The DOI matches its Crossref record; 42 of the 43 references it cites were found in a registry or an index.
Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
Open accessAbstract
Quantum computers can be used to address electronic-structure problems and problems in materials science and condensed matter physics that can be formulated as interacting fermionic problems, problems which stretch the limits of existing high-performance computers. Finding exact solutions to such problems numerically has a computational cost that scales exponentially with the size of the system, and Monte Carlo methods are unsuitable owing to the fermionic sign problem. These limitations of classical computational methods have made solving even few-atom electronic-structure problems interesting for implementation using medium-sized quantum computers. Yet experimental implementations have so far been restricted to molecules involving only hydrogen and helium. Here we demonstrate the experimental optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms, determining the ground-state energy for molecules of increasing size, up to BeH 2. We achieve this result by using a variational quantum eigenvalue solver (eigensolver) with efficiently prepared trial states that are tailored specifically to the interactions that are available in our quantum processor, combined with a compact encoding of fermionic Hamiltonians and a robust stochastic optimization routine. We demonstrate the flexibility of our approach by applying it to a problem of quantum magnetism, an antiferromagnetic Heisenberg model in an external magnetic field. In all cases, we find agreement between our experiments and numerical simulations using a model of the device with noise. Our results help to elucidate the requirements for scaling the method to larger systems and for bridging the gap between key problems in high-performance computing and their implementation on quantum hardware.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
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?
In the citing paper
“Pauli strings that commute qubit-wise, i.e. the Pauli operators on each qubit commute, can be measured at the same time (Kandala et al. , 2017; McClean et al. , 2016).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Kandala et al., 2017
In the citing paper
“Aclass of hardware-efficient ansätze (see Fig. 3(b)) has been proposed to accommodate device constraints (Kandala et al. , 2017).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Kandala et al., 2017
In the citing paper
“While the quantum analog of #P , #BQP , has been defined and has been shown to contain important physical problems, it turns out to be of equal complexity to #P 67 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [67]
In the citing paper
“The most prominent example of this class of algorithms relevant for electronic structure calculations is the variational quantum eigensolver (VQE), which presents a variational (and thus heuristic) algorithm to upper bounding the ground state energy problem.[126][127][128]”
From Quantum Computing for Molecular Biology** (2023) · cites this paper as [127]
Citations
Cites
Szabó, A., & Ostlund, N. S. (1982) · Cited by 6,239
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
Multivariate stochastic approximation using a simultaneous perturbation gradient approximation
Spall, J. C. (1992) · IEEE Transactions on Automatic Control · doi:10.1109/9.119632 · Cited by 2,283
The theory of variational hybrid quantum-classical algorithms
McClean, J. R., Romero, J., Babbush, R., & Aspuru-Guzik, A. (2016) · New Journal of Physics · doi:10.1088/1367-2630/18/2/023023 · Cited by 2,227
A Quantum Approximate Optimization Algorithm
Farhi, E., Goldstone, J., & Gutmann, S. (2014) · arXiv · doi:10.48550/arxiv.1411.4028 · Cited by 1,789
Simulated Quantum Computation of Molecular Energies
Aspuru-Guzik, A., Dutoi, A. D., Love, P. J., & Head-Gordon, M. (2005) · Science · doi:10.1126/science.1113479 · Cited by 1,418
Error Mitigation for Short-Depth Quantum Circuits
