Efficient quantum algorithms for simulating sparse hamiltonians

Communications in Mathematical Physics

Volumn 270, Issue 2, 2007, Pages 359-371

  Berry, Dominic W ^a,b   Ahokas, Graeme ^b   Cleve, Richard ^b,c   Sanders, Barry C ^b,d  

^a UNIVERSITY OF QUEENSLAND   (Australia)

^b UNIVERSITY OF CALGARY   (Canada)

^c UNIVERSITY OF WATERLOO   (Canada)

^d MACQUARIE UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846486283     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-006-0150-x     Document Type: Article

References (21)

1. 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
2. Grover, L.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325-328 (1997)
3. Kempe, J., Kitaev, A., Regev, O.: The complexity of the local Hamiltonian problem. SIAM J. Computing 35, 1070-1097 (2006)
4. Feynman, R.P.: Simulating physics with computers. Int. J. Theoret. Phys. 21, 467-488 (1982)
5. Lloyd, S.: Universal quantum simulators. Science 273, 1073-1078 (1996)
6. Aharonov, D., Ta-Shma, A.: Adiabatic quantum state generation and statistical zero knowledge. In: Proc. 35th Annual ACM Symp. on Theory of Computing, New York:ACM, 2003, pp. 20-29
7. Childs, A., Farhi, E., Gutmann, S.: An example of the difference between quantum and classical random walks. J. Quant. Inf. Proc. 1, 35-43 (2002)
8. Shenvi, N., Kempe, J., Whaley, K.B.: Quantum random-walk search algorithm. Phys. Rev. A 67, 052307 (2003)
9. Childs, A., Goldstone, J.: Spatial search by quantum walk. Phys. Rev. A 70, 022314 (2004)
10. 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
11. Ambainis, A., Kempe, J., Rivosh, A.: Coins make quantum walks faster. In: Proc. 16th ACM-SIAM SODA, Philadelphia, PA:SIAM, 2005, pp. 1099-1108
12. Suzuki, M.: Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations. Phys. Lett. A 146, 319-323 (1990)
13. Suzuki, M.: General theory of fractal path integrals with applications to many-body theories and statistical physics. J. Math. Phys. 32, 400-407 (1991)
14. Childs, A.M.: Quantum information processing in continuous time. Ph.D. Thesis, Massachusetts Institute of Technology, 2004
15. Cole, R., Vishkin, U.: Deterministic coin tossing with applications to optimal parallel list ranking. Inform, and Control 70, 32-53 (1986)
16. Linial, N.: Locality in distributed graph algorithms. SIAM J. Comput. 21, 193-201 (1992)
17. Childs, A.M., Cleve, R., Deotto, E., Farhi, E., Guttman, S., Spielman, D.A.: Exponential algorithmic speedup by quantum walk. In : Proc. 35th Annual ACM Symp. on Theory of Computing, New York: ACM, 2003, pp. 59-68
18. Ahokas, G.: Improved algorithms for approximate quantum Fourier transforms and sparse Hamiltonian simulations. M.Sc. Thesis, University of Calgary, 2004
19. Beals, R., Buhrman, H., Cleve, R., Mosca, M., de Wolf, R.: Quantum lower bounds by polynomials. J. ACM 48, 778-797 (2001)
20. Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: Limit on the speed of quantum computation in determining parity. Phys. Rev. Lett. 81, 5442-5444 (1998)
21. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge: Cambridge University Press, 2000