AN OPEN SYSTEM APPROACH TO QUANTUM COMPUTERS

摘要

Two of the basic characteristics of any computational procedure are: ⅰ) iteration of a basic operation ⅱ) convergence to the result in a finite number of steps.rnDenoting V the basic operation of item (ⅰ), item (ⅱ) can be rephrased as follows: for every input state Ψ_(in) there exists an output state Ψ_(out) (possibly depending on Ψ_(in)) and an integer TV (also depending on Ψ_(in) in general) such that for each n ≥ NrnV~nΨ_(in)=Ψ_(out) (1.1)rnThe relation (1.1) means that the final state is reached after a finite number of steps and that the final state is a fixed point for the basic iteration procedure, i.e.rnVΨ_(out)=Ψ_(out) (1.2)rnIf V is invertible, then (1.2) holds also for V~(-1) and therefore (1.1) is possible if and only if Ψ_(in) = Ψ_(out).