Quantum control by decomposition of SU(1, 1)

Constructive algorithms are presented for controlling quantum systems evolving on the SU(1, 1) Lie group. These procedures are performed via structured decomposition of SU(1, 1), which achieve precise controls without any approximations or iterative computations, under the sufficient condition that examines the existence of such decomposition. The technique is applied to controlling transitions between SU(1, 1) coherent states. These results open up new perspectives on the control design of infinite-dimensional quantum systems involving discrete or continuous spectra.