Quantum logic as a sum over classical logic gates
Bruno Nachtergaele, Vipul Periwal
Abstract
It is shown that certain natural quantum logic gates, i.e. unitary time evolution matrices for spin-12 quantum spins, can be represented as sums, with appropriate phases, over classical logic gates, 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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