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 number N and Turing machine Q there exists a Hamiltonian HNQ and a class of appropriate initial states such that if c is such an initial state, then ψQN(t)=exp(-1 HNQt)ψQN(0) correctly describes at times t3, t6,⋯, t3N model states that correspond to the completion of the first, second, ⋯, Nth computation step of Q. The model parameters can be adjusted so that for an arbitrary time interval Δ around t3, t6,⋯, t3N, the "machine" part of ψQN(t) is stationary. © 1980 Plenum Publishing Corporation.