of gates high enough that it can be executed without quantum error correction. Such quantum state preparation can be used in variational approaches, optimizing parameters in the circuit to minimize the energy of the constructed quantum state for a given problem Hamiltonian. For this purpose we propose a simple-to-implement class of quantum states motivated by adiabatic state preparation. We test its accuracy and determine the required circuit depth for a Hubbard model on ladders with up to 12 sites (24 spin orbitals), and for small molecules. We find that this ansatz converges faster than previously proposed schemes based on unitary coupled clusters. While the required number of measurements is astronomically large for quantum chemistry applications to molecules, applying the variational approach to the Hubbard model (and related models) is found to be far less demanding and potentially practical on small quantum computers. We also discuss another application of quantum state preparation using short quantum circuits, to prepare trial ground states of models faster than using adiabatic state preparation.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“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
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“To this end, VQE (McClean et al. , 2016; Peruzzo et al. , 2014) has been proposed, to find the ground state of a Hamiltonian H in a manner that is suited for NISQ devices (Wecker et al. , 2015).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Wecker et al. , 2015
In the citing paper
“The AQC model has been shown to be computationally equivalent to the gate model 62 , meaning that algorithms written in either model can be translated to ones in the other model without incurring prohibitive computational overhead.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [62]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
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
Flagged first, then by citations
Cited by
Sorted by citations
Items 401–500 of 722
Quantum frontiers in high energy physics
Fang, Y., Gao, C., Li, Y.-Y., Shu, J., Wu, Y., Xing, H., Xu, B., Xu, L., & Zhou, C. (2025) · Science China Physics Mechanics and Astronomy · doi:10.1007/s11433-024-2635-4 · Cited by 13
From Ansätze to Z-Gates: A NASA View of Quantum Computing
Rieffel, E. G., Hadfield, S., Hogg, T., Mandrà, S., Marshall, J., Mossi, G., O’Gorman, B., Plamadeala, E., Tubman, N. M., Venturelli, D., et al. (2019) · Advances in parallel computing · doi:10.3233/apc190010 · Cited by 15
Ge, Y., & Dunjko, V. (2020) · Journal of Mathematical Physics · doi:10.1063/1.5119235 · Cited by 12
Incoherent quantum algorithm dynamics of an open system with near-term devices
Mahdian, M., & Yeganeh, H. D. (2020) · Quantum Information Processing · doi:10.1007/s11128-020-02800-8 · Cited by 12
Neural network enhanced measurement efficiency for molecular groundstates
Iouchtchenko, D., Gonthier, J. F., Perdomo‐Ortiz, A., & Melko, R. G. (2023) · Machine Learning Science and Technology · doi:10.1088/2632-2153/acb4df · Cited by 13
“These approaches require multiple states to be prepared on a quantum computer, with very many measurements performed over the course of the algorithm [25, 26].”
BackgroundQuantum data learning for quantum simulations in high-energy physics
Nagano, L., Miessen, A., Onodera, T., Tavernelli, I., Tacchino, F., & Terashi, K. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.043250 · Cited by 18
Fast variational quantum algorithms for training neural networks and solving convex optimizations
Shao, C. (2019) · Physical Review A · doi:10.1103/physreva.99.042325 · Cited by 13
Variational Discrete Action Theory
Cheng, Z., & Marianetti, C. A. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.206402 · Cited by 14
Resource estimations for the Hamiltonian simulation in correlated electron materials
Kanno, S., Endo, S., Utsumi, T., & Tada, T. (2022) · Physical Review A · doi:10.1103/physreva.106.012612 · Cited by 11
Evaluation of vibrational energies and wave functions of CO2 on a quantum computer
Lötstedt, E., Yamanouchi, K., & Tachikawa, Y. (2022) · AVS Quantum Science · doi:10.1116/5.0091144 · Cited by 11
Adaptive Problem Solving Dynamics in Gate-Model Quantum Computers
Gyöngyösi, L. (2022) · Entropy · doi:10.3390/e24091196 · Cited by 12
Quantum Computing Meets Artificial Intelligence: Innovations and Challenges
Metawei, M. A., ElDeeb, H. E., Nassar, S. M., & Taher, M. (2022) · Artificial intelligence-enhanced software and systems engineering · doi:10.1007/978-3-031-08202-3_12 · Cited by 11
Quantum algorithms for generator coordinate methods
Zheng, M., Peng, B., Wiebe, N., Li, A., Yang, X., & Kowalski, K. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023200 · Cited by 14
Efficient ground state preparation in variational quantum eigensolver with symmetry-breaking layers
Park, C.-Y. (2024) · APL Quantum · doi:10.1063/5.0186205 · Cited by 12
Energy-dependent barren plateau in bosonic variational quantum circuits
Zhang, B., & Zhuang, Q. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad80bf · Cited by 11
“As a general approach of designing quantum circuits, VQCs have also found applications in the approximation [25], preparation [26, 27], classification [28–32] and tomography [33] of quantum states.”
Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation
Kiss, O., Azad, U., Requena, B., Roggero, A., Wakeham, D., & Arrazola, J. M. (2025) · Quantum · doi:10.22331/q-2025-04-01-1682 · Cited by 17
“Despite its numerous applications [7–18], scaling to larger systems remains challenging due to the substantial sample requirements [19, 20] and trainability issues [21–23].”
Quantum computing quantum Monte Carlo algorithm
Zhang, Y., Huang, Y., Sun, J., Lv, D., & Yuan, X. (2025) · Physical Review A · doi:10.1103/jt8s-hzhd · Cited by 27
“(C8) Note that the sample complexity is similar to that of the energy measurement process for near-term quantum devices using the frequentist approach [92, 102] as the quantity that we estimate here has a similar form to the energy.”
A quantum genetic algorithm for optimization problems on the Bloch sphere
Amal, R. S., & Ivan, J. S. (2022) · Quantum Information Processing · doi:10.1007/s11128-021-03368-7 · Cited by 13
“[ 24–27].”
A hybrid quantum algorithm to detect conical intersections
Koridon, E., Fraxanet, J., Dauphin, A., Visscher, L., Brien, T. E. O. A., & Polla, S. (2024) · Quantum · doi:10.22331/q-2024-02-20-1259 · Cited by 12
“In chemistry, where VQEs are often proposed as a method to resolve ground state energies to high accuracy, the number of required samples to achieve such accuracy can become prohibitively large [15].”
MethodVQE-generated quantum circuit dataset for machine learning
Nakayama, A., Mitarai, K., Placidi, L., Sugimoto, T., & Fujii, K. (2025) · Physical Review Research · doi:10.1103/c43x-9866 · Cited by 24
“This ansatz is physically motivated by the adiabatic evolution [35, 36].”
Recycling qubits in near-term quantum computers
Anikeeva, G., Kim, I. H., & Hayden, P. M. (2021) · Physical Review A · doi:10.1103/physreva.103.042613 · Cited by 12
Accelerating Variational Quantum Algorithms Using Circuit ConcurrencyPreprint
Resch, S., Gutierrez, A., Huh, J. S., Bharadwaj, S., Eckert, Y., Loh, G. H., Oskin, M., & Tannu, S. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2109.01714 · Cited by 21
“As with QAOA, the main limitation for performance of VQE is the number of samples required [38].”
BackgroundCan shallow quantum circuits scramble local noise into global white noise?
Foldager, J., & Koczor, B. (2023) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ad0ac7 · Cited by 14
“3 (a), i.e., using a HVA ansatz for the TFI spin model at random circuit parameters, but we appended to each layer a series of parametrised Rz gates on each qubit.”
