On the Efficiency of Quantum Algorithms for Hamiltonian Simulation

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E. Farhi, J. Goldstone, S. Gutmann, M. Sipser, Quantum computation by adiabatic evolution, quant-ph/0001106 (2000)

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M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, UK, 2000

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A. Childs, E. Farhi, S. Gutmann, An example of the difference between quantum and classical random walks, J. Quant. Inf. Proc. 1, 35-43 (2002)

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D. Aharonov, A. Ta-Shma, Adiabatic quantum state generation and statistical zero knowledge, Proc. 35th Annual ACM Symp. on Theory of Computing, 20-29 (2003)

2003

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D. W. Berry, G. Ahokas, R. Cleve, B. C. Sanders, Efficient quantum algorithms for simulating sparse Hamiltonians, Communications in Mathematical Physics 270, 359 (2007)

E. Farhi, J. Goldstone, S. Gutmann, A Quantum Algorithm for the Hamiltonian NAND Tree, quant-ph/0702144 (2007)

2007

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I. Kassal, S. P. Jordan, P. J. Love, M. Mohseni, A. Aspuru-Guzik, Polynomial-time quantum algorithm for the simulation of chemical dynamics, Proc. Natl. Acad. Sci. 105, 18681(2008)

2008

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A. Childs, On the relationship between continuous- and discrete-time quantum walk, quant-ph/0810.0312 (2008)

2008

Later among the works it cites.

A. Childs, Universal computation by quantum walk, Phys. Rev. Lett., 102, 180501 (2009)

2009

Later among the works it cites.

N. Wiebe, D. Berry, P. Hoyer, B. C. Sanders, Higher order decompositions of ordered operator exponentials, J. Phys. A: Math. Theor., 43, 065203 (2010)

2010

Closest in time.