The DOI matches its Crossref record; 44 of the 44 references it cites were found in a registry or an index.
Variational Quantum Computation of Excited States
Open accessAbstract
The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational quantum eigenvalue solver (VQE), have been used to determine ground state energies, methods for calculating excited states currently involve the implementation of high-depth controlled-unitaries or a large number of additional samples. Here we show how overlap estimation can be used to deflate eigenstates once they are found, enabling the calculation of excited state energies and their degeneracies. We propose an implementation that requires the same number of qubits as VQE and at most twice the circuit depth. Our method is robust to control errors, is compatible with error-mitigation strategies and can be implemented on near-term quantum computers.
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“In fact, amplifying the noise strength (that is increasing the quantity s ), deteriorates the solution quality.”
From Variational quantum algorithms (2021) · cites this paper as [106]
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“Due to the presence of hardware noise the estimated energy ˜ E G has a gap with the true energy.”
From Variational quantum algorithms (2021) · cites this paper as [106]
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“The VQE algorithm can be used to estimate the ground state energy E G of a molecule.”
From Variational quantum algorithms (2021) · cites this paper as [106]
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“Combined with the unitary coupled-cluster ansatz, the orthogonally constrained VQE can find excited states of small molecules (Higgott et al. , 2019; Lee et al. , 2018).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Higgott et al. , 2019
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“For example, a recent paper 381 initiated the use of low-rank tensor decompositions for improving the performance of certain quantum algorithms for chemistry simulation.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [381]
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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 · cited 4×
“a folded spectrum method [30] which requires finding the expectation of the squared Hamiltonian with quadratically more terms, or symmetrybased methods which are non-systematic [23].”
BackgroundMethodInfluential
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Variational quantum algorithms
Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S. C., Endo, S., Fujii, K., McClean, J. R., Mitarai, K., Yuan, X., Cincio, L., et al. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00348-9 · Cited by 3,385
“Then, H ′ = H + a|ψ̃G〉〈ψ̃G| is a Hamiltonian whose ground state is the first excited state of H [90].”
Noisy intermediate-scale quantum algorithms
Bharti, K., Cervera-Lierta, A., Kyaw, T. H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J. S., Menke, T., et al. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.015004 · Cited by 2,231
Quantum computational chemistry
McArdle, S., Endo, S., Aspuru-Guzik, A., Benjamin, S. C., & Yuan, X. (2020) · Reviews of Modern Physics · doi:10.1103/revmodphys.92.015003 · Cited by 1,621
Quantum Chemistry in the Age of Quantum Computing
Cao, Y., Romero, J., Olson, J. P., Degroote, M., Johnson, P. D., Kieferová, M., Kivlichan, I. D., Menke, T., Peropadre, B., Sawaya, N. P. D., et al. (2019) · Chemical Reviews · doi:10.1021/acs.chemrev.8b00803 · Cited by 1,560
Quantum Chemistry in the Age of Quantum Computing
Cao, Y., Romero, J., Olson, J., Degroote, M., Johnson, P., Kieferová, M., Kivlichan, I., Menke, T., Peropadre, B., Sawaya, N., et al. (n.d.) · OPUS - Open Publications of UTS Scholars (University of Technology Sydney) · Cited by 1,265
Metadata
- Authors
- Higgott, O., Wang, D., & Brierley, S.
- Affiliations
- Riverlane (United Kingdom) (GB)
- Venue
- Quantum
- Published
- 2019-07-01
- Volume
- 3
- Pages
- 156
- ISSN
- 2521-327X (ISSN-L)
- OpenAlex
- W2803208764
- Cited by
- 463
- References
- 44
- Citations by year
- 2026: 48 · 2025: 68 · 2024: 69 · 2023: 68 · 2022: 69 · 2021: 83 · 2020: 42 · 2019: 14
- FWCI
- 23.46
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Quantum (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University) (cc-by)
- 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
- excitation energies, circuit depth, control error, error mitigation, near-term quantum devices
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