MethodInfluentialPure quantum gradient descent algorithm and full quantum variational eigensolver
Chen, R., Guang, Z., Guo, C., Feng, G., & Hou, S. (2023) · Frontiers of Physics · doi:10.1007/s11467-023-1346-7 · Cited by 14
Robust quantum federated learning with noise
Chen, L., Yan, L., & Zhang, S. (2024) · Physica Scripta · doi:10.1088/1402-4896/ad4df2 · Cited by 11
Artificial-intelligence-driven shot reduction in quantum measurement
Liang, S., Zhu, L., Liu, X., Yang, C., & Li, X. (2024) · Chemical Physics Reviews · doi:10.1063/5.0219663 · Cited by 14
Optimization of Reinforcement Learning Using Quantum Computation
Ravish, R., Bhat, N. R., Nandakumar, N., Sagar, S., Sunil, & Honnavalli, P. B. (2024) · IEEE Access · doi:10.1109/access.2024.3506656 · Cited by 12
Quantum phase transition detection via quantum support vector machine
Wang, Y., & Cao, L. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad985f · Cited by 11
Improving the efficiency of learning-based error mitigation
Czarnik, P., McKerns, M. M., Sornborger, A. T., & Cincio, Ł. (2025) · Quantum · doi:10.22331/q-2025-05-05-1727 · Cited by 28
“Thus, these results demonstrate that preventing clustering of the training data indeed improves the shot-efficiency of CDR error mitigation.”
Amplitude Reordering Accelerates the Adaptive Variational Quantum Eigensolver Algorithms
Lan, Z., & Liang, W. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00403 · Cited by 13
Sun, Z., Wang, Y., Cui, J., & Fan, H. (2023) · New Journal of Physics · doi:10.1088/1367-2630/acb22c · Cited by 13
Al-Bayaty, A., & Perkowski, M. A. (2024) · Entropy · doi:10.3390/e26100843 · Cited by 10
Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit
Sumeet, Hörmann, M., & Schmidt, K. P. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.155128 · Cited by 10
Neutron-proton pairing correlations described on quantum computers
Zhang, J., Denis Lacroix, A., & Beaujeault-Taudière, Y. (2024) · Physical Review C · doi:10.1103/physrevc.110.064320 · Cited by 13
“One example is the Variational Hamiltonian Ansatz (VHA) [68–70].”
Ziems, K. M., Kjellgren, E. R., Sauer, S. P. A., Kongsted, J., & Coriani, S. (2025) · Chemical Science · doi:10.1039/d4sc05839a · Cited by 10
Ma, Y., Wang, W., Mu, X., Cai, W., Hua, Z., Pan, X., Deng, D., Wu, R.-B., Zou, C., Wang, L., et al. (2025) · Science China Physics Mechanics and Astronomy · doi:10.1007/s11433-025-2620-6 · Cited by 9
“Among the algorithms designed for these NISQ devices, the variational quantum eigensolver (VQE) stands out due to its hybrid quantum-classical approach, which has proven effective in finding the ground state energies of quantum systems [8–10].”
Yoshikawa, T., Takanashi, T., & Nakai, H. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00602 · Cited by 10
Resource frugal optimizer for quantum machine learning
Moussa, C., Gordon, M. H., Bączyk, M., Cerezo, M., Cincio, Ł., & Coles, P. J. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/acef55 · Cited by 12
Sabaawi, A. M. A., Almasaoodi, M. R., Gaily, S. E., & Imre, S. (2023) · IET Networks · doi:10.1049/ntw2.12104 · Cited by 9
Qin, Z., Li, X., Zhou, Y., Zhang, S., Li, R., Du, C., & Xiao, Z. (2024) · New Journal of Physics · doi:10.1088/1367-2630/ad634a · Cited by 13
“The HVA [16] is aimed at constructing a series of quantum gate operations based on the specific Hamiltonian.”
