On the efficiency of quantum algorithms for Hamiltonian simulation

Quantum Information Processing

Volumn 11, Issue 2, 2012, Pages 541-561

  Papageorgiou, Anargyros ^a   Zhang, Chi ^a  

^a Columbia University ^*  (United States)

Author keywords

Complexity; Hamiltonian evolution; Order of convergence; Quantum simulation; Splitting methods

Indexed keywords

COMPLEXITY; EXPONENTIALS; HIGH ORDER; ORDER OF CONVERGENCE; QUANTUM ALGORITHMS; QUANTUM HAMILTONIANS; QUANTUM SIMULATIONS; SPLITTING METHOD; UPPER BOUND;

ALGORITHMS; QUANTUM CHEMISTRY; QUANTUM OPTICS; QUANTUM THEORY;

HAMILTONIANS;

EID: 84861100841     PISSN: 15700755     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11128-011-0263-9     Document Type: Article

References (18)

1. Feynman, R.P.: Simulating physics with computers. Int. J. Theoret. Phys. 21, 467-488 (1982)
2. Lloyd, S.: Universal quantum simulators. Science 273, 1073-1078 (1996) (Pubitemid 26278158)
3. Kassal, I., Jordan, S.P., Love, P.J., Mohseni, M., Aspuru-Guzik, A.: Polynomial-time quantum algorithm for the simulation of chemical dynamics. Proc. Nat. Acad. Sci. 105, 18681 (2008)
4. Buluta, I., Nori, F.: Quantum simulators. Science 326, 108 (2009)
5. Zalka, C.: Simulating quantum systems on a quantum computer. Proc. R. Soc. Lond. A 454, 313 (1998)
6. Zalka, C.: Efficient simulation of quantum systems by quantum computers. Fortschritte der Physik 46, 877 (1998)
7. Aharonov, D., Ta-Shma, A.: Adiabatic quantum state generation and statistical zero knowledge. In: Proceedings of the 35th Annual ACM Symposium on Theory of Computing, pp. 20-29 (2003)
8. Farhi, E., Goldstone, J., Gutmann, S., Sipser M.: Quantum computation by adiabatic evolution, quant-ph/0001106 (2000)
9. 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)
10. Farhi, E., Goldstone, J., Gutmann, S.: A Quantum algorithm for the Hamiltonian NAND Tree, quant-ph/0702144 (2007)
11. Childs, A.: Universal computation by quantum walk. Phys. Rev. Lett. 102, 180501 (2009)
12. Childs, A.: On the relationship between continuous- and discrete-time quantum walk. Commun. Math. Phys. 294, 581-603 (2010)
13. Berry, D.W., Ahokas, G., Cleve, R., Sanders, B.C.: Efficient quantum algorithms for simulating sparse Hamiltonians. Commun. Math. Phys. 270, 359 (2007)
14. Suzuki, M.: Fractal decomposition of exponential operators with application to many-body theories and Monte Carlo simulations. Phys. Lett. A 146, 319-323 (1990)
15. Suzuki, M.: General theory of fractal path integrals with application to many-body theories and statistical physics. J. Math. Phys. 32, 400-407 (1991)
16. Wiebe, N., Berry, D., Hoyer, P., Sanders, B.C.: Higher order decompositions of ordered operator exponentials. J. Phys. A: Math. Theor. 43, 065203 (2010)
17. Klar, B.: Boundson tail probabilities of discrete distributions. Probab. Eng. Inf. Sci.14, 161-171 (2000)
18. Abramowitz, M., Stegun, A.: Handbook of Mathematical Functions. Dover, New York (1972)