Quantum computation of eigenvalues within target intervals
Open accessAbstract
There is widespread interest in calculating the energy spectrum of a Hamiltonian, for example to analyze optical spectra and energy deposition by ions in materials. In this study, we propose a quantum algorithm that samples the set of energies within a target energy-interval without requiring good approximations of the target energy-eigenstates. We discuss the implementation of direct and iterative amplification protocols and give resource and runtime estimates. We illustrate initial applications by amplifying excited states on molecular hydrogen.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
A fast quantum mechanical algorithm for database search
Grover, L. K. (1996) · Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96 · doi:10.1145/237814.237866 · Cited by 8,830 · see citing works
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539795293172 · Cited by 8,472 · see citing works
Quantum Mechanics Helps in Searching for a Needle in a Haystack
Grover, L. K. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.325 · Cited by 4,306 · see citing works
Quantum amplitude amplification and estimation
Brassard, G., Høyer, P., Mosca, M., & Tapp, A. (2002) · Contemporary Mathematics · doi:10.1090/conm/305/05215 · Cited by 1,680 · see citing works
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 · see citing works
Self-citationQuantum computations: algorithms and error correction
Kitaev, A. Y. (1997) · Russian Mathematical Surveys · doi:10.1070/rm1997v052n06abeh002155 · Cited by 1,424 · see citing works
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 · see citing works
Self-citationCleve, R., EKERT, A. K., Macchiavello, C., & Mosca, M. (1998) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.1998.0164 · Cited by 1,279 · see citing works
Parrish, R. M., Burns, L. A., Smith, D. G. A., Simmonett, A. C., DePrince, A. E., Hohenstein, E. G., Bozkaya, U., Sokolov, A. Y., Remigio, R. D., Richard, R. M., et al. (2017) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.7b00174 · Cited by 1,253 · see citing works
Quantum computation and decision trees
Farhi, E., & Gutmann, S. (1998) · Physical Review A · doi:10.1103/physreva.58.915 · Cited by 1,215 · see citing works
Psi4: an open‐source ab initio electronic structure program
Turney, J. M., Simmonett, A. C., Parrish, R. M., Hohenstein, E. G., Evangelista, F. A., Fermann, J. T., Mintz, B. J., Burns, L. A., Wilke, J. J., Abrams, M. L., et al. (2011) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.93 · Cited by 1,089 · see citing works
Suzuki, M. (1990) · Physics Letters A · doi:10.1016/0375-9601(90)90962-n · Cited by 842 · see citing works
Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors
Abrams, D. S., & Lloyd, S. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.5162 · Cited by 817 · see citing works
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 · see citing works
Self-citationSuzuki, M. (1991) · Journal of Mathematical Physics · doi:10.1063/1.529425 · Cited by 761 · see citing works
Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
Abrams, D. S., & Lloyd, S. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.2586 · Cited by 745 · see citing works
Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
Berry, D. W., Ahokas, G., Cleve, R., & Sanders, B. C. (2007) · Communications in Mathematical Physics · doi:10.1007/s00220-006-0150-x · Cited by 692 · see citing works
Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states
McClean, J. R., Kimchi-Schwartz, M. E., Carter, J., & de Jong, W. A. (2017) · Physical Review A · doi:10.1103/physreva.95.042308 · Cited by 516 · see citing works
SciNet: Lessons Learned from Building a Power-efficient Top-20 System and Data Centre
Loken, C., Gruner, D., Groer, L., Peltier, R., Bunn, N., Craig, M., Henriques, T., Dempsey, J., Yu, C.-H., Chen, J., et al. (2010) · Journal of Physics Conference Series · doi:10.1088/1742-6596/256/1/012026 · Cited by 493 · see citing works
Variational Quantum Computation of Excited States
Higgott, O., Wang, D., & Brierley, S. (2019) · Quantum · doi:10.22331/q-2019-07-01-156 · Cited by 463 · see citing works
Generalized Unitary Coupled Cluster Wave functions for Quantum Computation
Lee, J., Huggins, W. J., Head-Gordon, M., & Whaley, K. B. (2019) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.8b01004 · Cited by 432 · see citing works
Variational quantum algorithms for discovering Hamiltonian spectra
Jones, T., Endo, S., McArdle, S., Yuan, X., & Benjamin, S. C. (2019) · Physical Review A · doi:10.1103/physreva.99.062304 · Cited by 256 · see citing works
Amplitude estimation without phase estimation
Suzuki, Y., Uno, S., Raymond, R., Tanaka, T., Onodera, T., & Yamamoto, N. (2020) · Quantum Information Processing · doi:10.1007/s11128-019-2565-2 · Cited by 249 · see citing works
Fixed-Point Quantum Search with an Optimal Number of Queries
Yoder, T. J., Low, G. H., & Chuang, I. L. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.210501 · Cited by 223 · see citing works
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 · see citing works
Dobšíček, M., Johansson, G., Shumeiko, V., & Wendin, G. (2007) · Physical Review A · doi:10.1103/physreva.76.030306 · Cited by 208 · see citing works
Low-overhead constructions for the fault-tolerant Toffoli gate
Jones, C. (2013) · Physical Review A · doi:10.1103/physreva.87.022328 · Cited by 200 · see citing works
Quantum Approximate Counting, Simplified
Aaronson, S., & Rall, P. (2019) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611976014.5 · Cited by 128 · see citing works
Five two-qubit gates are necessary for implementing the Toffoli gate
Yu, N., Duan, R., & Ying, M. (2013) · Physical Review A · doi:10.1103/physreva.88.010304 · Cited by 77 · see citing works
Optimal simulation of Deutsch gates and the Fredkin gate
Yu, N., & Ying, M. (2015) · Physical Review A · doi:10.1103/physreva.91.032302 · Cited by 38 · see citing works
Obtaining a linear combination of the principal components of a matrix on quantum computers
Daskin, A. (2016) · Quantum Information Processing · doi:10.1007/s11128-016-1388-7 · Cited by 17 · see citing works
Mean excitation energies for molecular ions
Jensen, P. W. K., Sauer, S. P. A., Oddershede, J., & Sabin, J. R. (2017) · Nuclear Instruments and Methods in Physics Research Section B Beam Interactions with Materials and Atoms · doi:10.1016/j.nimb.2016.12.034 · Cited by 16 · see citing works
Self-citationNew techniques for fault-tolerant decomposition of Multi-Controlled Toffoli gate
Biswal, L., Bhattacharjee, D., Chattopadhyay, A., & Rahaman, H. (2019) · Physical Review A · doi:10.1103/physreva.100.062326 · Cited by 11 · see citing works
Flagged first, then by citations
2 of the 36 references couldn’t be matched to a known paper.