Foundations of variational discrete action theory
Cheng, Z., & Marianetti, C. A. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.103.195138 · Cited by 11
Preparing ground states with a broken symmetry with variational quantum algorithms
Vogt, N., Zanker, S., Reiner, J.-M., Marthaler, M., Eckl, T., & Marusczyk, A. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/abe568 · Cited by 21
OPTIC: A Practical Quantum Binary Classifier for Near-Term Quantum Computers
Patel, T., Silver, D., & Tiwari, D. (2022) · Design, Automation, and Test in Europe · doi:10.23919/date54114.2022.9774707 · Cited by 10
Peng, B., & Kowalski, K. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.043172 · Cited by 9
A hybrid quantum-classical method for electron-phonon systems
Denner, M. M., Miessen, A., Yan, H., Tavernelli, I., Neupert, T., Demler, E., & Wang, Y. (2023) · Communications Physics · doi:10.1038/s42005-023-01353-3 · Cited by 11
“Here, we employ the Hamiltonian variational ansatz 72 , which can be naturally extended to nonlocal interactions: inspired by the quantum adiabatic theorem, it starts from an ef fi cient encoding of the non-interacting lattice model with translational symmetry 73 – 76 , and then evolves the state…”
MethodIteration Complexity of Variational Quantum Algorithms
Kungurtsev, V., Korpas, G., Mareček, J., & Zhu, E. Y. (2024) · Quantum · doi:10.22331/q-2024-10-10-1495 · Cited by 14
“With the advent of variational quantum algorithms (VQAs) [45, 21, 59, 38, 62, 11], noisy intermediate scale quantum (NISQ) devices [47], which suffer from short coherence times, coherent and incoherent noise, a limited number of qubits and connectivity of those, they can be utilized in the hope of…”
Quantum computing for classical problems: variational quantum eigensolver for activated processes
Pravatto, P., Castaldo, D., Gallina, F., Fresch, B., Corni, S., & Moro, G. J. (2021) · New Journal of Physics · doi:10.1088/1367-2630/ac3ff9 · Cited by 11
“The importance of this question is highlighted by the large amount of research on the ansatze efficiency when this kind of algorithms are applied to quantum chemistry problems [25, 38, 39].”
BackgroundMethodInfluentialCompressed variational quantum eigensolver for the Fermi-Hubbard modelPreprint
Montanaro, A., & Stanisic, S. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2006.01179 · Cited by 14
“We used the VQE algorithm to optimize over circuits operating on this space, using the Hamiltonian variational ansatz [7] within the optimized framework developed in [12].”
MethodORQVIZ: Visualizing High-Dimensional Landscapes in Variational Quantum AlgorithmsPreprint
Rudolph, M. S., Sim, S., Raza, A., Stęchły, M., McClean, J. R., Anschuetz, E. R., Serrano, L., & Perdomo‐Ortiz, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2111.04695 · Cited by 19
“For instance, if the main objective is to implement a VQE instance on a near-term quantum computer, this rules out ansätze with large circuit depths such as UCCSD [10] or the Variational Hamiltonian Ansatz (VHA) [11].”
Uttarkar, A., & Niranjan, V. (2024) · Quantum Information Processing · doi:10.1007/s11128-024-04261-9 · Cited by 8
“The classical part of a VQA consists of an optimization routine that is used to find the optimal parameters for the PQC [20, 21] The choice of PQC has a significant impact on the performance of a VQA.”
Quantum neural compressive sensing for ghost imaging
Zhai, X., Xiao, T., Huang, J., Jianping Fan, B., & Zeng, G. (2025) · Physical Review Applied · doi:10.1103/physrevapplied.23.014018 · Cited by 8
“The Heisenberg-evolution encoding makes use of a Hamiltonian evolution ansatz which is well-studied in the literature of quantum many-body physics [66–68].”
