Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
Open accessThe 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
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.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The operators b_i_k, b†_i_k can always be mapped to products of Pauli matrices using the Jordan-Wigner transformation.
“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]
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.
“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]
The method maps products of fermionic operators onto nonlocal spin operators via the Jordan-Wigner transformation.
“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]
The Jordan-Wigner mapping 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.
“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]
After the four photons pass through PBS 3, PBS 4 and PBS 5, Hong-Ou-Mandel type interference was observed among the four photons.
“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]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Simulating physics with computers
Feynman, R. P. (1982) · International Journal of Theoretical Physics · doi:10.1007/bf02650179 · Cited by 7,691 · see citing works
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× · see citing works
“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× · see citing works
“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 · see citing works
Locality in Distributed Graph Algorithms
Linial, N. (1992) · SIAM Journal on Computing · doi:10.1137/0221015 · Cited by 870 · see citing works
Suzuki, M. (1990) · Physics Letters A · doi:10.1016/0375-9601(90)90962-n · Cited by 842 · see citing works
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 · see citing works
Self-citationSuzuki, M. (1991) · Journal of Mathematical Physics · doi:10.1063/1.529425 · Cited by 761 · see citing works
Spatial search by quantum walk
Childs, A. M., & Goldstone, J. (2004) · Physical Review A · doi:10.1103/physreva.70.022314 · Cited by 725 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
Flagged first, then by citations
Research works printed but not linked: 7
- [1]Shor, P. W.: Algorithms for quantum computation: Discrete logarithms and factoring. Proc. 35th Symp. on Foundations of Computer Science, 124-134 (1994)
- [9]Ambainis, A.: Quantum walk algorithm for element distinctness. http://arxiv.org/abs/quant-ph/0311001 (2003) · arXiv
- [10]Ambainis, A., Kempe, J., and Rivosh, A.: Coins make quantum walks faster. http://arxiv.org/abs/quant-ph/0402107 (2004) · arXiv
- [11]Farhi, E., Goldstone, J., Gutmann, S., and Sipser, M.: Quantum computation by adiabatic evolution. http://arxiv.org/abs/quant-ph/0001106 (2000) · arXiv
- [14]Childs, A.M.: Quantum information processing in continuous time. Ph.D. Thesis, Massachusetts Institute of Technology, 2004
- [18]Ahokas, G.: Improved algorithms for approximate quantum Fourier transforms and sparse Hamiltonian simulations. M.Sc. Thesis, University of Calgary, 2004
- [20]Nielsen, M.A. and Chuang, I.L.: Quantum Computation and Quantum Information . Cambridge: Cambridge University Press, 2000
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 · see citing works
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 · see citing works
Georgescu, I. M., Ashhab, S., & Nori, F. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.153 · Cited by 2,932 · see citing works
“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 · see citing works
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 · see citing works
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 · see citing works
Quantum principal component analysis
Lloyd, S., Mohseni, M., & Rebentrost, P. (2014) · Nature Physics · doi:10.1038/nphys3029 · Cited by 1,385 · see citing works
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 · see citing works
Optimal Hamiltonian Simulation by Quantum Signal Processing
Low, G. H., & Chuang, I. L. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.010501 · Cited by 770 · see citing works
Elucidating reaction mechanisms on quantum computers