Cited by
Sorted by citations
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 1,726 · see citing works
Self-citationHybrid Quantum-Classical Algorithms and Quantum Error Mitigation
Endo, S., Cai, Z., Benjamin, S. C., & Yuan, X. (2021) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.90.032001 · Cited by 566 · see citing works
A feasible approach for automatically differentiable unitary coupled-cluster on quantum computers
Kottmann, J. S., Anand, A., & Aspuru‐Guzik, A. (2021) · Chemical Science · doi:10.1039/d0sc06627c · Cited by 80 · see citing works
Self-citationKottmann, J. S., & Aspuru‐Guzik, A. (2022) · Physical Review A · doi:10.1103/physreva.105.032449 · Cited by 42 · see citing works
Self-citationFaster Coherent Quantum Algorithms for Phase, Energy, and Amplitude Estimation
Rall, P. (2021) · Quantum · doi:10.22331/q-2021-10-19-566 · Cited by 39 · see citing works
State Preparation Boosters for Early Fault-Tolerant Quantum Computation
Wang, G., Sim, S., & Johnson, P. D. (2022) · Quantum · doi:10.22331/q-2022-10-06-829 · Cited by 21 · see citing works
Jensen, P. W. K., Kjellgren, E. R., Reinholdt, P., Ziems, K. M., Coriani, S., Kongsted, J., & Sauer, S. P. A. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.4c00069 · Cited by 19 · see citing works
Self-citationQuantum computation for predicting electron and phonon properties of solids
Choudhary, K. (2021) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/ac1154 · Cited by 11 · see citing works
Efficient Quantum Algorithm for Filtering Product States
Irmejs, R., Bañuls, M. C., & Cirac, J. I. (2024) · Quantum · doi:10.22331/q-2024-06-27-1389 · Cited by 9 · see citing works
Sakuma, R., Wada, K., Kanno, S., Keithley, K., Sugisaki, K., Abe, T., Nakamura, H., & Yamamoto, N. (2025) · Physical Review A · doi:10.1103/m85k-7q32 · Cited by 5 · see citing works
Jensen, P. W. K., Johnson, P. D., & Kunitsa, A. A. (2023) · Physical Review A · doi:10.1103/physreva.108.022422 · Cited by 4 · see citing works
Self-citationQuantum computation of the electronic structure of some prototype solids
Khandelwal, N., Verma, N., Jamdagni, P., & Kumar, A. (2025) · Scientific Reports · doi:10.1038/s41598-025-27675-6 · Cited by 2 · see citing works
Short proof of a spectral Chernoff bound for local HamiltoniansPreprint
Abrahamsen, N. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2009.04993
- Authors
- Jensen, P. W. K., Kristensen, L. B., Kottmann, J. S., & Aspuru-Guzik, A.
- Affiliations
- University of Toronto (CA)
- Aarhus University (DK)
- Corresponding author
- Jensen, Phillip W K
- Kristensen, Lasse Bjørn
- Kottmann, Jakob S
- Venue
- Quantum Science and Technology
- Publisher
- IOP Publishing
- Published
- 2020-11-10
- Volume
- 6
- Issue
- 1
- Pages
- 015004
- ISSN
- 2058-9565 (ISSN-L)
- OpenAlex
- W3029159576
- Cited by
- 13
- References
- 36
- Citations by year
- 2025: 2 · 2024: 2 · 2023: 1 · 2022: 3 · 2021: 4 · 2020: 1
- FWCI
- 0.88
- Type
- journal article
- Language
- en
- Open access
- green
- pure.au.dk
- Licence
- Locations
- Quantum Science and Technology (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OPUS (Augsburg University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy (DE-AC02-05CH11231)
- Carlsbergfondet
- 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 › Quantum Mechanics and Applications
- Keywords
- quantum algorithms, energy spectrum, eigenvalue computation, excited states, molecular hydrogen, resource estimation, execution time prediction
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
