The DOI matches its Crossref record; 37 of the 37 references it cites were found in a registry or an index.
Optimal Hamiltonian Simulation by Quantum Signal Processing
Open accessAbstract
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly simulation of physical systems. Surprisingly, this has been challenging, with current Hamiltonian simulation algorithms remaining abstract and often the result of sophisticated but unintuitive constructions. We contend that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation. Specifically, we show that the query complexity of implementing time evolution by a d-sparse Hamiltonian H[over ^] for time-interval t with error ε is O[td∥H[over ^]∥_{max}+log(1/ε)/loglog(1/ε)], which matches lower bounds in all parameters. This connection is made through general three-step "quantum signal processing" methodology, comprised of (i) transducing eigenvalues of H[over ^] into a single ancilla qubit, (ii) transforming these eigenvalues through an optimal-length sequence of single-qubit rotations, and (iii) projecting this ancilla with near unity success probability.
Overview
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
Verification
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.
Citations
Cites
Handbook of Mathematical Functions
McQuarrie, D. A. (1966) · American Journal of Physics · doi:10.1119/1.1972842 · Cited by 40,433
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
W., J. W., Abramowitz, M., & Stegun, I. A. (1965) · Mathematics of Computation · doi:10.2307/2004114 · Cited by 18,663
Simulating physics with computers
Feynman, R. P. (1982) · International Journal of Theoretical Physics · doi:10.1007/bf02650179 · Cited by 7,691
Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J., & Knuth, D. E. (1996) · Advances in Computational Mathematics · doi:10.1007/bf02124750 · Cited by 6,150
Lloyd, S. (1996) · Science · doi:10.1126/science.273.5278.1073 · Cited by 3,088 · cited 3×
“[11] S. Lloyd, Science 273, 1073 (1996).”
BackgroundGeorgescu, I. M., Ashhab, S., & Nori, F. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.153 · Cited by 2,932
A computer program for designing optimum FIR linear phase digital filters
McClellan, J., Parks, T., & Rabiner, L. (1973) · IEEE Transactions on Audio and Electroacoustics · doi:10.1109/tau.1973.1162525 · Cited by 1,139
Universal Computation by Quantum Walk
Childs, A. M. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.180501 · Cited by 1,002
Approximation Theory and Approximation Practice
Trefethen, L. N. (2013) · Cited by 917
Sinc approximation of algebraically decaying functions
Sytnyk, D. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1809.07369 · Cited by 821
Cited by
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 Algorithms for Quantum Chemistry and Quantum Materials Science
Bauer, B., Bravyi, S., Motta, M., & Chan, G. K.-L. (2020) · Chemical Reviews · doi:10.1021/acs.chemrev.9b00829 · Cited by 848
Hamiltonian Simulation by Qubitization
Low, G. H., & Chuang, I. L. (2019) · Quantum · doi:10.22331/q-2019-07-12-163 · Cited by 854
Self-citationToward the first quantum simulation with quantum speedup
Childs, A. M., Maslov, D., Nam, Y., Ross, N. J., & Su, Y. (2018) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1801723115 · Cited by 551
Metadata
- Authors
- Low, G. H., & Chuang, I. L.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2017-01-05
- Volume
- 118
- Issue
- 1
- Pages
- 010501-010501
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2415656260
- Cited by
- 769
- References
- 37
- FWCI
- 21.16
- Type
- journal article
- Language
- en
- Open access
- bronze
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
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Optimal Hamiltonian Simulation by Quantum Signal Processing. https://app.cochat.ai/papers/10.1103/physrevlett.118.010501
- The paper
- Low, G. H., & Chuang, I. L. (2017). Optimal Hamiltonian Simulation by Quantum Signal Processing. Physical Review Letters. https://doi.org/10.1103/physrevlett.118.010501
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