Reiher, M., Wiebe, N., Svore, K. M., Wecker, D., & Troyer, M. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1619152114 · Cited by 745 · see citing works
Simulating Hamiltonian Dynamics with a Truncated Taylor Series
Berry, D. W., Childs, A. M., Cleve, R., Kothari, R., & Somma, R. D. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.090502 · Cited by 742 · see citing works
Self-citationEfficient Variational Quantum Simulator Incorporating Active Error Minimization
Li, Y., & Benjamin, S. C. (2017) · Physical Review X · doi:10.1103/physrevx.7.021050 · Cited by 686 · see citing works
Gilyén, A., Su, Y., Low, G. H., & Wiebe, N. (2019) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/3313276.3316366 · Cited by 685 · see citing works
Toward 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 · see citing works
Theory of Trotter Error with Commutator Scaling
Childs, A. M., Su, Y., Tran, M. C., Wiebe, N., & Zhu, S. (2021) · Physical Review X · doi:10.1103/physrevx.11.011020 · Cited by 545 · see citing works
Quantum Algorithm for Data Fitting
Wiebe, N., Braun, D., & Lloyd, S. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.050505 · Cited by 528 · see citing works
Quantum Algorithms for Quantum Field Theories
Jordan, S. P., Lee, K. S. M., & Preskill, J. P. (2012) · Science · doi:10.1126/science.1217069 · Cited by 511 · see citing works
Simulation of electronic structure Hamiltonians using quantum computers
Whitfield, J. D., Biamonte, J., & Aspuru-Guzik, A. (2011) · Molecular Physics · doi:10.1080/00268976.2011.552441 · Cited by 472 · see citing works
On the Relationship Between Continuous- and Discrete-Time Quantum Walk
Childs, A. M. (2010) · Communications in Mathematical Physics · doi:10.1007/s00220-009-0930-1 · Cited by 411 · see citing works
Adiabatic Quantum Computation Is Equivalent to Standard Quantum Computation
Aharonov, D., van Dam, W., Kempe, J., Landau, Z., Lloyd, S., & Regev, O. (2008) · SIAM Review · doi:10.1137/080734479 · Cited by 395 · see citing works
Polynomial-time quantum algorithm for the simulation of chemical dynamics
Kassal, I., Jordan, S. P., Love, P. J., Mohseni, M., & Aspuru-Guzik, A. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0808245105 · Cited by 385 · see citing works
Hamiltonian Simulation with Nearly Optimal Dependence on all Parameters
Berry, D. W., Childs, A. M., & Kothari, R. (2015) · 2015 IEEE 56th Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2015.54 · Cited by 372 · see citing works
Self-citationVariational Quantum Linear Solver
Bravo-Prieto, C., LaRose, R., Cerezo, M., Subaşı, Y., Cincio, Ł., & Coles, P. J. (2023) · Quantum · doi:10.22331/q-2023-11-22-1188 · Cited by 359 · see citing works
Simulating Chemistry Using Quantum Computers
Kassal, I., Whitfield, J. D., Perdomo-Ortiz, A., Yung, M.-H., & Aspuru-Guzik, A. (2011) · Annual Review of Physical Chemistry · doi:10.1146/annurev-physchem-032210-103512 · Cited by 352 · see citing works
Random Compiler for Fast Hamiltonian Simulation
Campbell, E. T. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.070503 · Cited by 346 · see citing works
Low-Depth Quantum Simulation of Materials
Babbush, R., Wiebe, N., McClean, J., McClain, J., Neven, H., & Chan, G. K.-L. (2018) · Physical Review X · doi:10.1103/physrevx.8.011044 · Cited by 335 · see citing works
Strawberry Fields: A Software Platform for Photonic Quantum Computing
Killoran, N., Izaac, J., Quesada, N., Bergholm, V., Amy, M., & Weedbrook, C. (2019) · Quantum · doi:10.22331/q-2019-03-11-129 · Cited by 327 · see citing works
Exponential improvement in precision for simulating sparse Hamiltonians
Berry, D. W., Childs, A. M., Cleve, R., Kothari, R., & Somma, R. D. (2014) · Proceedings of the forty-sixth annual ACM symposium on Theory of computing · doi:10.1145/2591796.2591854 · Cited by 324 · see citing works
Self-citationEngineered Open Systems and Quantum Simulations with Atoms and Ions
Müller, M., Diehl, S., Pupillo, G., & Zoller, P. (2012) · Advances in atomic, molecular, and optical physics · doi:10.1016/b978-0-12-396482-3.00001-6 · Cited by 323 · see citing works
Can one trust quantum simulators?
