The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines

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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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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Key words

  • Computer as a physical system
  • microscopic Hamiltonian models of computers
  • Schrödinger equation description of Turing machines
  • Coleman model approximation
  • closed conservative system
  • quantum spin lattices