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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
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]
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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
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Agrawal, A. A., Getelina, J. C., Francis, A., & Kemper, A. F. (2025) · Physical Review A · doi:10.1103/physreva.111.032607 · Cited by 1
Saha, D., Richerme, P., & Iyengar, S. S. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.4c01343 · Cited by 1
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Umer, M., Mastorakis, E., & Angelakis, D. G. (2025) · Quantum Science and Technology · doi:10.1088/2058-9565/add55e · Cited by 2
“…adopted cost function in VQAs is the expectation value of an observable, which is considered for various problems across diverse domains, including quantum chemistry [11, 12, 14], quantum approximate optimization algorithm (QAOA) [27], and quadratic un-constrained binary optimization (QUBO) [29].”
InfluentialVariational quantum Hamiltonian engineering
Zhao, B., & Fujii, K. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.023123 · Cited by 1
Optimization of the Qubit Coupled Cluster Ansatz on Classical Computers
Ryabinkin, I. G., Jenab, S. M. H., & Genin, S. N. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5c00345 · Cited by 2
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Verma, S., D’Cunha, R., Mitra, A., Hermes, M. R., Gray, S. K., Otten, M., & Gagliardi, L. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5c00745 · Cited by 2
Gresch, A., Tepe, U., & Kliesch, M. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5c00370 · Cited by 3
Batched Line Search Strategy for Navigating through Barren Plateaus in Quantum Circuit Training
Nádori, J., Morse, G., Villám, B. F., Majnay-Takács, Z., Zimborás, Z., & Rakyta, P. (2025) · Quantum · doi:10.22331/q-2025-08-29-1841 · Cited by 8
“Therefore, to increase the efficiency of the VQE execution measurement strategies are studied to minimize the number of the required repetitions [15, 50, 51].”
Guo, Y., & Gao, X. B. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5c00517 · Cited by 5
Hao, C., Ma, Q., Chen, Y., Zhang, H., & Qu, D. (2025) · Journal of King Saud University - Computer and Information Sciences · doi:10.1007/s44443-025-00274-1 · Cited by 2
“PQCs are commonly used to implement quantum neural networks (Wecker et al. 2015; Chen et al. 2025).”
Slice-wise initial state optimization to improve cost and accuracy of the VQE on lattice models
Gaberle, C., & Jattana, M. S. (2025) · Physica Scripta · doi:10.1088/1402-4896/ae26f8 · Cited by 2
“Some developed physics-inspired ansätze, incorporating physically interesting phenomena and symmetries of the problem Hamiltonian into the ansatz to increase its expressivity [2, 7, 8, 9].”
Quantum Glassiness from Efficient Learning
Anschuetz, E. R. (2026) · Communications in Mathematical Physics · doi:10.1007/s00220-025-05536-7 · Cited by 1
Frustration-Free Control and Absorbing-State Transport in Entangled State Preparation
Dörstel, T., Iadecola, T., Wilson, J. H., & Buchhold, M. (2026) · Physical Review Letters · doi:10.1103/zp25-ppgk · Cited by 1
Deep Variational Quantum Circuits with Barren-Plateau-Free Architectures
Zhang, K., Hsieh, M.-H., & Tao, D. (2026) · Artificial Intelligence Science and Engineering · doi:10.23919/aise.2026.000005 · Cited by 1
Training Parameterized Quantum Circuits with Triplet Loss
Wendenius, C., Kuehn, E., & Streit, A. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-26419-1_31 · Cited by 1
Simulating Kondo quantum dots on NISQ devices
Riso, G. D., Bisogno, V., Cipriani, F., Schiavo, M. L., Villani, L., Romano, A., & Noce, C. (2023) · IEEE Nanotechnology Materials and Devices Conference (NMDC) · doi:10.1109/nmdc57951.2023.10343849 · Cited by 1
“Here, we use the Hamiltonian Variational Ansatz (HVA) [10] as trial state to evaluate the Hamiltonian expectation values.”
