The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
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In the citing paper
“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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Citations
Cites
Simulating physics with computers
Feynman, R. P. (1982) · International Journal of Theoretical Physics · doi:10.1007/bf02650179 · Cited by 7,691
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 · cited 1×
“There are three main applications of quantum computer algorithms: the hidden subgroup problem, with Shor’s factorization algorithm one important example [1], search problems [2], and simulation of quantum systems [3, 4].”
Lloyd, S. (1996) · Science · doi:10.1126/science.273.5278.1073 · Cited by 3,088 · cited 4×
“Here we apply the higher-order integrators of Suzuki [12, 13] to reduce the temporal scaling from t 3 / 2 [5] or t 2 [4] to the slightly superlinear scaling t 1+1 / 2 k , where k is the order of the integrator and may be an arbitrarily large integer.”
BackgroundMethodInfluentialQuantum random-walk search algorithm
Shenvi, N., Kempe, J., & Whaley, K. B. (2003) · Physical Review A · doi:10.1103/physreva.67.052307 · Cited by 1,150
Locality in Distributed Graph Algorithms
Linial, N. (1992) · SIAM Journal on Computing · doi:10.1137/0221015 · Cited by 870
Suzuki, M. (1990) · Physics Letters A · doi:10.1016/0375-9601(90)90962-n · Cited by 842
Exponential algorithmic speedup by a quantum walk
Childs, A. M., Cleve, R., Deotto, E., Farhi, E., Gutmann, S., & Spielman, D. A. (2003) · Proceedings of the thirty-fifth annual ACM symposium on Theory of computing · doi:10.1145/780542.780552 · Cited by 825
Self-citationSuzuki, M. (1991) · Journal of Mathematical Physics · doi:10.1063/1.529425 · Cited by 761
Spatial search by quantum walk
Childs, A. M., & Goldstone, J. (2004) · Physical Review A · doi:10.1103/physreva.70.022314 · Cited by 725
The Complexity of the Local Hamiltonian Problem
Kempe, J., Kitaev, A., & Regev, O. (2006) · SIAM Journal on Computing · doi:10.1137/s0097539704445226 · Cited by 648
Quantum lower bounds by polynomials
Beals, R., Buhrman, H., Cleve, R., Mosca, M., & de Wolf, R. (2001) · Journal of the ACM · doi:10.1145/502090.502097 · Cited by 639
Self-citationAn Example of the Difference Between Quantum and Classical Random Walks
Childs, A. M., Farhi, E., & Gutmann, S. (2002) · Quantum Information Processing · doi:10.1023/a:1019609420309 · Cited by 481
Deterministic coin tossing with applications to optimal parallel list ranking
Cole, R. J., & Vishkin, U. (1986) · Information and Control · doi:10.1016/s0019-9958(86)80023-7 · Cited by 413
Adiabatic quantum state generation and statistical zero knowledge
Aharonov, D., & Ta-Shma, A. (2003) · Proceedings of the thirty-fifth annual ACM symposium on Theory of computing · doi:10.1145/780542.780546 · Cited by 322
Limit on the Speed of Quantum Computation in Determining Parity
Farhi, E., Goldstone, J., Gutmann, S., & Sipser, M. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.5442 · Cited by 175
Flagged first, then by citations
Research works printed but not linked: 6
- Shor, P. W.: Algorithms for quantum computation: Discrete logarithms and factoring. In: Proc. 35th Symp. on Foundations of Computer Science, Los Alamitos, CA:IEEE, 1994, pp. 124–134
- Ambainis, A.: Quantum walk algorithm for element distinctness. In: Proc. 45th Symp. on Foundations of Computer Science, Los Alamitos, CA: IEEE, 2004, pp. 22–31
- Ambainis, A., Kempe, J., Rivosh, A.: Coins make quantum walks faster. In: Proc. 16th ACM-SIAM SODA, Philadelphia, PA:SIAM, 2005, pp. 1099–1108
- Childs A.M. Quantum information processing in continuous time. Ph.D. Thesis, Massachusetts Institute of Technology, 2004
- Ahokas, G.: Improved algorithms for approximate quantum Fourier transforms and sparse Hamiltonian simulations. M.Sc. Thesis, University of Calgary, 2004
- Nielsen M.A., Chuang I.L., (2000) Quantum Computation and Quantum Information. Cambridge, Cambridge University Press
Cited by
Sorted by citations
A variational eigenvalue solver on a photonic quantum processor
Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P. J., Aspuru-Guzik, A., & O’Brien, J. L. (2014) · Nature Communications · doi:10.1038/ncomms5213 · Cited by 4,552
Quantum Algorithm for Linear Systems of Equations
Harrow, A. W., Hassidim, A., & Lloyd, S. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.150502 · Cited by 3,325
Georgescu, I. M., Ashhab, S., & Nori, F. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.153 · Cited by 2,932
“This question has been thoroughly studied, and several methods have been developed (see, e.g., (Berry et al., 2007; Bravyi et al., 2008; Bremner et al., 2005; Brown et al., 2011; Dodd et al., 2002; Dür et al., 2008; Hastings, 2006; Wang and Zanardi, 2002; Wocjan et al., 2002a,b,c)), but it still…”
MethodQuantum Support Vector Machine for Big Data Classification
Rebentrost, P., Mohseni, M., & Lloyd, S. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.130503 · Cited by 1,951
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
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
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