Hauke, P., Cucchietti, F. M., Tagliacozzo, L., Deutsch, I., & Lewenstein, M. (2012) · Reports on Progress in Physics · doi:10.1088/0034-4885/75/8/082401 · Cited by 315 · see citing works
Quantum Computer Systems for Scientific Discovery
Alexeev, Y., Bacon, D., Brown, K. R., Calderbank, R., Carr, L. D., Chong, F. T., DeMarco, B., Englund, D. R., Farhi, E., Fefferman, B., et al. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.017001 · Cited by 311 · see citing works
Quantum Algorithm Implementations for Beginners
Jayakumar, A., Adedoyin, A. A., Ambrosiano, J. J., Anisimov, P. M., Casper, W., Chennupati, G., Coffrin, C., Djidjev, H. N., Gunter, D., Karra, S., et al. (2022) · ACM Transactions on Quantum Computing · doi:10.1145/3517340 · Cited by 299 · see citing works
Gate-count estimates for performing quantum chemistry on small quantum computers
Wecker, D., Bauer, B., Clark, B. K., Hastings, M. B., & Troyer, M. (2014) · Physical Review A · doi:10.1103/physreva.90.022305 · Cited by 296 · see citing works
Preconditioned Quantum Linear System Algorithm
Clader, B. D., Jacobs, B. C., & Sprouse, C. R. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.250504 · Cited by 288 · see citing works
High-order quantum algorithm for solving linear differential equations
Berry, D. W. (2014) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/47/10/105301 · Cited by 277 · see citing works
Self-citationQuantum Simulation of Time-Dependent Hamiltonians and the Convenient Illusion of Hilbert Space
Poulin, D., Qarry, A., Somma, R., & Verstraete, F. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.170501 · Cited by 265 · see citing works
Simulating Large Quantum Circuits on a Small Quantum Computer
Peng, T., Harrow, A. W., Ozols, M., & Wu, X. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.150504 · Cited by 264 · see citing works
Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics
Salathé, Y., Mondal, M., Oppliger, M., Heinsoo, J., Kurpiers, P., Potočnik, A., Mezzacapo, A., Heras, U. L., Lamata, L., Solano, E., et al. (2015) · Physical Review X · doi:10.1103/physrevx.5.021027 · Cited by 249 · see citing works
Accelerated Variational Quantum Eigensolver
Wang, D., Higgott, O., & Brierley, S. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.140504 · Cited by 241 · see citing works
Efficient quantum algorithm for dissipative nonlinear differential equations
Liu, J.-P., Kolden, H. Ø., Krovi, H., Loureiro, N., Trivisa, K., & Childs, A. M. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2026805118 · Cited by 241 · see citing works
Variational fast forwarding for quantum simulation beyond the coherence time
Cîrstoiu, C., Holmes, Z., Iosue, J., Cincio, L., Coles, P. J., & Sornborger, A. (2020) · npj Quantum Information · doi:10.1038/s41534-020-00302-0 · Cited by 232 · see citing works
Automated optimization of large quantum circuits with continuous parameters
Nam, Y., Ross, N. J., Su, Y., Childs, A. M., & Maslov, D. (2018) · npj Quantum Information · doi:10.1038/s41534-018-0072-4 · Cited by 221 · see citing works
Berry, D. W., Childs, A. M., Ostrander, A., & Wang, G. (2017) · Communications in Mathematical Physics · doi:10.1007/s00220-017-3002-y · Cited by 218 · see citing works
Self-citationHigher order decompositions of ordered operator exponentials
Wiebe, N., Berry, D., Høyer, P., & Sanders, B. C. (2010) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/43/6/065203 · Cited by 208 · see citing works
Self-citationEntanglement-Based Machine Learning on a Quantum Computer
Cai, X., Wu, D., Su, Z.-E., Chen, M.-C., Wang, X., Li, L., Liu, N.-L., Lu, C., & Pan, J.-W. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.110504 · Cited by 205 · see citing works