MethodRobustness of optimized numerical estimation schemes for noisy variational quantum algorithms
Teo, Y. S. (2024) · Physical Review A · doi:10.1103/physreva.109.012620 · Cited by 1
Wu, G., Huang, D., Shuang, F., & Gao, F. (2024) · Computer Physics Communications · doi:10.1016/j.cpc.2024.109117 · Cited by 1
Two methods for breaking down a quantum algorithm
Murça, M., Magano, D., & Omar, Y. (2024) · Physical Review A · doi:10.1103/physreva.109.022412 · Cited by 1
Quantum-Assisted Open-Pit Optimization
Paradezhenko, G. V., Pervishko, A. A., & Yudin, D. (2024) · Journal of Experimental and Theoretical Physics Letters · doi:10.1134/s0021364023604256 · Cited by 2
Hybrid quantum-gap-estimation algorithm using a filtered time series
Lee, W., Scott, R., & Scarola, V. W. (2024) · Physical Review A · doi:10.1103/physreva.109.052403 · Cited by 1
“Unfortunately, the circuit depth needed to implement time evolution is known to scale rather pro-hibitively for a speedup advantage [22–26] thus casting doubt on prospects for compact circuit design with QPE.”
BackgroundActive learning for quantum mechanical measurements
Zhu, R., Pike-Burke, C., & Mintert, F. (2024) · Physical Review A · doi:10.1103/physreva.109.062404 · Cited by 1
Preparing ground and excited states using adiabatic CoVaR
Hwang, W., & Koczor, B. (2025) · New Journal of Physics · doi:10.1088/1367-2630/adb173 · Cited by 2
“Second, we consider a special case that can be applied when the Hamiltonian decomposes into a—potentially dominant—contribution H 0 whose eigenstates can be solved analytically and can be prepared with shallow circuits, and into additional terms as H = H 0 + H 1 [27].”
Enhancing Quantum Expectation Values Via Exponential Error Suppression and CVaR Optimization
Atif, T. A., Tate, R., & Eidenbenz, S. (2025) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit63088.2025.11195610
Quantum-enhanced neural exchange-correlation functionals
Sokolov, I. O., Both, G., Bochevarov, A. D., Dub, P. A., Levine, D. S., Brown, C. T., Acheche, S., Barkoutsos, P. K., & Elfving, V. E. (2025) · Physical Review A · doi:10.1103/m51l-fys2 · Cited by 1
Quantum phases classification using quantum machine learning with SHAP-driven feature selection
Franco, G. S., Mahlow, F. R. P., Prado, P. B. B., Pexe, G. E. L., Rattighieri, L. A. M., & Fanchini, F. F. (2026) · Quantum Information Processing · doi:10.1007/s11128-026-05132-1 · Cited by 7
“Finally, we present the Quantum Support Vector Classifier (QSVC) and the Variational Quantum Classifier to predict the phase diagram of the ANNNI model.”
Approximation Method for Optimization Problems in Gate-Model Quantum Computers
Gyöngyösi, L. (2021) · Chaos Solitons & Fractals X · doi:10.1016/j.csfx.2021.100066 · Cited by 1
Simulation and randomized measurement of topological phase on a trapped-ion quantum computer
Ahn, C.-E., & Cho, G. Y. (2022) · Journal of the Korean Physical Society · doi:10.1007/s40042-022-00536-5 · Cited by 1
“While QAOA was originally developed for approximate solutions to combinatorial problems [20], we use a later generalization as a variational quantum ansatz circuit, sometimes called the Hamiltonian variational ansatz [21, 22].”
MethodInsights from an adaptive variational wave function study of the Fermi-Hubbard ModelPreprint
Gyawali, G., & Lawler, M. J. (2021) · arXiv (Cornell University) · Cited by 1
Localized Quantum Chemistry on Quantum ComputersPreprint
Otten, M., Hermes, M. R., Pandharkar, R., Alexeev, Y., Gray, S. K., & Gagliardi, L. (2021) · doi:10.33774/chemrxiv-2021-0nmwt · Cited by 4
Optimization of Quantum Algorithm Protocols without Barren PlateausPreprint
Broers, L., & Mathey, L. (2021) · arXiv (Cornell University) · Cited by 2
Probing many-body localization by excited-state VQEPreprint
Liu, S., Zhang, S., Hsieh, C., Zhang, S., & Yao, H. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2111.13719 · Cited by 1
Variational quantum iterative power algorithms for global optimizationPreprint
Kyaw, T. H., Soley, M. B., Allen, B., Bergold, P., Sun, C., Batista, V. S., & Aspuru‐Guzik, A. (2022) · arXiv (Cornell University) · doi:10.48550/arxiv.2208.10470 · Cited by 1
Algorithm-Aware Qubit MappingPreprint
Ji, Y., & Polian, I. (2022) · doi:10.36227/techrxiv.21786146.v1 · Cited by 1
Quantum computing enhanced computational catalysis (Molecular integrals)