Simulating Quantum Circuits with Arbitrary Local Noise Using Pauli Propagation
Angrisani, A., Mele, A. A., Rudolph, M. S., Cerezo, M., & Holmes, Z. (2026) · PRX Quantum · doi:10.1103/fb28-wlv2 · Cited by 65
Circuit-Efficient Qubit Excitation-Based Variational Quantum Eigensolver
Sun, Z., Li, X., Liu, J., Li, Z., & Yang, J. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5c00119 · Cited by 11
Critical Limitations in Quantum-Selected Configuration Interaction Methods
Reinholdt, P., Ziems, K. M., Kjellgren, E. R., Coriani, S., Sauer, S. P. A., & Kongsted, J. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5c00375 · Cited by 32
Fault-tolerant operation and materials science with neutral atom logical qubits
Chung, W. C., Cole, D. C., Gokhale, P., Jones, E. B., Kuper, K. W., Mason, D., Omole, V., Radnaev, A. G., Rines, R., Teo, M. H., et al. (2025) · npj Quantum Information · doi:10.1038/s41534-025-01095-w · Cited by 16
Double-Bracket Quantum Algorithms for Quantum Imaginary-Time Evolution
Gluza, M., Son, J., Tiang, B. H., Zander, R., Seidel, R., Suzuki, Y., Holmes, Z., & Ng, N. H. Y. (2025) · Physical Review Letters · doi:10.1103/rw81-k8vk · Cited by 34
“…product of singlet states (214) of consecutive qubits, and b) a type of the so-called problem-specific Hamiltonian Variational Ansatz (HVA) [98–100] | HVA p ( t ) = p j =1 ( e − it j, 0 ˆ H 0 e − it j, 1 ˆ H 1 ) Singlet where ˆ H 0 , ˆ H 1 are obtained from ˆ H by restricting to summation…”
Coarse-grained intermolecular interactions on quantum processors
Anderson, L. W., Kiffner, M., Barkoutsos, P. K., Tavernelli, I., Crain, J. N., & Jaksch, D. (2022) · Physical Review A · doi:10.1103/physreva.105.062409 · Cited by 8
“A standard method [103] using Lagrange multipliers to optimally distribute measurements between circuits gives a total number experimental shots of”
BackgroundMethodComputation of Green's function by local variational quantum compilation
Kanasugi, S., Tsutsui, S., Nakagawa, Y. O., Maruyama, K., Oshima, H., & Sato, S. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.033070 · Cited by 13
“Then, we optimize the HST or LHST cost functions with the so-called variational Hamiltonian ansatz [49, 50] inspired by the Trotter decomposition of the time-evolution operator.”
MethodQuantum Circuit Ansatz: Patterns of Abstraction and Reuse of Quantum Algorithm Design
Guo, X., Muta, T., & Zhao, J. (2024) · IEEE International Conference on Quantum Software (QSW) · doi:10.1109/qsw62656.2024.00021 · Cited by 12
“The Hamiltonian Variational Ansatz (HVA) [64] introduces a hierarchical structure and adjustable parameters to more effectively manage and control the complexity of quantum circuits, making it easier to solve complex quantum computing problems.”
BackgroundMethodExploiting symmetries in nuclear Hamiltonians for ground state preparation
Gibbs, J., Holmes, Z., & Stevenson, P. D. (2025) · Quantum Machine Intelligence · doi:10.1007/s42484-025-00242-y · Cited by 8
“Here, we investigate the Hamiltonian variational ansatz (Wecker et al. 2015) (HVA) as applied to nuclear problems, beginning with the highly simplified and very symmetric Lipkin model, then moving on to the Agassi model, where we deliberately add a perturbation to explore breaking symmetries of the…”
InfluentialQuantum technology: a financial risk assessment
Nguyen, P.-N. (2025) · Digital Finance · doi:10.1007/s42521-025-00127-6 · Cited by 12
“Variational Quantum Eigensolver (VQE) (Peruzzo et al. 2014; Wecker et al. 2015) and Quantum Phase Estimation (QPE) (Kitaev 1995) are employed to determine ground and excited state energies with applications in drug discovery and material science.”
