Natural variables for controlling quantum dynamics

A quantum control landscape is the expectation value of an observable expressed as a function of the control variables, and the local geometry of the landscape for state-to-state transitions is explored for its implications upon practical searches for optimal controls. The gradient of the landscape with respect to the control field is shown to always lie in a low-dimensional subspace spanned by basis functions bearing specific knowledge of the system physics, thereby comprising a “natural” set of variables for the particular optimal control application. The enumeration of these basis functions provides an upper bound on the required number of properly identified control variables. A specific experimental protocol is suggested to utilize the geometric structure of the landscape for identifying a reduced set of control variables for practical laboratory implementation. Simulations on simple systems are used to illustrate the characteristics of the natural control variables and the prospective experimental protocol.