Von Burg, V., Low, G. H., Häner, T., Steiger, D. S., Reiher, M., Roetteler, M., & Troyer, M. (2021) · Figshare · doi:10.5281/zenodo.4769112 · Cited by 1
Self-citationVariational Quantum Algorithms: From Theory to NISQ-Era Applications Challenges and OpportunitiesPreprint
Benamer, H. (2025) · Preprints.org · doi:10.20944/preprints202508.1482.v1 · Cited by 2
Nambury, S. B. (2026) · Research Square · doi:10.21203/rs.3.rs-9953338/v1 · Cited by 1
García-Pérez, G., Rossi, M. A., Sokolov, B., Tacchino, F., Barkoutsos, P. K., Mazzola, G., Tavernelli, I., & Maniscalco, S. (2021) · Zenodo (CERN European Organization for Nuclear Research) · doi:10.5281/zenodo.5137310 · Cited by 1
Investigating the lower bound of minimum gate times using optimal control
Zhang, X.-P., Shao, B., & Zou, J. (2018) · Modern Physics Letters B · doi:10.1142/s0217984918503220
Noise Analysis of Quantum Approximate Optimization Algorithm on Weighted MAX-CUT
Priyadarshi, L., & Azad, U. (2019) · IEEE Conference on Information and Communication Technology (CICT) · doi:10.1109/cict48419.2019.9066254
Explorations in machine learning for interacting many-body systems.
Schulz-Beach, J. M. (2020) · UWSpace (University of Waterloo)
Applications of Near-Term Quantum Computers
Huggins, W. J. (2020) · eScholarship (California Digital Library)
Scoggins, M. T., & Rahmani, A. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.043165
“The idea has been explored for state preparation [9–11], and has showed remarkable theoretical [12–26] and experimental [27–34] success, particularly, in quantum chemistry simulations.”
BackgroundКвантовая теория физических явлений и квантовые вычисления
Капитан, В. Ю., Dyachenko, O. I., Nefedev, K. V., & Belokon, V. I. (2020) · Publishing House of the Far Eastern Federal University eBooks · doi:10.24866/7444-4849-3
Fast suppression of classification error in variational quantum circuitsPreprint
Zhang, B., & Zhuang, Q. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2107.08026
Shallow Trotter circuits fulfil error-resilient quantum simulation of imaginary timePreprint
Huo, M., & Li, Y. (2021) · arXiv (Cornell University)
Blank, C., & Petruccione, F. (2021) · Digitale Welt · doi:10.1007/s42354-021-0403-z
Blázquez-Cruz, G., & Dallaire-Demers, P.-L. (2021) · arXiv (Cornell University)
Isawi, A. S. H. A., & Çevik, M. (2022) · International Congress on Human-Computer Interaction, Optimization and Robotic Applications (ICHORA) · doi:10.1109/hora55278.2022.9799832
Understanding the Mapping of Encode Data Through An Implementation of Quantum Topological AnalysisPreprint
Vlasic, A., & Pham, A. T. (2022) · Research Square · doi:10.21203/rs.3.rs-2346302/v1
Report on scipost_202206_00017v2
Wiersema, R., Zhou, C., Carrasquilla, J., et al. (2022) · SciPost Physics · doi:10.21468/scipost.report.6291
Report on scipost_202206_00017v1
Wiersema, R., Zhou, C., Carrasquilla, J., et al. (2022) · SciPost Physics · doi:10.21468/scipost.report.5465
Report on scipost_202206_00017v1
Wiersema, R., Zhou, C., Carrasquilla, J., et al. (2022) · SciPost Physics · doi:10.21468/scipost.report.5303
Real-time hybrid quantum-classical computations for trapped ions with Python control-flow
Schmale, T., Temesi, B., Trittschanke, N., Pulido-Mateo, N., Elenskiy, I., Krinner, L., Dubielzig, T., Ospelkaus, C., Weimer, H., & Borcherding, D. (2023) · IEEE International Conference on Quantum Software (QSW) · doi:10.1109/qsw59989.2023.00031 · Cited by 1
Algorithm-Aware Qubit MappingPreprint
Ji, Y., & Polian, I. (2023) · doi:10.36227/techrxiv.21786146.v2
Simulation of optimal work extraction for quantum systems with work storage
宋, P.-F. 鹏. S., & Zhang, D.-B. (2023) · Chinese Physics B · doi:10.1088/1674-1056/ad09d0
Quantum optimization methods in energy systems
Muhamediyeva, D. (2024) · ITM Web of Conferences · doi:10.1051/itmconf/20245901009
Cho, C., Su, J.-W., Yu, L.-P., Chang, C., Chen, P., Lin, T.-W., Liu, S.-H., Li, T.-H., & Lee, Y.-Y. (2024) · Industrial & Engineering Chemistry Research · doi:10.1021/acs.iecr.3c03331
Hamiltonian-reconstruction distance as a success metric for the variational quantum eigensolver
Moon, L. J. I., Sohoni, M. M., Shimizu, M. A., Viswanathan, P., Zhang, K., Kim, E.-A., & McMahon, P. L. (2026) · Quantum Science and Technology · doi:10.1088/2058-9565/ae528d
“Canonical examples include unitary coupled-cluster-type constructions [1, 11–14], symmetry-preserving ansatze [15–17], and ansatze based on Trotterized evolutions of Hamiltonian terms [18, 19].”
