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.
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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
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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
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Franken, L., Georgiev, B., Mücke, S., Wolter, M., Heese, R., Bauckhage, C., & Piatkowski, N. (2022) · IEEE Congress on Evolutionary Computation (CEC) · doi:10.1109/cec55065.2022.9870269 · Cited by 21
Advances in Quantum Computation and Quantum Technologies: A Design Automation Perspective
Micheli, G. D., Jiang, J.-H. R., Rand, R. W., Smith, K. N., & Soeken, M. (2022) · IEEE Journal on Emerging and Selected Topics in Circuits and Systems · doi:10.1109/jetcas.2022.3205174 · Cited by 23
The Potential of Quantum Computing for Geoscience
Sahimi, M., & Tahmasebi, P. (2022) · Transport in Porous Media · doi:10.1007/s11242-022-01855-8 · Cited by 22
Augmenting QAOA Ansatz with Multiparameter Problem-Independent Layer
Chalupnik, M., Melo, H., Alexeev, Y., & Galda, A. (2022) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce53715.2022.00028 · Cited by 27
Finite-size criticality in fully connected spin models on superconducting quantum hardware
Grossi, M., Kiss, O., Luca, F. D., Zollo, C., Gremese, I., & Mandarino, A. (2023) · Physical review. E · doi:10.1103/physreve.107.024113 · Cited by 23
Scalable flux controllers using adiabatic superconductor logic for quantum processors
Takeuchi, N., Yamae, T., Luo, W., Hirayama, F., Yamamoto, T., & Yoshikawa, N. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.013145 · Cited by 21
Energy-Efficient Cluster Head Selection via Quantum Approximate Optimization
Choi, J., Oh, S., & Kim, J. (2020) · Electronics · doi:10.3390/electronics9101669 · Cited by 20
Quantum Information and Computation for Chemistry
Olson, J., Cao, Y., Romero, J., Johnson, P., Dallaire-Demers, P.-L., Sawaya, N., Narang, P., Kivlichan, I., Wasielewski, M., & Aspuru-Guzik, A. (2017) · arXiv · doi:10.48550/arxiv.1706.05413 · Cited by 15
“These demonstrations were followed by the demonstration of VQE with a hardware-based ansatz for to H 2 , lithium hydride (LiH) and beryllium hydride (BeH 2 ) in a system with six qubits (Kandala et al., 2017) by the IBM quantum computing team.”
MethodDevelopment of transmon qubits solely from optical lithography on 300 mm wafers
Foroozani, N., Hobbs, C., Hung, C. C., Olson, S., Ashworth, D., Holland, E., Malloy, M., Kearney, P., O’Brien, B., Bunday, B., et al. (2019) · Quantum Science and Technology · doi:10.1088/2058-9565/ab0ca8 · Cited by 13
Quinones, M. P., & Junqueira, C. (2020) · arXiv · doi:10.48550/arxiv.2007.13245 · Cited by 6
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
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