Quantum lattice gases and their invariants

International Journal of Modern Physics C

Volumn 8, Issue 4, 1997, Pages 717-735

  Meyer, David A ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Conserved Quantities; Exactly Solvable Model; Quantum Computation; Quantum Lattice Gas

Indexed keywords

EID: 0031496560     PISSN: 01291831     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129183197000618     Document Type: Article

References (37)

1. D. P. DiVincenzo, Science 270, 255 (1995); I. L. Chuang, R. Laflamme, P. W. Shor, and W. H. Zurek, Science 270, 1633 (1995); A. Barenco and A. Ekert, Acta Physica Slovaca 45, 1 (1995); and references therein.
2. D. P. DiVincenzo, Science 270, 255 (1995); I. L. Chuang, R. Laflamme, P. W. Shor, and W. H. Zurek, Science 270, 1633 (1995); A. Barenco and A. Ekert, Acta Physica Slovaca 45, 1 (1995); and references therein.
3. D. P. DiVincenzo, Science 270, 255 (1995); I. L. Chuang, R. Laflamme, P. W. Shor, and W. H. Zurek, Science 270, 1633 (1995); A. Barenco and A. Ekert, Acta Physica Slovaca 45, 1 (1995); and references therein.
4. T. Ando, A. B. Fowler, and F. Stem, Rev. Mod. Phys. 54, 437 (1982); B. L. Altshuler, V. E. Kravtsov, and I. V. Lerner, "Distribution of mesoscopic fluctuations and relaxation processes in disordered conductors," in Mesoscopic Phenomena in Solids, eds. B. L. Altshuler, P. A. Lee, and R. A. Webb (North-Holland, Amsterdam, 1991), pp. 449-521; D. K. Ferry and H. L. Grubin, "Modeling of quantum transport in semiconductor devices," in Solid State Physica: Advances in Research and Applications 49, eds. H. Ehrenreich and F. Spaepen (1995), pp. 283-448; and references therein.
5. T. Ando, A. B. Fowler, and F. Stem, Rev. Mod. Phys. 54, 437 (1982); B. L. Altshuler, V. E. Kravtsov, and I. V. Lerner, "Distribution of mesoscopic fluctuations and relaxation processes in disordered conductors," in Mesoscopic Phenomena in Solids, eds. B. L. Altshuler, P. A. Lee, and R. A. Webb (North-Holland, Amsterdam, 1991), pp. 449-521; D. K. Ferry and H. L. Grubin, "Modeling of quantum transport in semiconductor devices," in Solid State Physica: Advances in Research and Applications 49, eds. H. Ehrenreich and F. Spaepen (1995), pp. 283-448; and references therein.
6. T. Ando, A. B. Fowler, and F. Stem, Rev. Mod. Phys. 54, 437 (1982); B. L. Altshuler, V. E. Kravtsov, and I. V. Lerner, "Distribution of mesoscopic fluctuations and relaxation processes in disordered conductors," in Mesoscopic Phenomena in Solids, eds. B. L. Altshuler, P. A. Lee, and R. A. Webb (North-Holland, Amsterdam, 1991), pp. 449-521; D. K. Ferry and H. L. Grubin, "Modeling of quantum transport in semiconductor devices," in Solid State Physica: Advances in Research and Applications 49, eds. H. Ehrenreich and F. Spaepen (1995), pp. 283-448; and references therein.
7. W. D. Hillis, Int. J. Theor. Phys. 21, 255 (1982); N. Margolus, "Parallel quantum computation," in Complexity, Entropy, and the Physics of Information, Proceedings of the SFI Workshop, Santa Fe, NM, 29 May-10 June 1989, SFI Studies in the Sciences of Complexity VIII, ed. W. H. Zurek (Addison-Wesley, Redwood City, CA, 1990), pp. 273-287; B. Hasslacher, "Parallel billiards and monster systems," in A New Era in Computation, eds. N. Metropolis and G.-C. Rota (MTT Press, Cambridge, 1993), pp. 53-65; R. Mainieri, "Design constraints for nanometer scale quantum computers," preprint (1993) LA-UR 93-4333, cond-mat/9410109; M. Biafore, Physica D70, 415 (1994).
8. W. D. Hillis, Int. J. Theor. Phys. 21, 255 (1982); N. Margolus, "Parallel quantum computation," in Complexity, Entropy, and the Physics of Information, Proceedings of the SFI Workshop, Santa Fe, NM, 29 May-10 June 1989, SFI Studies in the Sciences of Complexity VIII, ed. W. H. Zurek (Addison-Wesley, Redwood City, CA, 1990), pp. 273-287; B. Hasslacher, "Parallel billiards and monster systems," in A New Era in Computation, eds. N. Metropolis and G.-C. Rota (MTT Press, Cambridge, 1993), pp. 53-65; R. Mainieri, "Design constraints for nanometer scale quantum computers," preprint (1993) LA-UR 93-4333, cond-mat/9410109; M. Biafore, Physica D70, 415 (1994).