Real-time dynamics of the Schwinger model via variational quantum algorithms
Nagano, L., Bapat, A., & Bauer, C. (2024) · International Symposium on Lattice Field Theory (LATTICE) · doi:10.22323/1.453.0222
“Each layer is given by :even where This ansatz, called the Hamiltonian variational ansatz (HVA) [12–14], mimics the Suzuki-Trotter decomposition of real-time/adiabatic time evolution and is thus expected to be useful for both state preparation and real-time evolution.”
BackgroundAnsatz optimization of the variational quantum eigensolver tested on the atomic Anderson model
Riso, G. D., Cipriani, F., Villani, L., Bisogno, V., Schiavo, M. L., Romano, A., & Noce, C. (2024) · New Journal of Physics · doi:10.1088/1367-2630/ad5a61
“In this work we employ three different variational ansatz: the HEA [27], the HVA [28], and the SPA [29].”
MethodFast-forwarding molecular ground state preparation with optimal control on analog quantum simulators
Castaldo, D., Rosa, M., & Corni, S. (2024) · The Journal of Chemical Physics · doi:10.1063/5.0204618
“Among the plethora of ansatze proposed in literature to solve quantum chemistry problems, the works of Wecker et al. 29 and Choquette et al. 30 are closely related to this work.”
BackgroundVariatsionnaya kvantovaya optimizatsiya otkrytogo kar'era
Paradezhenko, G. V., Pervishko, A. A., & Yudin, D. (2024) · Письма в Журнал экспериментальной и теоретической физики · doi:10.31857/s1234567824060090
Numerical Investigation of the Quantum Inverse Algorithm on Small Molecules
Cainelli, M., Baba, R., & Kurashige, Y. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.4c00483 · Cited by 1
“33,34 The Schrödinger equation is then solved only in the space defined by the ansatz.”
BackgroundSupporting Computing-centred Intuitions for Quantum Computing through Play
Beardow, C. (2024) · Annual Symposium on Computer-Human Interaction in Play · doi:10.1145/3665463.3678850 · Cited by 1
“I am currently exploring how a turn-based game format might support intuitions for the programmatic implementation of variational quantum algorithms (an algorithm type with near-term feasibility and industrial applicability [12, 39, 55]).”
Ding, X., & Clark, B. K. (2024) · Physical Review A · doi:10.1103/physreva.110.062403
Quantum computing’s paradigm shift : Implications and Opportunities for Cloud Computing
Ainala, V. B., Arikatla, Y., Seru, V., Dasu, S., & Bikram, B. (2024) · Buana Information Technology and Computer Sciences (BIT and CS) · doi:10.36805/bit-cs.v5i2.6649
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Guerrero, R. D. (2025) · The Journal of Chemical Physics · doi:10.1063/5.0240466
Mohseni, M., Cunha, I., Miravet, D., Rodrigues, A. W., Allami, H., Assi, I. A., Korkusiński, M., & Hawrylak, P. (2025) · physica status solidi (b) · doi:10.1002/pssb.202400552
Two-dimensional physics-constrained hardware-efficient ansatz on quantum computers
Xiao, X., Fang, W., & Li, Z. (2025) · Chinese Science Bulletin (Chinese Version) · doi:10.1360/tb-2024-1146
“变分算法关键在于波函数拟设的选择 , 现有的波函数拟设从设计思路上分为两类 , 一是物理 启发式波函数拟设 , 包括 UCC 及其衍生形式 [12,17~19] 、 自适应波函数拟设 [20~22] 、哈密顿变分波函数拟设 (HVA) [23~25] 等 .”
