Black-box Hamiltonian simulation and unitary implementation

G. Strang, On the construction and comparison of difference schemes , SIAM J. Numer. Anal. 5

1968

Earlier work this paper cites.

R. P. Feynman, Simulating physics with computers , International Journal of Theoretical Physics 21

1982

Earlier work this paper cites.

M. Suzuki, Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations , Phys. Lett. A 146

1990

Earlier work this paper cites.

M. Suzuki, General theory of fractal path integrals with applications to many-body theories and statistical physics , J. Math. Phys. 32

1991

Earlier work this paper cites.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Experimental realization of any discrete unitary operator , Phys. Rev. Lett. 73

1994

Earlier work this paper cites.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, and H. Weinfurter, Elementary gates for quantum computation , Phys. Rev. A 52

1995

Earlier work this paper cites.

E. Knill, Approximation by quantum circuits , Technical Report LAUR-95-2225, Los Alamos National Laboratory, 1995; arXiv:quant-ph/9508006

1995

Earlier work this paper cites.

S. Lloyd, Universal quantum simulators , Science 273

1996

Earlier work this paper cites.

L. K. Grover, A fast quantum mechanical algorithm for database search , in Proceedings of the 28th Annual ACM Symposium on Theory of Computing (ACM, New York, 1996), pp. 212–219; arXiv:quant-ph/9605043

1996

Earlier work this paper cites.

A. Y. Kitaev, Quantum computations: Algorithms and error correction , Russ. Math. Surveys 52

1997

Earlier work this paper cites.

C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani, Strengths and weaknesses of quantum computing , SIAM J. Comput. 26

1997

Cited alongside, same era.

G. Brassard and P. Høyer, An exact quantum polynomial-time algorithm for Simon’s problem , in Proceedings of Fifth Israeli Symposium on Theory of Computing and Systems (IEEE, Los Alamitos, CA, 1997), pp. 12–23; arXiv:quant-ph/9704027

1997

Cited alongside, same era.

L. K. Grover, Quantum computers can search rapidly by using almost any transformation , Phys. Rev. Lett. 80

1998

Cited alongside, same era.

L. K. Grover, Synthesis of quantum superpositions by quantum computation , Phys. Rev. Lett. 85

2000

Cited alongside, same era.

A. Y. Kitaev, A. H. Shen, and M. N. Vyalyi, Classical and Quantum Computation , Graduate Studies in Mathematics Vol. 47 (American Mathematical Society, Providence, RI, 2002)

M. Szegedy, Quantum speed-up of Markov chain based algorithms , Proceedings of the 45th IEEE Symposium on Foundations of Computer Science (IEEE, Los Alamitos, CA, 2004), pp. 32–41; arXiv:quant-ph/0401053

2004

Later among the works it cites.

D. W. Berry, G. Ahokas, R. Cleve, and B. C. Sanders, Efficient quantum algorithms for simulating sparse Hamiltonians , Commun. Math. Phys. 270

2007

Later among the works it cites.

E. Farhi, J. Goldstone, and S. Gutmann, A quantum algorithm for the Hamiltonian NAND tree , Theory of Computing 4

2008

Later among the works it cites.

A. M. Childs, R. Cleve, S. P. Jordan, and D. Yonge-Mallo, Discrete-query quantum algorithm for NAND trees , Theory of Computing 5

2009

Closest in time.

A. W. Harrow, A. Hassidim, and S. Lloyd, Quantum algorithm for linear systems of equations , Phys. Rev. Lett. 103

2009