9. W. D. Hillis, Int. J. Theor. Phys. 21, 255 (1982); N. Margolus, "Parallel quantum computation," in Complexity, Entropy, and the Physics of Information, Proceedings of the SFI Workshop, Santa Fe, NM, 29 May-10 June 1989, SFI Studies in the Sciences of Complexity VIII, ed. W. H. Zurek (Addison-Wesley, Redwood City, CA, 1990), pp. 273-287; B. Hasslacher, "Parallel billiards and monster systems," in A New Era in Computation, eds. N. Metropolis and G.-C. Rota (MTT Press, Cambridge, 1993), pp. 53-65; R. Mainieri, "Design constraints for nanometer scale quantum computers," preprint (1993) LA-UR 93-4333, cond-mat/9410109; M. Biafore, Physica D70, 415 (1994).
10. W. D. Hillis, Int. J. Theor. Phys. 21, 255 (1982); N. Margolus, "Parallel quantum computation," in Complexity, Entropy, and the Physics of Information, Proceedings of the SFI Workshop, Santa Fe, NM, 29 May-10 June 1989, SFI Studies in the Sciences of Complexity VIII, ed. W. H. Zurek (Addison-Wesley, Redwood City, CA, 1990), pp. 273-287; B. Hasslacher, "Parallel billiards and monster systems," in A New Era in Computation, eds. N. Metropolis and G.-C. Rota (MTT Press, Cambridge, 1993), pp. 53-65; R. Mainieri, "Design constraints for nanometer scale quantum computers," preprint (1993) LA-UR 93-4333, cond-mat/9410109; M. Biafore, Physica D70, 415 (1994).
11. W. D. Hillis, Int. J. Theor. Phys. 21, 255 (1982); N. Margolus, "Parallel quantum computation," in Complexity, Entropy, and the Physics of Information, Proceedings of the SFI Workshop, Santa Fe, NM, 29 May-10 June 1989, SFI Studies in the Sciences of Complexity VIII, ed. W. H. Zurek (Addison-Wesley, Redwood City, CA, 1990), pp. 273-287; B. Hasslacher, "Parallel billiards and monster systems," in A New Era in Computation, eds. N. Metropolis and G.-C. Rota (MTT Press, Cambridge, 1993), pp. 53-65; R. Mainieri, "Design constraints for nanometer scale quantum computers," preprint (1993) LA-UR 93-4333, cond-mat/9410109; M. Biafore, Physica D70, 415 (1994).
12. T. Toffoli, Physica D10, 117 (1984); B. Hasslacher, Los Alamos Science 15, 175, 211 (1988).
13. T. Toffoli, Physica D10, 117 (1984); B. Hasslacher, Los Alamos Science 15, 175, 211 (1988).
14. R. P. Feynman, Int. J. Theor. Phys. 21, 467 (1982).
15. S. Succi and R. Benzi, Physica D69, 327 (1993); S. Succi, Phys. Rev. E53, 1969 (1996).
16. S. Succi and R. Benzi, Physica D69, 327 (1993); S. Succi, Phys. Rev. E53, 1969 (1996).
17. B. M. Boghosian and W. Taylor, IV, "A quantum lattice-gas model for the many-particle Schrodinger equation in d dimensions," preprint, 1996, PUPT-1615, BU-CCS-960401, quant-ph/9604035, to appear in Phys. Rev. E.
18. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
19. I. Bialynicki-Birula, Phys. Rev. D49, 6920 (1994).
20. D. A. Meyer, J. Stat. Phys. 85, 551 (1996).
21. A. Messiah, Quantum Mechanics, Vol. II, translated from French by J. Potter (North-Holland, Amsterdam, 1962), Chap. XX, Sec. V.
22. O. Klein, Z. Physik 53, 157 (1929).
23. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, New York, 1982); and references therein.
24. P. A. M. Dirac, The Principles of Quantum Mechanics, fourth edition (Oxford University Press, Oxford, 1958).
25. H. Weyl, The Theory of Groups and Quantum Mechanics, translated from the second (revised) German edition by H. P. Robertson (Dover, New York, 1950).
26. D. A. Meyer, Phys. Rev. E55, 5261 (1997).
27. G. V. Riazanov, Sov. Phys. JETP 6, 1107 (1958).
28. G. Zanetti, Phys. Rev. A40, 1539 (1989); Z. Cheng, J. L. Lebowitz, and E. R. Speer, Commun. Pure Appl. Math. XLIV, 971 (1991).
29. G. Zanetti, Phys. Rev. A40, 1539 (1989); Z. Cheng, J. L. Lebowitz, and E. R. Speer, Commun. Pure Appl. Math. XLIV, 971 (1991).
30. B. Hasslacher and D. A. Meyer, J. Stat. Phys. 68, 575 (1992).
31. G.'t Hooft, "A two-dimensional model with discrete general coordinate-invariance," Duke University preprint, 1989.
32. E. H. Lieb, Phys. Rev. 162, 162 (1967).
33. H. A. Bethe, Z. Physik 71, 205 (1931).
34. A. B. Zamolodchikov, Sov. Phys. JETP 52, 325 (1980); Commun. Math. Phys. 79, 489 (1981); R. J. Baxter, Commun. Math. Phys. 88, 185 (1983); J. M. Maillet and F. Nijhoff, Phys. Lett. B224, 389 (1989).
35. A. B. Zamolodchikov, Sov. Phys. JETP 52, 325 (1980); Commun. Math. Phys. 79, 489 (1981); R. J. Baxter, Commun. Math. Phys. 88, 185 (1983); J. M. Maillet and F. Nijhoff, Phys. Lett. B224, 389 (1989).
36. A. B. Zamolodchikov, Sov. Phys. JETP 52, 325 (1980); Commun. Math. Phys. 79, 489 (1981); R. J. Baxter, Commun. Math. Phys. 88, 185 (1983); J. M. Maillet and F. Nijhoff, Phys. Lett. B224, 389 (1989).
37. A. B. Zamolodchikov, Sov. Phys. JETP 52, 325 (1980); Commun. Math. Phys. 79, 489 (1981); R. J. Baxter, Commun. Math. Phys. 88, 185 (1983); J. M. Maillet and F. Nijhoff, Phys. Lett. B224, 389 (1989).