Miháliková, I., Krejčí, M., & Friák, M. (2025) · Scientific Reports · doi:10.1038/s41598-025-00151-x · Cited by 6
Variational Methods for Solving High-Dimensional Quantum Systems
Li, D. (2025) · Journal of Modern Physics · doi:10.4236/jmp.2025.165038
“…initial state | ψ 0 . prepare ˆ H Here η > 0 is the learning rate. i i i The variational Hamiltonian ansatz also aims to a trial ground states for a given Hamiltonian = k ˆ H k (where ˆ H k are Hermitian operators, usual Pauli strings) by Trotterizing an adiabatic state preparation process [114].”
Variational Quantum Eigensolver for Classification in Distributed Data Sets
Wiśniewska, J., & Sawerwain, M. (2025) · Lecture notes in computer science · doi:10.1007/978-3-031-90200-0_4
Lee, D., & Ryu, H. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5c00961
“The sampling error has been analyzed in the context of VQE where the Hamiltonian is expressed as a linear combination of Pauli strings [44, 45], and, in the same vain, here we discuss the sampling error involved in estimating the expectation of an observable ˆ O in Eq.”
Variational simulation of quantum phase transitions induced by boundary fields
Duriez, A., Saguia, A., & Sarandy, M. S. (2025) · Physical review. B./Physical review. B · doi:10.1103/zfdt-1k63
“To mitigate hardware noise from the device, we have used the randomized compiling [26] and the twirled readout error extinction (T-REX) [27] methods, with the standard configurations found in Qiskit IBM Runtime.”
Guo, Y., Yu, J., & Gao, X. B. (2025) · Chinese Journal of Chemical Physics · doi:10.1063/1674-0068/cjcp2505077
Preparing the Gutzwiller wave function for attractive SU(3) fermions on a quantum computer
Xu, H., Seki, K., & Yunoki, S. (2025) · Physical Review Research · doi:10.1103/rc6z-837q
Quantum speedup for solving the one-dimensional Hubbard model using quantum annealing
Vyas, K., Jin, F., Raedt, H. A. D., & Michielsen, K. F. L. (2026) · Physical Review Research · doi:10.1103/bj6c-t252
Spectral quantum algorithm for numerical differentiation and integration
Cioni, J., & Semperlotti, F. (2026) · Physical Review Applied · doi:10.1103/t8kt-5f2n
“Owing to the prevalence of gradient descent methods in variational quantum algorithms and Quantum Approximate Optimization Algorithms (QAOA) [21, 22], efforts have been made to expand the capabilities of Jordan’s algorithm for these purposes [4, 5].”
Li, H., Yang, Y., Wang, ., Xie, S., Zha, Z., Sun, H., Chen, J., Sun, J., & Ying, S. (2026) · Annalen der Physik · doi:10.1002/andp.202500333
“[ 29 ]), the Variational Hamiltonian Ansatz (VHA) [ 36, 37 ] provides a robust solution.”
Variational quantum generative modeling by sampling expectation values of tunable observables
Shen, K., Kurkin, A., Pérez-Salinas, A., Shishenina, E., Dunjko, V., & Wang, H. (2025) · npj Quantum Information · doi:10.1038/s41534-025-01121-x · Cited by 1
Utility-Scale Quantum State Preparation: Classical Training using Pauli Path Simulation
Lin, C.-J., Gharibyan, H., & Su, V. P. (2026) · Quantum · doi:10.22331/q-2026-03-09-2014
“For models whose ground-state energies can be determined exactly, such as the 1D transverse-field Ising model and the Kitaev honeycomb model, we benchmark PPS results against exact values.”
Barren-plateau free variational quantum simulation of Z 2 lattice gauge theories
Azad, F., Inajetovic, M. A., Kühn, S., & Pappa, A. (2026) · Physical review. D/Physical review. D. · doi:10.1103/rvrq-1scy
“For the local Hamiltonian H = H K , where each H K consists of commuting Pauli operators, the HVA can be written [34, 35] as: Initialization strategies to avoid barren plateaus have been proposed for both the HEA [36] and HVA [37].”
A quantum eigenvalue solver based on tensor networks
Leimkuhler, O., & Whaley, K. B. (2025) · npj Quantum Information · doi:10.1038/s41534-025-01128-4 · Cited by 3
“The intuition behind the TNQE ansatz, which may be tested empirically, is that χ can be made constant in N , provided that the non-local correlations are recovered through the inclusion of multiple”
Combinatorial Optimization with Few Qubits
Raymond, R., Buts, A., & Pistoia, M. (2025) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce65121.2025.00015
“For example, in quantum chemistry where computing the ground state is considered difficult for classical computers, the number of measurements required to calculate the ground state of a molecular Hamiltonian by a variational quantum algorithm is Ω( n 4 ) [49].”