Quantum algorithm and circuit design solving the Poisson equation
Cao, Y., Papageorgiou, A., Petras, I., Traub, J., & Kais, S. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/1/013021 · Cited by 204 · see citing works
Poulin, D., & Wocjan, P. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.220502 · Cited by 201 · see citing works
Ciavarella, A. N., Klco, N., & A, M. J. S. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.094501 · Cited by 195 · see citing works
Adiabatic Quantum Simulation of Quantum Chemistry
Babbush, R., Love, P. J., & Aspuru-Guzik, A. (2014) · Scientific Reports · doi:10.1038/srep06603 · Cited by 191 · see citing works
Thermalization in Nature and on a Quantum Computer
Riera, A., Gogolin, C., & Eisert, J. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.080402 · Cited by 189 · see citing works
Faster quantum simulation by randomization
Childs, A. M., Ostrander, A., & Su, Y. (2019) · Quantum · doi:10.22331/q-2019-09-02-182 · Cited by 186 · see citing works
QASMBench: A Low-Level Quantum Benchmark Suite for NISQ Evaluation and Simulation
Li, A., Stein, S., Krishnamoorthy, S., & Ang, J. (2023) · ACM Transactions on Quantum Computing · doi:10.1145/3550488 · Cited by 183 · see citing works
Quantum Algorithms for Systems of Linear Equations Inspired by Adiabatic Quantum Computing
Subaşı, Y., Somma, R. D., & Orsucci, D. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.060504 · Cited by 183 · see citing works
Emerging quantum computing algorithms for quantum chemistry
Motta, M., & Rice, J. E. (2021) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.1580 · Cited by 180 · see citing works
Quantum Hopfield neural network
Rebentrost, P., Bromley, T. R., Weedbrook, C., & Lloyd, S. (2018) · Physical Review A · doi:10.1103/physreva.98.042308 · Cited by 176 · see citing works
Experimental Quantum Computing to Solve Systems of Linear Equations
Cai, X.-D., Weedbrook, C., Su, Z.-E., Chen, M.-C., Gu, M., Zhu, M.-J., Li, L., Liu, N.-L., Lu, C.-Y., & Pan, J.-W. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.230501 · Cited by 173 · see citing works
Standard model physics and the digital quantum revolution: thoughts about the interface
Klco, N., Roggero, A., & A, M. J. S. (2022) · Reports on Progress in Physics · doi:10.1088/1361-6633/ac58a4 · Cited by 173 · see citing works
Nearly Optimal Lattice Simulation by Product Formulas
Childs, A. M., & Su, Y. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.050503 · Cited by 172 · see citing works
A quantum machine learning algorithm based on generative models
Gao, X.-S., Zhang, Z., & Duan, L. (2018) · Science Advances · doi:10.1126/sciadv.aat9004 · Cited by 166 · see citing works
Quantum algorithm for simulating the wave equation
Costa, P. C. S., Jordan, S. P., & Ostrander, A. (2019) · Physical Review A · doi:10.1103/physreva.99.012323 · Cited by 159 · see citing works
Quantum Algorithm for Simulating Real Time Evolution of Lattice Hamiltonians
Haah, J., Hastings, M. B., Kothari, R., & Low, G. H. (2021) · SIAM Journal on Computing · doi:10.1137/18m1231511 · Cited by 155 · see citing works
Quantum Algorithms for Simulating the Lattice Schwinger Model
Shaw, A. F., Lougovski, P., Stryker, J. R., & Wiebe, N. (2020) · Quantum · doi:10.22331/q-2020-08-10-306 · Cited by 155 · see citing works
Dissipative Quantum Church-Turing Theorem
Kliesch, M., Barthel, T., Gogolin, C., Kastoryano, M., & Eisert, J. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.120501 · Cited by 154 · see citing works
Quantum Simulation of Helium Hydride Cation in a Solid-State Spin Register
Wang, Y., Dolde, F., Biamonte, J., Babbush, R., Bergholm, V., Yang, S., Jakobi, I., Neumann, P., Aspuru‐Guzik, A., Whitfield, J. D., et al. (2015) · ACS Nano · doi:10.1021/acsnano.5b01651 · Cited by 147 · see citing works
