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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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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
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 ›
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