Physics – Quantum Physics
Scientific paper
1998-02-19
Acta Phys.Slov. 48 (1998) 157
Physics
Quantum Physics
one 1/4 changed to 1/2, conclusions unchanged
Scientific paper
Recenty Abrams and Lloyd have proposed a fast algorithm that is based on a nonlinear evolution of a state of a quantum computer. They have explicitly used the fact that nonlinear evolutions in Hilbert spaces do not conserve scalar products of states, and applied a description of separated systems taken from Weinberg's nonlinear quantum mechanics. On the other hand it is known that violation of orthogonality combined with the Weinberg-type description generates unphysical, arbitrarily fast influences between noninteracting systems. It was not therefore clear whether the algorithm is fast because arbitrarily fast unphysical effects are involved. In these notes I show that this is not the case. I analyze both algorithms proposed by Abrams and Lloyd on concrete, simple models of nonlinear evolution. The description I choose is known to be free of the unphysical influences (therefore it is not the Weinberg one). I show, in particular, that the correct local formalism allows even to simplify the algorithm.
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