  We present deterministic algorithms for the simultaneous control of an
arbitrary number of quantum observables. Unlike optimal control approaches
based on cost function optimization, quantum multiobservable tracking control
(MOTC) is capable of tracking predetermined homotopic trajectories to target
expectation values in the space of multiobservables. The convergence of these
algorithms is facilitated by the favorable critical topology of quantum control
landscapes. Fundamental properties of quantum multiobservable control
landscapes that underlie the efficiency of MOTC, including the multiobservable
controllability Gramian, are introduced. The effects of multiple control
objectives on the structure and complexity of optimal fields are examined. With
minor modifications, the techniques described herein can be applied to general
quantum multiobjective control problems.
