Abstract
In this paper a microscopic quantum mechanical model of computers as represented by Turing machines is constructed. It is shown that for each numberN and Turing machineQ there exists a HamiltonianH N Q and a class of appropriate initial states such that if c is such an initial state, thenψ Q N (t)=exp(−1H N Q t)ψ Q N (0) correctly describes at timest 3,t 6,⋯,t 3N model states that correspond to the completion of the first, second, ⋯, Nth computation step ofQ. The model parameters can be adjusted so that for an arbitrary time intervalΔ aroundt 3,t 6,⋯,t 3N, the “machine” part ofψ Q N (t) is stationary.
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References
M. Kac,Am. Math. Monthly 54 (1957).
M. Dresden and F. Feiock,J. Stat. Phys. 4:111 (1972).
A. Muriel,Am. J. Phys. 45:701 (1977).
J. von Neumann,The Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, N.J., 1955), Chapter VI.
G. Emch,Helv. Phys. Acta 45:1049 (1972); Whitten-Wolfe and G. Emch,Helv. Phys. Acta 49:45 (1976).
J. S. Bell,Helv. Phys. Acta 48:93 (1975).
A. Shimony,Am. J. Phys. 31:755 (1963).
C. Patton and J. Wheeler,Include the Observer in the Wave Function?, Preprint.
I. Prigogine,Science 201:777 (1978).
R. Landauer,IBM J. Res. Dev. 5:183 (1961).
R. Landauer and J. W. F. Woo,J. Appl. Phys. 42:2301 (1971).
R. W. Keyes and R. Landauer,IBM J. Res. Dev. 14:152 (1970).
R. Landauer,Ber. Bunsenges. Phys. Chem. 80:1048 (1976).
C. H. Bennett,IBM J. Res. Dev. 17:525 (1973).
H. J. Bremermann,Part I: Limitations on Data Processing Arising from Quantum Theory, inSelf-Organizing Systems, M. C. Yovits, G. T. Jacobi, and G. D. Goldstein, eds. (Spartan Books, Washington, D.C., 1962);Complexity and Transcomputability, in theEncyclopedia of Ignorance, R. Duncan and M. Weston-Smith, eds. (Pergamon Press, Oxford, England, 1977), pp. 167–174.
Martin Davis,Computability and Unsolvability (McGraw-Hill, New York, 1958).
Hartley Rogers, Jr.,Theory of Recursive Functions and Effective Computability (McGraw-Hill, New York, 1967).
K. Hepp,Helv. Phys. Acta 45:237 (1972).
P. J. Davis,Am. Math. Monthly 79:252 (1972).
T. Kato,Perturbation Theory for Linear Operators (Springer-Verlag, Berlin, 1966), pp. 495–497.
F. J. Dyson,Phys. Rev. 75:486, 1736 (1949); see also S. S. Schweber,Relativistic Quantum Field Theory (Row Peterson, Illinois, 1961), Section 11f.
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Benioff, P. The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines. J Stat Phys 22, 563–591 (1980). https://doi.org/10.1007/BF01011339
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DOI: https://doi.org/10.1007/BF01011339