Temme, K., Bravyi, S., & Gambetta, J. M. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.180509 · Cited by 1,379
Self-citationScalable Quantum Simulation of Molecular Energies
O’Malley, P. J. J., Babbush, R., Kivlichan, I. D., Romero, J., McClean, J. R., Barends, R., Kelly, J., Roushan, P., Tranter, A., Ding, N., et al. (2016) · Physical Review X · doi:10.1103/physrevx.6.031007 · Cited by 1,059
Bravyi, S. B., & Kitaev, A. Y. (2002) · Annals of Physics · doi:10.1006/aphy.2002.6254 · Cited by 1,033
Towards quantum chemistry on a quantum computer
Lanyon, B. P., Whitfield, J. D., Gillett, G. G., Goggin, M. E., Almeida, M. P., Kassal, I., Biamonte, J. D., Mohseni, M., Powell, B. J., Barbieri, M., et al. (2010) · Nature Chemistry · doi:10.1038/nchem.483 · Cited by 796
Cited by
Sorted by citations
Items 101–200 of 1,010
Low-cost error mitigation by symmetry verification
Bonet-Monroig, X., Sagastizabal, R., Singh, M., & O'Brien, T. E. (2018) · Physical Review A · doi:10.1103/physreva.98.062339 · Cited by 250
Exploring Entanglement and Optimization within the Hamiltonian Variational Ansatz
Wiersema, R., Zhou, C., de Sereville, Y., Carrasquilla, J., Kim, Y. B., & Yuen, H. (2020) · PRX Quantum · doi:10.1103/prxquantum.1.020319 · Cited by 289
Maciejewski, F. B., Zimborás, Z., & Oszmaniec, M. (2020) · Quantum · doi:10.22331/q-2020-04-24-257 · Cited by 271
Accelerated Variational Quantum Eigensolver
Wang, D., Higgott, O., & Brierley, S. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.140504 · Cited by 241
Error-Mitigated Digital Quantum Simulation
McArdle, S., Yuan, X., & Benjamin, S. C. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.180501 · Cited by 253
Variational Quantum Simulation of General Processes
Endo, S., Sun, J., Li, Y., Benjamin, S. C., & Yuan, X. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.010501 · Cited by 237
Limitations of optimization algorithms on noisy quantum devices
França, D. S., & García−Patrón, R. (2021) · Nature Physics · doi:10.1038/s41567-021-01356-3 · Cited by 280
Programming languages and compiler design for realistic quantum hardware
Chong, F. T., Franklin, D. M., & Martonosi, M. (2017) · Nature · doi:10.1038/nature23459 · Cited by 252
The prospects of quantum computing in computational molecular biology
Outeiral, C., Strahm, M., Shi, J., Morris, G. M., Benjamin, S. C., & Deane, C. M. (2021) · WIREs Computational Molecular Science · doi:10.1002/wcms.1481 · Cited by 232
Simulating the vibrational quantum dynamics of molecules using photonics
Sparrow, C., Martín-López, E., Maraviglia, N., Neville, A., Harrold, C., Carolan, J., Joglekar, Y. N., Hashimoto, T., Matsuda, N., O’Brien, J. L., et al. (2018) · Nature · doi:10.1038/s41586-018-0152-9 · Cited by 230
Exact parameterization of fermionic wave functions via unitary coupled cluster theory
Evangelista, F. A., Chan, G. K.-L., & Scuseria, G. E. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5133059 · Cited by 225
VQE method: a short survey and recent developments
Fedorov, D. A., Peng, B., Govind, N., & Alexeev, Y. (2022) · Materials Theory · doi:10.1186/s41313-021-00032-6 · Cited by 224
A quantum computing view on unitary coupled cluster theory
Anand, A., Schleich, P., Alperin-Lea, S., Jensen, P. W. K., Sim, S., Díaz‐Tinoco, M., Kottmann, J. S., Degroote, M., Izmaylov, A. F., & Aspuru‐Guzik, A. (2022) · Chemical Society Reviews · doi:10.1039/d1cs00932j · Cited by 251
Granular aluminium as a superconducting material for high-impedance quantum circuits
Grünhaupt, L., Spiecker, M., Gusenkova, D., Maleeva, N., Skacel, S. T., Takmakov, I., Valenti, F., Winkel, P., Rotzinger, H., Wernsdorfer, W., et al. (2019) · Nature Materials · doi:10.1038/s41563-019-0350-3 · Cited by 239
Sequential minimal optimization for quantum-classical hybrid algorithms
Nakanishi, K. M., Fujii, K., & Todo, S. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.043158 · Cited by 221
Structure optimization for parameterized quantum circuits
Ostaszewski, M., Grant, E., & Benedetti, M. (2021) · Quantum · doi:10.22331/q-2021-01-28-391 · Cited by 220
Stochastic gradient descent for hybrid quantum-classical optimization
