Optimal control of a single qubit by direct inversion
Markus Wenin, W. Pötz · Physical Review A · 2006
Optimal control of a driven single dissipative qubit is formulated as an inverse problem. We show that direct inversion is possible which allows an analytic construction of optimal control fields. Exact inversion is shown to be possible for dissipative qubits which can be described by a Lindblad equation. It is shown that optimal solutions are not unique. For a qubit with weak coupling to phonons we choose, among the set of exact solutions for the dissipationless qubit, one which minimizes the dissipative contribution in the kinetic equations. Examples are given for state trapping and $Z$-gate operation. Using analytic expressions for optimal control fields, favorable domains for dynamic stabilization in the Bloch sphere are identified. In the case of approximate inversion, the identified approximate solution may be used as a starting point for further optimization following standard methods.