A fixed point algorithm for improving fidelity of quantum gates

This work considers the problem of quantum gate generation for controllable systems with drift. It is assumed that an approximate solution called seed pre-computed by some known algorithm. presents a method, Fixed-Point Algorithm (FPA) able to improve arbitrarily fidelity given seed. When infidelity small enough and attractive in context tracking control (that verified probability one, sense), Banach Theorem allows prove exponential convergence FPA. Even when FPA does not converge, several iterated applications may produce desired fidelity. The produces only corrections pulses preserves original bandwidth computational effort each step corresponds one numerical integration stabilized closed loop system. A piecewise-constant smooth implementations are developed. Several experiments N -qubit system illustrates effectiveness method different including conversion into ones reduction their bandwidth.