Sweke, R., Wilde, F., Meyer, J., Schuld, M., Faehrmann, P. K., Meynard-Piganeau, B., & Eisert, J. (2020) · Quantum · doi:10.22331/q-2020-08-31-314 · Cited by 219
Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor
Ollitrault, P. J., Kandala, A., Chen, C.-F., Barkoutsos, P. K., Mezzacapo, A., Pistoia, M., Sheldon, S., Woerner, S., Gambetta, J. M., & Tavernelli, I. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.043140 · Cited by 232
Self-citationDiagnosing Barren Plateaus with Tools from Quantum Optimal Control
Larocca, M., Czarnik, P., Sharma, K., Muraleedharan, G., Coles, P. J., & Cerezo, M. (2022) · Quantum · doi:10.22331/q-2022-09-29-824 · Cited by 272
Oxide– and Silicate–Water Interfaces and Their Roles in Technology and the Environment
Bañuelos, J. L., Borguet, E., Brown, G. E., Cygan, R. T., DeYoreo, J. J., Dove, P. M., Gaigeot, M., Geiger, F. M., Gibbs, J. M., Grassian, V. H., et al. (2023) · Chemical Reviews · doi:10.1021/acs.chemrev.2c00130 · Cited by 227
Quantum chemistry as a benchmark for near-term quantum computers
McCaskey, A., Parks, Z. P., Jakowski, J., Moore, S., Morris, T., Humble, T. S., & Pooser, R. C. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0209-0 · Cited by 216
Laser-annealing Josephson junctions for yielding scaled-up superconducting quantum processors
Hertzberg, J. B., Zhang, E. J., Rosenblatt, S., Magesan, E., Smolin, J. A., Yau, J.-B., Adiga, V. P., Sandberg, M., Brink, M., Chow, J. M., et al. (2021) · npj Quantum Information · doi:10.1038/s41534-021-00464-5 · Cited by 216
Self-citationQuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits
Wang, H., Ding, Y., Gu, J., Lin, Y., Pan, D. Z., Chong, F. T., & Han, S. (2022) · IEEE International Symposium on High-Performance Computer Architecture (HPCA) · doi:10.1109/hpca53966.2022.00057 · Cited by 236
Training of quantum circuits on a hybrid quantum computer
Zhu, D., Linke, N. M., Benedetti, M., Landsman, K. A., Nguyen, N. H., Alderete, C. H., Perdomo-Ortiz, A., Korda, N., Garfoot, A., Brecque, C., et al. (2019) · Science Advances · doi:10.1126/sciadv.aaw9918 · Cited by 215
Coherent quantum annealing in a programmable 2,000 qubit Ising chain
King, A. D., Suzuki, S., Raymond, J., Zucca, A., Lanting, T., Altomare, F., Berkley, A. J., Ejtemaee, S., Hoskinson, E., Huang, S., et al. (2022) · Nature Physics · doi:10.1038/s41567-022-01741-6 · Cited by 213
Witnessing eigenstates for quantum simulation of Hamiltonian spectra
Santagati, R., Wang, J., Gentile, A. A., Paesani, S., Wiebe, N., McClean, J. R., Morley-Short, S., Shadbolt, P. J., Bonneau, D., Silverstone, J. W., et al. (2018) · Science Advances · doi:10.1126/sciadv.aap9646 · Cited by 211
Correlating Decoherence in Transmon Qubits: Low Frequency Noise by Single Fluctuators
Schlör, S., Lisenfeld, J., Müller, C., Bilmes, A., Schneider, A., Pappas, D. P., Ustinov, A. V., & Weides, M. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.190502 · Cited by 209
Challenges and Opportunities of Near-Term Quantum Computing Systems
Corcoles, A. D., Kandala, A., Javadi-Abhari, A., McClure, D. T., Cross, A. W., Temme, K., Nation, P. D., Steffen, M., & Gambetta, J. M. (2020) · Proceedings of the IEEE · doi:10.1109/jproc.2019.2954005 · Cited by 203
Self-citationComputational Chemistry: The Fate of Current Methods and Future Challenges
Grimme, S., & Schreiner, P. R. (2017) · Angewandte Chemie International Edition · doi:10.1002/anie.201709943 · Cited by 205
Quantum variational autoencoder
Khoshaman, A., Vinci, W., Denis, B., Andriyash, E., Sadeghi, H., & Amin, M. H. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aada1f · Cited by 218
Quantum agents in the Gym: a variational quantum algorithm for deep Q-learning
Skolik, A., Jerbi, S., & Dunjko, V. (2022) · Quantum · doi:10.22331/q-2022-05-24-720 · Cited by 240
Variational quantum state diagonalization
LaRose, R., Tikku, A., O’Neel-Judy, É., Cincio, L., & Coles, P. J. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0167-6 · Cited by 199
Quantum circuit architecture search for variational quantum algorithms