Quantum algorithm for linear regression
Wang, G. (2017) · Physical Review A · doi:10.1103/physreva.96.012335 · Cited by 145 · see citing works
Quantum annealing initialization of the quantum approximate optimization algorithm
Sack, S. H., & Serbyn, M. (2021) · Quantum · doi:10.22331/q-2021-07-01-491 · Cited by 145 · see citing works
Quantum spin dynamics with pairwise-tunable, long-range interactions
Hung, C.-L., González-Tudela, A., Cirac, J. I., & Kimble, H. J. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1603777113 · Cited by 143 · see citing works
Improved techniques for preparing eigenstates of fermionic Hamiltonians
Berry, D. W., Kieferová, M., Scherer, A., Sanders, Y. R., Low, G. H., Wiebe, N., Gidney, C., & Babbush, R. (2018) · npj Quantum Information · doi:10.1038/s41534-018-0071-5 · Cited by 142 · see citing works
Self-citationQuantum eigenvalue estimation via time series analysis
Somma, R. D. (2019) · New Journal of Physics · doi:10.1088/1367-2630/ab5c60 · Cited by 137 · see citing works
Quantum localization bounds Trotter errors in digital quantum simulation
Heyl, M., Hauke, P., & Zoller, P. (2019) · Science Advances · doi:10.1126/sciadv.aau8342 · Cited by 136 · see citing works
Exponentially more precise quantum simulation of fermions in second quantization
Babbush, R., Berry, D. W., Kivlichan, I. D., Wei, A. Y., Love, P. J., & Aspuru-Guzik, A. (2016) · New Journal of Physics · doi:10.1088/1367-2630/18/3/033032 · Cited by 135 · see citing works
Self-citationQuantum Spectral Methods for Differential Equations
Childs, A. M., & Liu, J.-P. (2020) · Communications in Mathematical Physics · doi:10.1007/s00220-020-03699-z · Cited by 133 · see citing works
Quantum singular-value decomposition of nonsparse low-rank matrices
Rebentrost, P., Steffens, A., Marvian, I., & Lloyd, S. (2018) · Physical Review A · doi:10.1103/physreva.97.012327 · Cited by 132 · see citing works
Noisy intermediate-scale quantum computers
Cheng, B., Deng, X., Gu, X. Q., He, Y., Hu, G., Huang, P., Li, J., Lin, B., Lu, D., Lu, Y., et al. (2023) · Frontiers of Physics · doi:10.1007/s11467-022-1249-z · Cited by 131 · see citing works
Digital lattice gauge theories
Zohar, E., Farace, A., Reznik, B., & Cirac, J. I. (2017) · Physical Review A · doi:10.1103/physreva.95.023604 · Cited by 130 · see citing works
Using Quantum Computers for Quantum Simulation
Brown, K. L., Munro, W. J., & Kendon, V. M. (2010) · Entropy · doi:10.3390/e12112268 · Cited by 129 · see citing works
Approximating Gibbs states of local Hamiltonians efficiently with projected entangled pair states
Molnár, A., Schuch, N., Verstraete, F., & Cirac, J. I. (2015) · Physical Review B · doi:10.1103/physrevb.91.045138 · Cited by 128 · see citing works
Quantum Computation and Quantum InformationPreprint
Wang, Y. (2016) · Cited by 128 · see citing works
Exploiting Locality in Quantum Computation for Quantum Chemistry
McClean, J. R., Babbush, R., Love, P. J., & Aspuru-Guzik, A. (2014) · The Journal of Physical Chemistry Letters · doi:10.1021/jz501649m · Cited by 125 · see citing works
Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions
Casanova, J., Mezzacapo, A., Lamata, L., & Solano, E. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.190502 · Cited by 118 · see citing works
Quantum complexity of time evolution with chaotic Hamiltonians
Balasubramanian, V., DeCross, M. P., Kar, A., & Parrikar, O. (2020) · Journal of High Energy Physics · doi:10.1007/jhep01(2020)134 · Cited by 117 · see citing works
Digital quantum simulation, Trotter errors, and quantum chaos of the kicked top
