Unitarity plus causality implies localizability

Journal of Computer and System Sciences

Volumn 77, Issue 2, 2011, Pages 372-378

  Arrighi, Pablo ^a   Nesme, Vincent ^b   Werner, Reinhard ^b  

^a UNIV GRENOBLE ALPES   (France)

^b Leibniz Universität Hannover   (Germany)

Author keywords

Axiomatic quantum field theory; Discrete space time; Quantum walks

Indexed keywords

QUANTUM COMPUTERS; QUANTUM OPTICS; RELATIVITY;

CONSTRUCTIVE APPROACH; DISCRETE SPACES; ELEMENTARY OPERATORS; QUANTUM CELLULAR AUTOMATA; QUANTUM FIELD THEORY; QUANTUM WALK; REPRESENTATION THEOREM; SPECIAL RELATIVITY;

GRAPH THEORY;

EID: 78651292724     PISSN: 00220000     EISSN: 10902724     Source Type: Journal    
DOI: 10.1016/j.jcss.2010.05.004     Document Type: Article

References (32)

1. S. Aaronson, A. Ambainis, Quantum search of spatial regions, in: Foundations of Computer Science, 2003, Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, 2003, pp. 200-209.
2. P. Arrighi Algebraic characterizations of unitary linear quantum cellular automata Proceedings of MFCS Lecture Notes in Comput. Sci. vol. 4162 2006 Springer 122
3. P. Arrighi, V. Nesme, and R.F. Werner Quantum cellular automata over finite, unbounded configurations Proceedings of MFCS Lecture Notes in Comput. Sci. vol. 5196 2008 Springer 64 75
4. D. Beckman, D. Gottesman, M.A. Nielsen, and J. Preskill Causal and localizable quantum operations Phys. Rev. A 64 052309 2001
5. B.M. Boghosian, and W. Taylor Quantum lattice-gas model for the many-particle Schrödinger equation in d dimensions Phys. Rev. E 57 1 1998 54 66
6. B.M. Boghosian, and W. Taylor Simulating quantum mechanics on a quantum computer Phys. D 120 1-2 1998 30 42
7. G.K. Brennen, and J.E. Williams Entanglement dynamics in one-dimensional quantum cellular automata Phys. Rev. A 68 4 Oct. 2003 042311
8. D. Buchholz Current trends in axiomatic quantum field theory Lecture Notes in Phys. vol. 558 2000 43 64
9. G. Chang, W.-T. Ke, D. Kuo, D. Liu, and R. Yeh On L (d, 1 ) -labelings of graphs Discrete Math. 220 2000 57 66
10. C. Durr, H. Le Thanh, and M. Santha A decision procedure for well-formed linear quantum cellular automata Proceedings of STACS 96 Lecture Notes in Comput. Sci. 1996 Springer 281 292
11. R.P. Feynman Quantum mechanical computers Found. Phys. (Historical Archive) 16 6 1986 507 531
12. J. Fitzsimons, and J. Twamley Globally controlled quantum wires for perfect qubit transport, mirroring, and computing Phys. Rev. Lett. 97 9 2006 90502
13. D. Gross, V. Nesme, H. Vogts, and R. Werner Index theory of one dimensional quantum walks and cellular automata preprint arXiv:0910.3675 2009
14. G. Grössing, and A. Zeilinger Quantum cellular automata Complex Systems 2 2 1988 197 208
15. J. Gruska Quantum Computing Advanced Topics in Computer Science Series 1999 McGraw-Hill Companies
16. N. Inui, S. Inokuchi, Y. Mizoguchi, and N. Konno Statistical properties of a quantum cellular automaton Phys. Rev. A 72 3 2005 032323
17. N. Inui, K. Nakamura, Y. Ide, and N. Konno Effect of successive observation on quantum cellular automaton J. Phys. Soc. Japan 76 8 2007 084001
18. P. Love, and B. Boghosian From Dirac to diffusion: decoherence in quantum lattice gases Quantum Inf. Process. 4 2005 335 354
19. D. Meyer Unitarity in one dimensional nonlinear quantum cellular automata arXiv:quant-ph/9605023 1995
20. D.A. Meyer From quantum cellular automata to quantum lattice gases J. Stat. Phys. 85 1996 551 574
21. D.A. Meyer Quantum mechanics of lattice gas automata: boundary conditions and other inhomogeneities J. Phys. A 31 10 1998 2321 2340
22. D. Nagaj, and P. Wocjan Hamiltonian quantum cellular automata in 1D arXiv:0802.0886 2008
23. T. Osborne Approximate locality for quantum systems on graphs Phys. Rev. Lett. 101 14 Oct. 2008 140503
24. C.A. Pérez-Delgado, and D. Cheung Local unitary quantum cellular automata Phys. Rev. A 76 3 2007 32320
25. R. Raussendorf Quantum cellular automaton for universal quantum computation Phys. Rev. A 72 022301 2005
26. B. Schumacher, and R. Werner Reversible quantum cellular automata arXiv:quant-ph/0405174 2004
27. B. Schumacher, and M.D. Westmoreland Locality and information transfer in quantum operations Quantum Inf. Process. 4 1 2005 13 34
28. W. Van Dam, Quantum cellular automata, Masters thesis, University of Nijmegen, The Netherlands, 1996.
29. A.Y. Vlasov On quantum cellular automata arXiv:quant-ph/0406119 2004
30. K.G.H. Vollbrecht, and J.I. Cirac Reversible universal quantum computation within translation-invariant systems New J. Phys. Rev. A 73 2004 012324
31. J. von Neumann Theory of Self-Reproducing Automata 1966 University of Illinois Press Champaign, IL, USA
32. J. Watrous On one-dimensional quantum cellular automata Complex Systems 5 1 1991 19 30