Abstract
Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space ℋM and step operator UT. Since UT is not unitary in general, M, ℋM, and UT are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of UT. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement.
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