Du, Y., Huang, T., You, S., Hsieh, M.-H., & Tao, D. (2022) · npj Quantum Information · doi:10.1038/s41534-022-00570-y · Cited by 199
Quantum simulations of materials on near-term quantum computers
Ma, H., Govoni, M., & Galli, G. (2020) · npj Computational Materials · doi:10.1038/s41524-020-00353-z · Cited by 197
Unbiasing fermionic quantum Monte Carlo with a quantum computer
Huggins, W. J., O’Gorman, B., Rubin, N. C., Reichman, D. R., Babbush, R., & Lee, J. (2022) · Nature · doi:10.1038/s41586-021-04351-z · Cited by 220
Scalable error mitigation for noisy quantum circuits produces competitive expectation values
Kim, Y., Wood, C. J., Yoder, T. J., Merkel, S., Gambetta, J., Temme, K., & Kandala, A. (2023) · Nature Physics · doi:10.1038/s41567-022-01914-3 · Cited by 224
Self-citationOptimal metrology with programmable quantum sensors
Marciniak, C. D., Feldker, T., Pogorelov, I., Kaubruegger, R., Vasilyev, D. V., van Bijnen, R., Schindler, P., Zoller, P., Blatt, R., & Monz, T. (2022) · Nature · doi:10.1038/s41586-022-04435-4 · Cited by 205
IBM quantum computers: evolution, performance, and future directions
AbuGhanem, M. (2025) · The Journal of Supercomputing · doi:10.1007/s11227-025-07047-7 · Cited by 266
Efficient quantum measurement of Pauli operators in the presence of finite sampling error
Crawford, O., Straaten, B. V., Wang, D., Parks, T., Campbell, E., & Brierley, S. (2021) · Quantum · doi:10.22331/q-2021-01-20-385 · Cited by 188
Koh, J. M., Sun, S., Motta, M., & Minnich, A. J. (2023) · Nature Physics · doi:10.1038/s41567-023-02076-6 · Cited by 187
Romero, J., & Aspuru‐Guzik, A. (2021) · Advanced Quantum Technologies · doi:10.1002/qute.202000003 · Cited by 186
Solving nonlinear differential equations with differentiable quantum circuits
Kyriienko, O., Paine, A. E., & Elfving, V. E. (2021) · Physical Review A · doi:10.1103/physreva.103.052416 · Cited by 185
QASMBench: A Low-Level Quantum Benchmark Suite for NISQ Evaluation and Simulation
Li, A., Stein, S., Krishnamoorthy, S., & Ang, J. (2023) · ACM Transactions on Quantum Computing · doi:10.1145/3550488 · Cited by 183
A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons
Stair, N. H., Huang, R., & Evangelista, F. A. (2020) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.9b01125 · Cited by 183
Qiskit pulse: programming quantum computers through the cloud with pulses
Alexander, T., Kanazawa, N., Egger, D. J., Capelluto, L., Wood, C. J., Javadi-Abhari, A., & McKay, D. C. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/aba404 · Cited by 183
Designing metamaterials with quantum annealing and factorization machines
Kitai, K., Guo, J., Ju, S., Tanaka, S., Tsuda, K., Shiomi, J., & Tamura, R. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.013319 · Cited by 181
Emerging quantum computing algorithms for quantum chemistry
Motta, M., & Rice, J. E. (2021) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.1580 · Cited by 201
Tunable, Flexible, and Efficient Optimization of Control Pulses for Practical Qubits
Machnes, S., Assémat, E., Tannor, D. J., & Wilhelm, F. K. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.150401 · Cited by 192
Yen, T.-C., Verteletskyi, V., & Izmaylov, A. F. (2020) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.0c00008 · Cited by 178
Strategies for solving the Fermi-Hubbard model on near-term quantum computers
Cade, C., Mineh, L., Montanaro, A., & Stanisic, S. (2020) · Physical Review B · doi:10.1103/physrevb.102.235122 · Cited by 178
Trainability of Dissipative Perceptron-Based Quantum Neural Networks
Sharma, K., Cerezo, M., Cincio, Ł., & Coles, P. J. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.180505 · Cited by 212
Traversable wormhole dynamics on a quantum processor
Jafferis, D. L., Zlokapa, A., Lykken, J. D., Kolchmeyer, D. K., Davis, S. I., Lauk, N., Neven, H., & Spiropulu, M. (2022) · Nature · doi:10.1038/s41586-022-05424-3 · Cited by 189
Efficient Estimation of Pauli Observables by Derandomization
Huang, H.-Y., Kueng, R., & Preskill, J. P. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.030503 · Cited by 211
NISQ computing: where are we and where do we go?