Plazanet, M., & Ayral, T. (2025) · The Journal of Chemical Physics · doi:10.1063/5.0299885
“…the variational energy involves computing the empirical means of quantum measurement outcomes, yielding a central-limit-theorem-induced 1 /ϵ 2 dependence of the run time on the statistical error ϵ , leading to prohibitively long run time estimates for relevant quantum chemistry problems [39].”
Anurag, K. S. V., Patra, A. K., Ghevade, V. D., Shankar, P. S., Bhat, R., Raghavendra, V., Maitra, R., & Jaiganesh, G. (2026) · Journal of Computational Chemistry · doi:10.1002/jcc.70379 · Cited by 6
“The insights derived from these analyses form a practical foundation for optimizing molecular simulation workflows, guiding both quantum algorithmic design and hardware-level implementation choices.”
Efficient Quantum Simulation for Translationally Invariant Systems
Kattemölle, J., & Burkard, G. (2025) · Physical Review Letters · doi:10.1103/cswp-xy7k
“Tileable circuits also arise naturally in the task of finding ground states of lattice systems, for example, because the implementation of e − i τH is a core subroutine [43], or because ˜ U 1 determines the structure of a parameterized ansatz circuit [44, 45].”
Kelemen, Á. A., Perczel, A., & Jákli, I. (2026) · International Journal of Quantum Chemistry · doi:10.1002/qua.70160
Efficient Quantum Amplitude Encoding via Improved Success Probability
Lu, X. P., Li, X., Li, Y., Yi, X., Hou, S., & Pan, C. (2025) · International Conference on Computing, Communication, Perception and Quantum Technology (CCPQT) · doi:10.1109/ccpqt66408.2025.11382951
“…Quantum Algorithms (VQAs) based on Parametrized Quantum Circuits (PQCs), such as the Quantum Approximate Optimization Algorithm (QAOA) [17] and the Variational Quantum Eigensolver (VQE) [18]–[20], alongside with Quantum Neural Networks (QNN) [21]–[23], which are designed for machine learning tasks.”
Compile‐Once Block Encodings for Masked Similarity‐Transformed Effective Hamiltonians
Peng, B., Liu, Y., & Kowalski, K. (2026) · Advanced Quantum Technologies · doi:10.1002/qute.70410
Dwivedi, A., Saha, D., & Iyengar, S. S. (2026) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.5c08302
Introduction to the application of quantum computing in quantum chemistry
Chakravarti, D., & Guidoni, L. (2026) · Elsevier eBooks · doi:10.1016/b978-0-443-26596-9.00035-1
Li, X., Han, J., Feng, F., Liu, J., Zhang, J., Liu, K., Liu, S., Liu, W., Huang, Z., & Zhang, Q. (2026) · IEEE Transactions on Microwave Theory and Techniques · doi:10.1109/tmtt.2026.3672886
“Several notable designs have been proposed, such as hardware-e ffi cient ansatz [24], quantum alternating operator ansatz [49], variational hamiltonian ansatz [50], variable structure ansatz [51], and others [22].”
Enhancing the reachability of variational quantum algorithms via input-state design
Wu, S., Jin, S., Bayat, A., & Wang, X. (2026) · Communications Physics · doi:10.1038/s42005-026-02610-x · Cited by 3
“Thevariationalquantumeigensolver(VQE) 20,104,105 isaspecialcaseofVQAs in which the observable H is the Hamiltonian of a physical system.”
Quantum information processing for quantum simulations
Calonnec, C. L. (2023) · theses.fr (ABES) · doi:10.70675/b46267d0z0466z489dzbda2z220bc68889cb
Solving Quantum Many-Body Problems on Quantum Computers
Martin, B. A. (2023) · theses.fr (ABES) · doi:10.70675/911dc194ze97bz42d2z8611z3daf90a7419c
Quantum-classical hybrid algorithms for quantum many-body physics
Besserve, P. (2023) · theses.fr (ABES) · doi:10.70675/a5e8da3az4c08z4ae8z87a7ze5004c01bf42
Neutron-proton pairing problems simulated on quantum computers
Zhang, J. (2025) · theses.fr (ABES) · doi:10.70675/066a889bzbfb9z40d4z8957za0e98b2d394a · Cited by 1
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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