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Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
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“The operators b i k , b † i k can always be mapped to products of Pauli matrices, i.e., nonlocal spin operators, using the Jordan-Wigner transformation”
From Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions (2012) · cites this paper as [28]
In the citing paper
“Only in one spatial dimension, and for couplings extended to a reduced number of neighbors, the correspondence is from a local model to a similar one [28].”
From Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions (2012) · cites this paper as [28]
In the citing paper
“We map products of fermionic operators onto nonlocal spin operators and decompose the resulting dynamics in efficient steps with Trotter methods, yielding an overall protocol that employs only polynomial resources.”
From Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions (2012) · cites this paper as [28]
In the citing paper
“This technique establishes a correspondence between a set of fermionic operators and a set of spin operators, transforming a local Hamiltonian of fermions onto a nonlocal Hamiltonian of spins.”
From Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions (2012) · cites this paper as [28]
In the citing paper
“After the four photons pass through PBS 3 , PBS 4 and PBS 5 , we observed the Hong-Ou-Mandel type interference among the four photons [20, 21].”
From Experimental Quantum Computing to Solve Systems of Linear Equations (2013) · cites this paper as [20]
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Zhao, Z., Fitzsimons, J. K., & Fitzsimons, J. (2015) · Physical Review A · doi:10.1103/physreva.99.052331 · Cited by 124
An improved quantum algorithm for ridge regression
Yu, C., Gao, F., & Wen, Q. (2019) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2019.2937491 · Cited by 106
Alexeev, Y., Amsler, M., Barroca, M. A., Bassini, S., Battelle, T., Camps, D., Casanova, D., Choi, Y. J., Chong, F. T., Chung, C., et al. (2024) · Future Generation Computer Systems · doi:10.1016/j.future.2024.04.060 · Cited by 138
Calculating energy derivatives for quantum chemistry on a quantum computer
O’Brien, T. E., Senjean, B., Sagastizabal, R., Bonet-Monroig, X., Dutkiewicz, A., Buda, F., DiCarlo, L., & Visscher, L. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0213-4 · Cited by 108
Collision Models Can Efficiently Simulate Any Multipartite Markovian Quantum Dynamics
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Fast-forwarding of Hamiltonians and exponentially precise measurements
Atia, Y., & Aharonov, D. (2017) · Nature Communications · doi:10.1038/s41467-017-01637-7 · Cited by 120
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Bauman, N. P., Bylaska, E. J., Krishnamoorthy, S., Low, G. H., Wiebe, N., Granade, C., Roetteler, M., Troyer, M., & Kowalski, K. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5094643 · Cited by 103
Metadata
- Authors
- Berry, D. W., Ahokas, G., Cleve, R., & Sanders, B. C.
- Affiliations
- The University of Queensland (AU)
- University of Calgary (CA)
- University of Waterloo (CA)
- Venue
- Communications in Mathematical Physics
- Published
- 2006-12-14
- Volume
- 270
- Issue
- 2
- Pages
- 359-371
- ISSN
- 0010-3616 (ISSN-L)
- 1432-0916
- OpenAlex
- W2064906820
- Cited by
- 692
- References
- 15
- Citations by year
- 2026: 47 · 2025: 109 · 2024: 83 · 2023: 95 · 2022: 54 · 2021: 63 · 2020: 38 · 2019: 36 · 2018: 23 · 2017: 22 · 2016: 14 · 2015: 18 · 2014: 23 · 2013: 14 · 2012: 18
- FWCI
- 6.09
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Communications in Mathematical Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- 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 simulation, sparse Hamiltonians, quantum algorithms, quantum state evolution, sublinear time complexity, time complexity lower bounds
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.
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