Journal of Statistical Physics

, Volume 22, Issue 5, pp 563–591

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


  • Paul Benioff
    • Centre de Physique Théorique, Section IICNRS

DOI: 10.1007/BF01011339

Cite this article as:
Benioff, P. J Stat Phys (1980) 22: 563. doi:10.1007/BF01011339


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 HamiltonianHNQ and a class of appropriate initial states such that if c is such an initial state, thenψQN(t)=exp(−1HNQt)ψQN(0) correctly describes at timest3,t6,⋯,t3N 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 aroundt3,t6,⋯,t3N, the “machine” part ofψQN(t) is stationary.

Key words

Computer as a physical systemmicroscopic Hamiltonian models of computersSchrödinger equation description of Turing machinesColeman model approximationclosed conservative systemquantum spin lattices

Copyright information

© Plenum Publishing Corporation 1980