Near-term Quantum Algorithms for Quantum Many-body Systems
Ritter, M. B. (2019) · Journal of Physics Conference Series · doi:10.1088/1742-6596/1290/1/012003 · Cited by 8
Hybrid quantum-classical approach for coupled-cluster Green's function theory
Keen, T., Peng, B., Kowalski, K., Lougovski, P., & Johnston, S. (2022) · Quantum · doi:10.22331/q-2022-03-30-675 · Cited by 8
Fast decay of classification error in variational quantum circuits
Zhang, B., & Zhuang, Q. (2022) · Quantum Science and Technology · doi:10.1088/2058-9565/ac70f5 · Cited by 9
“…quantum circuits (VQCs) are a class of quantum–classical hybrid systems applicable to various tasks, including optimization [3], state preparation [4, 5], auto-encoding [6, 7], eigen-solvers [8–14], unsampling and state approximation [15, 16], state classification [17–20], state tomography [21],…”
Virtual distillation with noise dilution
Teo, Y. S., Shin, S., Kwon, H., Lee, S.-H., & Jeong, H. (2023) · Physical Review A · doi:10.1103/physreva.107.022608 · Cited by 9
Concurrent quantum eigensolver for multiple low-energy eigenstates
Xu, G., Guo, Y., Li, X., Wang, K., Fan, Z., Zhou, Z., Liao, H., & Xiang, T. (2023) · Physical Review A · doi:10.1103/physreva.107.052423 · Cited by 9
Optimizing parametrized quantum circuits via noise-induced breaking of symmetriesPreprint
Fontana, E., Cerezo, M., Arrasmith, A., Rungger, I., & Coles, P. J. (2020) · arXiv (Cornell University) · Cited by 15
Towards near-term quantum simulation of materialsPreprint
Clinton, L., Cubitt, T. S., Flynn, B., Gambetta, F. M., Klassen, J., Montanaro, A., Piddock, S., Santos, R. A., & Sheridan, E. (2022) · arXiv (Cornell University) · doi:10.48550/arxiv.2205.15256 · Cited by 12
“The Hamiltonian variational ansatz is a sequence of circuit layers l of the form Q k e it lk h k , with t lk variational parameters 19 .”
Exploiting many-body localization for scalable variational quantum simulation
Cao, C., Zhou, Y., Tannu, S., Shannon, N., & Joynt, R. (2025) · Quantum · doi:10.22331/q-2025-12-12-1942 · Cited by 20
“…classical optimizers to mitigate hardware limits like coherence times and connectivity, tackling tasks like ground-state preparation via the Variational Quantum Eigen-solver (VQE) for molecules [1, 2] or combinatorial optimization with the Quantum Approximate Optimization Algorithm (QAOA) [3, 4].”
Crognaletti, G., Bartolomeo, G. D., Vischi, M., & Viteritti, L. L. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad9be3 · Cited by 9
“In this study, we utilize a quantum circuit based on the Hamiltonian variational ansatz (HVA) [37, 43], which proved to be effective for approximating quantum many-body eigenstates [33, 44–49].”
Practicality of a quantum adiabatic algorithm for chemistry applications
Granet, E., Ghanem, K., & Dreyer, H. (2025) · Physical Review A · doi:10.1103/physreva.111.022428 · Cited by 10
Singh, H., Majumder, S., & Mishra, S. (2025) · The Journal of Chemical Physics · doi:10.1063/5.0249447 · Cited by 7
“This adds further to the cost and error in the measurements needed to estimate the expectation value of the Hamiltonian using VQE [34–37].”
MethodQuantifying fermionic nonlinearity of quantum circuits
Hakkaku, S., Tashima, Y., Mitarai, K., Mizukami, W., & Fujii, K. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.043100 · Cited by 12
“This type of operations appears in the simulation of interacting fermions and in VQE ansatze such as the UCC ansatz [5], and its variant, Jastrow-type ansatz [7, 29], or Hamiltonian variational ansatz (HVA) [8, 26].”