Lau, J. W. Z., Lim, K. H., Shrotriya, H., & Kwek, L. C. (2022) · AAPPS bulletin · doi:10.1007/s43673-022-00058-z · Cited by 199
Quantum Algorithms to Simulate Many-Body Physics of Correlated Fermions
Jiang, Z., Sung, K. J., Kechedzhi, K., Smelyanskiy, V. N., & Boixo, S. (2018) · Physical Review Applied · doi:10.1103/physrevapplied.9.044036 · Cited by 175
Hardware-efficient variational quantum algorithms for time evolution
Benedetti, M., Fiorentini, M., & Lubasch, M. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.033083 · Cited by 189
Does provable absence of barren plateaus imply classical simulability?
Cerezo, M., Larocca, M., García-Martín, D., Diaz, N. L., Braccia, P., Fontana, E., Rudolph, M. S., Bermejo, P., Ijaz, A., Thanasilp, S., et al. (2025) · Nature Communications · doi:10.1038/s41467-025-63099-6 · Cited by 310
Izmaylov, A. F., Yen, T.-C., Lang, R. A., & Verteletskyi, V. (2020) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.9b00791 · Cited by 171
Variational algorithms for linear algebra
Xu, X., Sun, J., Endo, S., Li, Y., Benjamin, S. C., & Yuan, X. (2021) · 中国科学通报：英文版 · doi:10.1016/j.scib.2021.06.023 · Cited by 195
Takeshita, T. Y., Rubin, N. C., Zhang, J., Lee, E., Babbush, R., & McClean, J. R. (2020) · Physical Review X · doi:10.1103/physrevx.10.011004 · Cited by 177
Discovering and understanding materials through computation
Louie, S. G., Chan, Y., da Jornada, F. H., Li, Z., & Qiu, D. Y. (2021) · Nature Materials · doi:10.1038/s41563-021-01015-1 · Cited by 169
Model-free readout-error mitigation for quantum expectation values
van den Berg, E., Minev, Z., & Temme, K. (2022) · Physical Review A · doi:10.1103/physreva.105.032620 · Cited by 214
Self-citationVariational quantum eigensolver with fewer qubits
Liu, J.-G., Zhang, Y.-H., Wan, Y., & Wang, L. (2019) · Physical Review Research · doi:10.1103/physrevresearch.1.023025 · Cited by 166
Digitization of scalar fields for quantum computing
Klco, N., & A, M. J. S. (2019) · Physical Review A · doi:10.1103/physreva.99.052335 · Cited by 204
Exploiting Dynamic Quantum Circuits in a Quantum Algorithm with Superconducting Qubits
Corcoles, A. D., Takita, M., Inoue, K., Lekuch, S., Minev, Z., Chow, J. M., & Gambetta, J. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.100501 · Cited by 201
Self-citationMitigating Depolarizing Noise on Quantum Computers with Noise-Estimation Circuits
Urbánek, M., Nachman, B. P., Pascuzzi, V. R., He, A., Bauer, C. W., & de Jong, W. A. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.270502 · Cited by 205
Quantum State Tomography with Conditional Generative Adversarial Networks
Ahmed, S., Muñoz, C. S., Nori, F., & Kockum, A. F. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.140502 · Cited by 179
Entanglement devised barren plateau mitigation
Patti, T. L., Najafi, K., Gao, X., & Yelin, S. F. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.033090 · Cited by 164
Quantum computing at the frontiers of biological sciences
Emani, P. S., Warrell, J., Anticevic, A., Bekiranov, S., Gandal, M., McConnell, M. J., Sapiro, G., Aspuru-Guzik, A., Baker, J. T., Bastiani, M., et al. (2021) · Nature Methods · doi:10.1038/s41592-020-01004-3 · Cited by 163
Fundamental limits of quantum error mitigation
Takagi, R., Endo, S., Minagawa, S., & Gu, M. (2022) · npj Quantum Information · doi:10.1038/s41534-022-00618-z · Cited by 206
Quantum adversarial machine learning
