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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“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
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“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
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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
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The Complexity of the Local Hamiltonian Problem
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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
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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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