Abstract
Quantum spin systems may provide physical realizations of quantum gate arrays. It is shown that certain natural unitary time evolution matrices for spin- quantum spins, interpreted in this context as quantum gate arrays, can be represented as coherent sums, with appropriate phases, over classical logic gate arrays, in a direct analogy with the Feynman path integral representation of quantum mechanics. On the other hand, it is shown that a natural quantum gate obtained by analytically continuing the transfer matrix of the anisotropic nearest-neighbour Ising model to imaginary time, does not admit such a representation.
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