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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Amplifying the noise strength deteriorates the solution quality.
“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]
Section 6, “Error accumulation” (page unavailable), studies VQD with sampling error, and the following results passage reports that the fifth excited state needs more samples to achieve chemical accuracy. This supports a narrower connection between sampling error and solution accuracy, but the paper does not identify a noise-strength parameter s or show that increasing it deteriorates solution quality. (LLM, conf=0.76)
Experimental — accuracy not yet measuredDue to the presence of hardware noise, the estimated energy E_G has a gap with the true energy.
“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]
Section 6, “Error accumulation” (page unavailable), says an inexact ground-state estimate can produce an energy error relative to the true value. Appendix F, “Error mitigation” (page unavailable), discusses bit-flip and two-qubit errors affecting energy measurements. The copy does not specifically establish hardware noise as the cause of the stated gap in ground-state energy. (LLM, conf=0.83)
Experimental — accuracy not yet measuredThe VQE algorithm can be used to estimate the ground state energy E_G of a molecule.
“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]
Orthogonally constrained VQE combined with the unitary coupled-cluster ansatz can find excited states of small molecules.
“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
A recent paper initiated the use of low-rank tensor decompositions for improving the performance of certain quantum algorithms for chemistry simulation.
“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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- 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 · 2018: 2
- 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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