Lu, S., Duan, L.-M., & Deng, D.-L. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033212 · Cited by 187
Electric field spectroscopy of material defects in transmon qubits
Lisenfeld, J., Bilmes, A., Megrant, A., Barends, R., Kelly, J., Klimov, P. V., Weiss, G., Martinis, J. M., & Ustinov, A. V. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0224-1 · Cited by 180
Quantum information processing with bosonic qubits in circuit QED
Joshi, A., Noh, K., & Gao, Y. Y. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/abe989 · Cited by 174
Doubling the Size of Quantum Simulators by Entanglement Forging
Eddins, A., Motta, M., Gujarati, T. P., Bravyi, S. B., Mezzacapo, A., Hadfield, C. F., & Sheldon, S. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.010309 · Cited by 181
Self-citationEstimating the gradient and higher-order derivatives on quantum hardware
Mari, A., Bromley, T. R., & Killoran, N. (2021) · Physical Review A · doi:10.1103/physreva.103.012405 · Cited by 159
Perspective: Multireference coupled cluster theories of dynamical electron correlation
Evangelista, F. A. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5039496 · Cited by 162
Is the Trotterized UCCSD Ansatz Chemically Well-Defined?
Grimsley, H. R., Claudino, D., Economou, S. E., Barnes, E., & Mayhall, N. J. (2019) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.9b01083 · Cited by 168
Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design
Luo, X.-Z., Liu, J.-G., Zhang, P., & Wang, L. (2020) · Quantum · doi:10.22331/q-2020-10-11-341 · Cited by 157
Quantum machine learning for electronic structure calculations
Xia, R., & Kais, S. (2018) · Nature Communications · doi:10.1038/s41467-018-06598-z · Cited by 161
IBM’s Qiskit Tool Chain: Working with and Developing for Real Quantum Computers
Wille, R., Meter, R. V., & Naveh, Y. (2019) · Design, Automation, and Test in Europe · doi:10.23919/date.2019.8715261 · Cited by 171
Quantum machine learning for chemistry and physics
Sajjan, M., Li, J., Selvarajan, R., Sureshbabu, S. H., Kale, S. S., Gupta, R., Singh, V., & Kais, S. (2022) · Chemical Society Reviews · doi:10.1039/d2cs00203e · Cited by 173
Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives
Tacchino, F., Chiesa, A., Carretta, S., & Gerace, D. (2019) · Advanced Quantum Technologies · doi:10.1002/qute.201900052 · Cited by 172
Variational quantum state eigensolver
Cerezo, M., Sharma, K., Arrasmith, A., & Coles, P. J. (2022) · npj Quantum Information · doi:10.1038/s41534-022-00611-6 · Cited by 174
Reducing Unitary and Spectator Errors in Cross Resonance with Optimized Rotary Echoes
Sundaresan, N., Lauer, I., Pritchett, E., Magesan, E., Jurcevic, P., & Gambetta, J. M. (2020) · PRX Quantum · doi:10.1103/prxquantum.1.020318 · Cited by 162
Self-citationAjagekar, A., & You, F. (2022) · Renewable and Sustainable Energy Reviews · doi:10.1016/j.rser.2022.112493 · Cited by 164
Application of fermionic marginal constraints to hybrid quantum algorithms
Rubin, N. C., Babbush, R., & McClean, J. (2018) · New Journal of Physics · doi:10.1088/1367-2630/aab919 · Cited by 152
Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges
Fauseweh, B. (2024) · Nature Communications · doi:10.1038/s41467-024-46402-9 · Cited by 152
The Matter Simulation (R)evolution
Aspuru‐Guzik, A., Lindh, R. H., & Reiher, M. (2018) · ACS Central Science · doi:10.1021/acscentsci.7b00550 · Cited by 152
A non-orthogonal variational quantum eigensolver
