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Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
Open accessAbstract
We construct quantum circuits that exactly encode the spectra of correlated electron models up to errors from rotation synthesis.By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use quantum phase estimation to sample states in the Hamiltonian eigenbasis with optimal query complexity Oðλ=ϵÞ, where λ is an absolute sum of Hamiltonian coefficients and ϵ is the target precision.For both the Hubbard model and electronic structure Hamiltonian in a second quantized basis diagonalizing the Coulomb operator, our circuits have T-gate complexity O(N þ logð1=ϵÞ), where N is the number of orbitals in the basis.This scenario enables sampling in the eigenbasis of electronic structure Hamiltonians with T complexity O(N 3 =ϵ þ N 2 logð1=ϵÞ=ϵ).Compared to prior approaches, our algorithms are asymptotically more efficient in gate complexity and require fewer T gates near the classically intractable regime.Compiling to surface code fault-tolerant gates and assuming per-gate error rates of one part in a thousand reveals that one can error correct phase estimation on interesting instances of these problems beyond the current capabilities of classical methods using only about a million superconducting qubits in a matter of hours.
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“Using Babbush et al.'s QROM read (section 3A of [2]), each table lookup has a Toffoli count and measurement depth of 2 c mul + c exp and uses a negligible O ( c mul + c exp ) ancillae.”
From How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits (2021) · cites this paper as [2]
Experimental — accuracy not yet measuredIn the citing paper
“Crosson et al. 298 demonstrated that this effect is common even for instances that do not exhibit noticeable symmetries.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [298]
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“Note that it is not always necessary to reach the adiabatic regime to achieve a significant overlap with the ground state.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [298]
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Fowler, A. G. (2013) · arXiv · doi:10.48550/arxiv.1310.0863 · Cited by 36
Self-citationHybrid grid/basis set discretizations of the Schrödinger equation
White, S. R. (2017) · The Journal of Chemical Physics · doi:10.1063/1.5007066 · Cited by 30
Representation and design of wavelets using unitary circuits
Evenbly, G., & White, S. R. (2018) · Physical Review A · doi:10.1103/physreva.97.052314 · Cited by 28
Imaginary time density-density correlations for two-dimensional electron gases at high density
Motta, M., Galli, D. E., Moroni, S., & Vitali, E. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4934666 · Cited by 27
ROM-based computation: quantum versus classical
Travaglione, B. C., Nielsen, M. A., Wiseman, H. M., & Ambainis, A. (2002) · Quantum Information and Computation · doi:10.26421/qic2.4-5 · Cited by 23
Synthesis of Arbitrary Quantum Circuits to Topological Assembly: Systematic, Online and Compact
Paler, A., Fowler, A. G., & Wille, R. (2017) · Scientific Reports · doi:10.1038/s41598-017-10657-8 · Cited by 18
Self-citationHardware-efficient Quantum Optimizer for Small Molecules and Quantum MagnetsPreprint
Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Chow, J. M., & Gambetta, J. (2017) · arXiv (Cornell University) · Cited by 12
Low-overhead surface code logical Hadamard
Fowler, A. G. (2012) · Quantum Information and Computation · doi:10.26421/qic12.11-12-5 · Cited by 11
Self-citationA constrained path auxiliary-field quantum Monte Carlo method for the homogeneous electron gas
Wilson, M. T., & Gyorffy, B. (1995) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/7/28/001 · Cited by 8
Low-overhead surface code logical HPreprint
Fowler, A. G. (2012) · arXiv (Cornell University) · Cited by 7
Self-citation
Flagged first, then by citations
2 of the 118 references couldn’t be matched to a known paper.
Research works printed but not linked: 2
- X. Fu, 2017, Proceedings of the 50th Annual IEEE/ACM International Symposium on Microarchitecture, Cambridge, Massachusetts, 2017
- D. Aharonov, 2003, Proceedings of the 35th ACM Symposium on Theory of Computing—STOC ’03
Cited by
Sorted by citations
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
Self-citationQuantum 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
The Variational Quantum Eigensolver: A review of methods and best practices
Tilly, J., Chen, H., Cao, S., Picozzi, D., Setia, K., Li, Y., Grant, E., Wossnig, L., Rungger, I., Booth, G. H., et al. (2022) · Physics Reports · doi:10.1016/j.physrep.2022.08.003 · Cited by 1,031
Metadata
- Authors
- Babbush, R., Gidney, C., Berry, D. W., Wiebe, N., McClean, J., Paler, A., Fowler, A., & Neven, H.
- Affiliations
- Google (United States) (US)
- Macquarie University (AU)
- Microsoft (United States) (US)
- ORCID
- Venue
- Physical Review X
- Publisher
- American Physical Society (APS)
- Published
- 2018-10-23
- Volume
- 8
- Issue
- 4
- ISSN
- 2160-3308 (ISSN-L)
- OpenAlex
- W2801305581
- Cited by
- 383
- References
- 118
- Citations by year
- 2026: 45 · 2025: 82 · 2024: 52 · 2023: 49 · 2022: 43 · 2021: 41 · 2020: 35 · 2019: 32 · 2018: 4
- FWCI
- 15.90
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Physical Review X (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Funders
- Australian Research Council (DP160102426)
- 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 Information and Cryptography
- Keywords
- quantum circuits, qubitization, quantum phase estimation, Hubbard model, superconducting qubits, query complexity, correlated electrons
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.
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