Journal of Statistical Physics

, Volume 29, Issue 3, pp 515-546

First online:

Quantum mechanical hamiltonian models of turing machines

  • Paul BenioffAffiliated withDivision of Environmental Impact Studies, Argonne National Laboratory

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Quantum mechanical Hamiltonian models, which represent an aribtrary but finite number of steps of any Turing machine computation, are constructed here on a finite lattice of spin-1/2 systems. Different regions of the lattice correspond to different components of the Turing machine (plus recording system). Successive states of any machine computation are represented in the model by spin configuration states. Both time-independent and time-dependent Hamiltonian models are constructed here. The time-independent models do not dissipate energy or degrade the system state as they evolve. They operate close to the quantum limit in that the total system energy uncertainty/computation speed is close to the limit given by the time-energy uncertainty relation. However, the model evolution is time global and the Hamiltonian is more complex. The time-dependent models do not degrade the system state. Also they are time local and the Hamiltonian is less complex.

Key words

Schrödinger equation description of Turing machines nondissipative models of computers quantum spin lattices