BackgroundChoi, M., & Ryu, H. (2025) · New Journal of Physics · doi:10.1088/1367-2630/add8b4 · Cited by 7
Digital quantum simulation of the BCS model with a central-spin-like quantum processor
Ruh, J., Finsterhoelzl, R., & Burkard, G. (2023) · Physical Review A · doi:10.1103/physreva.107.062604 · Cited by 11
Ge, Y., & Dunjko, V. (2020) · MPG.PuRe (Max Planck Society) · Cited by 7
Learning to measure: adaptive informationally complete POVMs for near-term quantum algorithmsPreprint
García-Pérez, G., Rossi, M. A. C., Sokolov, B., Tacchino, F., Barkoutsos, P. K., Mazzola, G., Tavernelli, I., & Maniscalco, S. (2021) · arXiv (Cornell University) · Cited by 7
Stabilizer-accelerated quantum many-body ground-state estimation
Robin, C. (2025) · Physical Review A · doi:10.1103/5qr5-7jkz · Cited by 14
“For example, one can use terms of the Hamiltonian itself, as done in Hamiltonian variational ansatz (see e.g. [87]), and/or commutators of Hamiltonian terms, to explore a larger part of the Hilbert space [88], as well as individual fermionic or qubit excitation operators [12, 89].”
Danilov, D., Moreno, J. R., Sung, K. J., Motta, M., & Shee, J. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5c01407 · Cited by 29
“While VQE requires measuring the expectation value of the Hamiltonian to high precision, which can incur a prohibitive sampling overhead on the quantum computer, 34 QSCI directly uses quantum samples for its classical diagonalization.”
Classically Computing Performance Bounds on Depolarized Quantum Circuits
Mishra, S. D., Frías-Pérez, M., & Trivedi, R. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.020317 · Cited by 6
Maximizing quantum-computing expressive power through randomized circuits
Yang, Y., Zhang, Z., Wang, A., Xu, X., Wang, X., & Li, Y. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.023098 · Cited by 8
“Fourthly, to have a concrete discussion about this trade-off feature, we specifically focus on the ground-state problem and take the Hamiltonian ansatz circuit [58] as an example.”
MethodNoise-Aware Variational Eigensolvers: A Dissipative Route for Lattice Gauge Theories
Cobos, J., Locher, D. F., Bermúdez, A., Müller, M., & Rico, E. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.030340 · Cited by 7
“Other examples of widely used variational algorithms are the Quantum Approximate Optimization Algorithm [87–89] the Hamiltonian Variational Ansatz (HVA) [90, 91] or the Unitary Coupled Cluster [72, 92– 94].”
MethodAb initio extended Hubbard model of short polyenes for efficient quantum computing
Yoshida, Y., Takemori, N., & Mizukami, W. (2024) · The Journal of Chemical Physics · doi:10.1063/5.0213525 · Cited by 6
Correr, G. I., Medina, I., Azado, P. C., Drinko, A., & Soares-Pinto, D. O. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad80be · Cited by 11
Efficient Quantum-Enhanced Classical Simulation for Patches of Quantum Landscapes
Lerch, S., Puig, R., Rudolph, M. S., Angrisani, A., Jones, T., Cerezo, M., Thanasilp, S., & Holmes, Z. (2026) · PRX Quantum · doi:10.1103/fhc5-8sm6 · Cited by 6
Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements
Zhang, F., Wang, C., Iadecola, T., Orth, P. P., & Yao, Y. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.094310 · Cited by 8
“In addition to AVQDS and AVQDS(T), we also simulated quantum dynamics with the first-order Trotter decomposition [48, 50] and VQDS with a fixed ansatz, namely the Hamiltonian variational ansatz (HVA) [51].”
