Single-qubit gates designed by means of the Madelung picture

Abstract

In this work the Madelung picture is applied to the single qubit systems. The projective aspect of the Madelung quantities and the polar expression of the components of the quantum state allow one to obtain a general dynamical system of equations. Even though this dynamical system of equations is nonlinear, it offers the advantage of designing single quibt gates in a straightforward manner. It only requires the specification of the initial and final points on the Bloch sphere, as well as the gate operation time. This application of the Madelung picture is particularily illustrated for the nuclear magnetic resonance processor case. It turns the problem of specifying the magnetic fields into a simpler problem of substitution.