Algorithms for quantum control without discontinuities; application to the simultaneous control of two qubits.

Domenico D'Alessandro, Benjamin Sheller

Abstract:

We propose a technique to design control algorithms for a class of finite dimensional quantum systems so that the control law does not present discontinuities. The class of models considered admits a group of symmetries which allows us to reduce the problem of control to
a quotient space where the control system is `fully actuated'. As a result we can prescribe a desired trajectory which is, to some extent, arbitrary and derive the corresponding control. We illustrate this technique with examples and focus on the application to the simultaneous control of two non-interacting spin $\frac{1}{2}$ particles with different gyromagnetic ratios in zero field nuclear magnetic resonance (NMR). Our method provides a flexible toolbox for the design of control algorithms to drive the state of finite dimensional quantum systems to any desired final configuration, with smooth controls.