Machine learning approach toward quantum error mitigation for accurate molecular energetics
Patil, S., Mondal, D., & Maitra, R. (2025) · The Journal of Chemical Physics · doi:10.1063/5.0274910 · Cited by 8
Weber, M., Anand, A., Cervera-Lierta, A., Kottmann, J. S., Kyaw, T. H., Li, B., Aspuru‐Guzik, A., Zhang, C., & Zhao, Z. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.033217 · Cited by 8
“…hindrance practically arises from various sources such as circuit noise and decoherence [1], limited expressibility of Ansätze [5,6], barren plateaus during optimization in variational hybrid quantum-classical algorithms [7–9], measurement noise, and other experimental imperfections [10,11].”
Parametrized quantum circuit for weight-adjustable quantum loop gas
Sun, R.-Y., Shirakawa, T., & Yunoki, S. (2022) · Physical review B · doi:10.1103/physrevb.107.l041109 · Cited by 7
Efficient measurement schemes for bosonic systems
Gu, T., Yuan, X., & Wu, B. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/ace6cd · Cited by 6
“Here, we show an alternative more general framework proposed by Wu et al [25] that unites classical shadow and other measurement schemes, including importance sampling [27, 28], grouping method [29–36], (local-biased) CS [13, 15], and overlapped grouping measurement (OGM) algorithm [25].”
Adaptive variational ground state preparation for spin-1 models on qubit-based architectures
Getelina, J. C., Wang, C., Iadecola, T., Yao, Y., & Orth, P. P. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.085128 · Cited by 6
Resource-efficient quantum-classical hybrid algorithm for energy gap evaluation
Yang, Y., Li, Y., Xu, X., & Yuan, X. (2024) · Physical Review A · doi:10.1103/physreva.109.052416 · Cited by 7
Retrieving Nonlinear Features from Noisy Quantum States
Zhao, B., Jing, M., Zhang, L., Zhao, X., Chen, Y.-A., Wang, K., & Wang, X. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.020357 · Cited by 6
Lim, H., Jeon, H.-N., Rhee, J. K., Oh, B., & No, K. T. (2022) · Scientific Reports · doi:10.1038/s41598-022-11537-6 · Cited by 7
“The first proposal of a VQA was the VQE [27–29], originally proposed to solve quantum chemistry problems, and the quantum approximate optimization algorithm [30] was proposed to solve combinatorial optimization problems.”
Robust Diabatic Grover Search by Landau–Zener–Stückelberg Oscillations
Atia, Y., Oren, Y., & Katz, N. (2019) · Entropy · doi:10.3390/e21100937 · Cited by 6
Neural network agent playing spin Hamiltonian games on a quantum computer
Sotnikov, O. M., & Mazurenko, V. V. (2020) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ab73ad · Cited by 6
Roadmap for quantum simulation of the fractional quantum Hall effect
Kaicher, M., Jäger, S. B., Dallaire-Demers, P.-L., & Wilhelm, F. K. (2020) · Physical Review A · doi:10.1103/physreva.102.022607 · Cited by 7
“Scaling analysis like these are important for determining upper bounds on the number of required measurements to estimate the ground state energy within a given precision and for various variational Ansätze U(θ) of the VQE, such as the Hamiltonian variational Ansatz [39], as it depends on both the number and the relat…”
BackgroundNEURAL NETWORK AGENT PLAYING SPIN HAMILTONIAN GAMES ON A QUANTUM COMPUTER
Sotnikov, O. M., & Mazurenko, V. V. (2020) · Electronic Archive of Ural Federal University (ELAR UrFU) · Cited by 6
Quantum simulation of Hamiltonian spectra on a silicon chipPreprint
Santagati, R., Wang, J.-C., Gentile, A. A., Paesani, S., Wiebe, N., McClean, J. R., Morley-Short, S., Shadbolt, P., Bonneau, D., Silverstone, J. W., et al. (2016) · arXiv (Cornell University) · Cited by 6
Adaptive shot allocation for fast convergence in variational quantum algorithmsPreprint
Gu, A., Lowe, A., Dub, P. A., Coles, P. J., & Arrasmith, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2108.10434 · Cited by 30
“In addition, shot noise (due to the variance of quantum observables) can result in a high shot cost during the optimization [44].”
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
