Simulating quantum mechanics on a quantum computer

Physica D: Nonlinear Phenomena

Volumn 120, Issue 1-2, 1998, Pages 30-42

  Boghosian, Bruce M ^a   Taylor IV, Washington ^b  

^a Boston University   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; ELEMENTARY PARTICLES;

DIRAC PARTICLES; GAUGE PARTICLES; NONRELATIVISTIC QUANTUM SYSTEMS; QUANTUM COMPUTERS; SCHRODINGER EQUATION;

QUANTUM THEORY;

EID: 0032162402     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00042-6     Document Type: Article

References (34)

1. P.W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, AT&T preprint quant-ph/9508027, August 1995.
2. D. Simon, On the power of quantum computation, in: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1994, pp. 116-123.
3. R. Feynman, Simulating physics with computers, Int. J. Theoret. Phys. 21 (1982) 467-488.
4. S. Lloyd, Universal quantum simulators, Science 273 (1996) 1073.
5. B. Boghosian, W. Taylor, A quantum lattice-gas model for the many-body Schrödinger equation in d dimensions, BU-CCS/PUPT preprint quant-ph/9604035, April 1996.
6. B. Boghosian, W. Taylor, Quantum lattice-gas models for the many-body Schrödinger equation, talk presented at the Sixth International Conference on Discrete Fluid Mechanics, Boston University, Boston, MA, August 1996, BU-CCS/PUPT preprint quant-ph/9701016, January 1997.
7. G. Grossing, A. Zeilinger, Quantum cellular automata, Complex Systems 2 (1988) 197-208.
8. D. Meyer, From quantum cellular automata to quantum lattice gases, UCSD preprint quant-ph/9604003, March 1996.
9. A. Ekert, R. Jozsa, Quantum computation and Shor's factoring algorithm, Rev. Modern. Phys. 68 (3) (1996) 733;
10. S. Lloyd, Quantum-mechanical computers, Sci. Amr. (Oct. 1995) 140;
11. D.P. DiVincenzo, Quantum computation, Science 270 (1995) 255.
12. D.P. DiVincenzo, Two-bit gates are universal for quantum computation, Phys. Rev. A 51 (1995) 1015-1022;
13. S. Lloyd, Almost any quantum logic gate is universal, Phys. Rev. Lett. 75 (1995) 346-349;
14. D. Deutsch, A. Barenco, A. Ekert, Universality of quantum computation, Proc. Roy. Soc. London Ser. A 449 (1995) 669-677;
15. A. Barenco, C.H. Bennett, R. Cleve, D. DiVincenzo, N.H. Margolus, P. Shor, T. Sleator, J. Smolin, H. Weinfurter, Elementary gates for quantum computation, Phys. Rev. A 52 (1995) 3457-3467.
16. R. Feynman, Quantum mechanical computers, Found. Phys. 16, (1986) 507-531;
17. D. Deutsch, Quantum computational networks, Proc. Roy. Soc. London, Ser. A 425, 73-90;
18. N. Margolus, Quantum computation, Ann. NY Acad. Sci. 480 (1986) 487-497.
19. B. Nachtergaele, V. Periwal, Quantum logic as a sum over classical logic gates, PUPT preprint quant-ph/9606018, June 1996.
20. S. Succi, R. Benzi, Lattice Boltzmann equation for quantum mechanics, Physica D 69 (1993) 327-332.
21. S. Succi, Numerical solution of the Schrödinger equation using discrete kinetic theory, IBM ECSEC preprint, 1995.
22. R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York, 1965, pp. 35-36;
23. see also Feynman's unpublished notes as reproduced in S.S. Schweber, Rev. Modern Phys. 58 (1986) 449.
24. D. Meyer, Quantum lattice gases and their invariants, Talk presented at the Sixth International Conference on Discrete Fluid Mechanics, Boston University, Boston, MA, August 1996.
25. D. Meyer, Quantum mechanics of lattice gas automata I. One particle plane waves and potentials, UCSD preprint quant-ph/9611005, October 1996.
26. U. Frisch, B. Hasslacher, Y. Pomeau, Lattice-gas automata for the Navier-Stokes equation, Phys. Rev. Lett. 56 (1986) 1505;
27. U. Frisch, D. d'Humières, B. Hasslacher, P. Lallemand, Y. Pomeau, J.-P. Rivet, Lattice gas hydrodynamics in two and three dimensions, Complex Systems 1 (1987) 648-707;
28. S. Wolfram, Cellular automaton fluids 1: basic theory, J. Stat. Phys. 45 (1986) 471-526.
29. D.S. Abrams, S. Lloyd, Simulation of Many-Body Fermi Systems on a Universal Quantum Computer, MIT preprint, November 1996.
30. I. Bialynicki-Birula, Weyl, Dirac and Maxwell equations on a lattice as unitary cellular automata, Phys. Rev. D 49 (1994) 6920-6927.
31. H.B. Nielsen, M. Ninomiya, A no-go theorem for regularizing chiral fermions, Phys. Lett. B 105 (1981) 219-223.
32. L. Susskind, Lattice fermions, Phys. Rev. D 16 (1977) 3031-3039.
33. J. Kogut, L. Susskind, Hamiltonian formulation of Wilson's lattice gauge theories, Phys. Rev. D 11 (1975) 395.
34. P.W. Shor, Fault-tolerant quantum computation, AT&T preprint quant-ph/9605011, May 1996, and references therein.