Huggins, W. J., Lee, J., Baek, U., O’Gorman, B., & Whaley, K. B. (2020) · New Journal of Physics · doi:10.1088/1367-2630/ab867b · Cited by 148
Exponential Error Suppression for Near-Term Quantum Devices
Koczor, B. (2021) · Physical Review X · doi:10.1103/physrevx.11.031057 · Cited by 147
Fluxonium: An Alternative Qubit Platform for High-Fidelity Operations
Bao, F., Deng, H., Ding, D., Gao, R., Gao, X., Huang, C., Xun, J., Ku, H., Li, Z., Ma, X., et al. (2022) · Physical Review Letters · doi:10.1103/physrevlett.129.010502 · Cited by 158
Formulating and Solving Routing Problems on Quantum Computers
Harwood, S., Gambella, C., Trenev, D., Simonetto, A., Bernal Neira, D., & Greenberg, D. (2021) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2021.3049230 · Cited by 145
Qubit-excitation-based adaptive variational quantum eigensolver
(2021) · doi:10.1038/s42005-021-00730-0 · Cited by 145
Group-Invariant Quantum Machine Learning
Larocca, M., Sauvage, F., Sbahi, F. M., Verdon, G., Coles, P. J., & Cerezo, M. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.030341 · Cited by 180
Hybrid quantum-classical algorithms in the noisy intermediate-scale quantum era and beyond
Callison, A., & Chancellor, N. (2022) · Physical Review A · doi:10.1103/physreva.106.010101 · Cited by 172
Compiler Design for Distributed Quantum Computing
Ferrari, D., Cacciapuoti, A. S., Amoretti, M., & Caleffi, M. (2021) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2021.3053921 · Cited by 161
Near-term quantum algorithms for linear systems of equations with regression loss functions
Huang, H.-Y., Bharti, K., & Rebentrost, P. (2021) · New Journal of Physics · doi:10.1088/1367-2630/ac325f · Cited by 193
Gate-Efficient Simulation of Molecular Eigenstates on a Quantum Computer
Ganzhorn, M., Egger, D. J., Barkoutsos, P., Ollitrault, P. J., Salis, G., Moll, N., Roth, M., Fuhrer, A., Mueller, P., Woerner, S., et al. (2019) · Physical Review Applied · doi:10.1103/physrevapplied.11.044092 · Cited by 154
Fermionic Partial Tomography via Classical Shadows
Zhao, A., Rubin, N. C., & Miyake, A. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.110504 · Cited by 169
An Adaptive Optimizer for Measurement-Frugal Variational Algorithms
Kübler, J. M., Arrasmith, A., Cincio, L., & Coles, P. J. (2020) · Quantum · doi:10.22331/q-2020-05-11-263 · Cited by 141
Metadata
- Authors
- Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J. M., & Gambetta, J. M.
- Affiliations
- IBM (United States) (US)
- Corresponding author
- Kandala, Abhinav
- Mezzacapo, Antonio
- ORCID
- Venue
- Nature
- Published
- 2017-09
- Volume
- 549
- Issue
- 7671
- Pages
- 242-246
- ISSN
- 0028-0836 (ISSN-L)
- 1476-4687
- OpenAlex
- W2755255888
- Cited by
- 2,982
- References
- 43
- Citations by year
- 2026: 334 · 2025: 423 · 2024: 439 · 2023: 419 · 2022: 386 · 2021: 405 · 2020: 284 · 2019: 173 · 2018: 101 · 2017: 15
- FWCI
- 93.44
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Nature (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- arXiv (Cornell University)
- 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 › Advanced Chemical Physics Studies
- Keywords
- variational quantum eigensolver, quantum simulation, ground state energy, small molecules, lithium hydride, beryllium hydride, Heisenberg model, quantum magnetism, superconducting qubits, stochastic optimization, quantum chemistry, quantum error correction, noise modeling
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