Sieberer, L. M., Olsacher, T., Elben, A., Heyl, M., Hauke, P., Haake, F., & Zoller, P. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0192-5 · Cited by 116 · see citing works
Quantum machine learning: from physics to software engineering
Melnikov, A. A., Kordzanganeh, M., Alodjants, A. P., & Lee, R. (2023) · Advances in Physics X · doi:10.1080/23746149.2023.2165452 · Cited by 115 · see citing works
Digital Quantum Simulation of Spin Systems in Superconducting Circuits
Heras, U. L., Mezzacapo, A., Lamata, L., Filipp, S., Wallraff, A. J., & Solano, E. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.200501 · Cited by 114 · see citing works
Non-Abelian SU(2) Lattice Gauge Theories in Superconducting Circuits
Mezzacapo, A., Rico, E., Sabín, C., Egusquiza, I. L., Lamata, L., & Solano, E. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.240502 · Cited by 113 · see citing works
Quantum complexity of time evolution with chaotic Hamiltonians
Balasubramanian, V. (2023) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · doi:10.1007/jhep01%282020%29134 · Cited by 113 · see citing works
Molecular Quantum Dynamics: A Quantum Computing Perspective
Ollitrault, P. J., Miessen, A., & Tavernelli, I. (2021) · Accounts of Chemical Research · doi:10.1021/acs.accounts.1c00514 · Cited by 112 · see citing works
Digital Quantum Rabi and Dicke Models in Superconducting Circuits
Mezzacapo, A., Las Heras, U., Pedernales, J. S., DiCarlo, L., Solano, E., & Lamata, L. (2014) · Scientific Reports · doi:10.1038/srep07482 · Cited by 111 · see citing works
Simulating quantum dynamics on a quantum computer
Wiebe, N., Berry, D. W., Høyer, P., & Sanders, B. C. (2011) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/44/44/445308 · Cited by 110 · see citing works
Self-citationTime-dependent Hamiltonian simulation with L 1 -norm scaling
Berry, D. W., Childs, A. M., Su, Y., Wang, X., & Wiebe, N. (2020) · Quantum · doi:10.22331/q-2020-04-20-254 · Cited by 109 · see citing works
Self-citationDigital quantum simulation of lattice gauge theories in three spatial dimensions
Bender, J., Zohar, E., Farace, A., & Cirac, J. I. (2018) · New Journal of Physics · doi:10.1088/1367-2630/aadb71 · Cited by 108 · see citing works
Efficient quantum walk on a quantum processor
Qiang, X., Loke, T., Montanaro, A., Aungskunsiri, K., Zhou, X., O’Brien, J. L., Wang, J. B., & Matthews, J. C. F. (2016) · Nature Communications · doi:10.1038/ncomms11511 · Cited by 108 · see citing works
Quantum-assisted Gaussian process regression
Zhao, Z., Fitzsimons, J., & Fitzsimons, J. F. (2019) · Physical Review A · doi:10.1103/physreva.99.052331 · Cited by 105 · see citing works
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 102 · see citing works
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 101 · see citing works
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 100 · see citing works
Collision Models Can Efficiently Simulate Any Multipartite Markovian Quantum Dynamics
Cattaneo, M., Chiara, G. D., Maniscalco, S., Zambrini, R., & Giorgi, G. L. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.130403 · Cited by 100 · see citing works
Fast-forwarding of Hamiltonians and exponentially precise measurements
Atia, Y., & Aharonov, D. (2017) · Nature Communications · doi:10.1038/s41467-017-01637-7 · Cited by 99 · see citing works
Efficient quantum circuit implementation of quantum walks
Douglas, B. L., & Wang, J. B. (2009) · Physical Review A · doi:10.1103/physreva.79.052335 · Cited by 98 · see citing works
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 98 · see citing works
- 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 › Computer Science › Artificial Intelligence › 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.
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
