Abstract:
Control over the quantum world is expected to open new horizons in this century. \Given
a quantum system, how best we can control its dynamics?" is the question at the heart of
quantum control technology. Several advancements in diverse elds such as spectroscopy,
quantum information science, communication science, chemical kinetics, imaging, and sensors
hinge upon establishing precise and robust control over the quantum dynamics. In this
thesis, we examine certain novel strategies for e ciently generating robust quantum controls.
First by using a suitable interaction frame, we separate the free evolution of the quantum
system from the external controls. Secondly, by coarse graining the external control parameters
we evaluate any general control propagator in terms of a small set of precalculated
unitaries. These strategies alleviate the complexity issues posed by standard propagator
evaluation methods, which are based on iteratively exponentiating the full Hamiltonian. We
benchmark the e ciency of our algorithm with standard algorithms in terms of computational
time. Further, we incorporate these strategies on a hybrid quantum control algorithm
which combines a global initial-optimization with a local nal-optimization. We also describe
the importance of our quantum control algorithms in quantum information as well as spectroscopy.
Finally, some applications in quantum information processing and spectroscopy
are demonstrated using nuclear spin-systems controlled by NMR techniques. Super-adiabatic
quantum state transfer in spin chains was demonstrated in a 3- qubit NMR system. Single
and multi-band selective inversion pulses were designed and used in the heat-bath algorithmic
cooling protocol to increase the polarisation of low natural abundance nuclear isotopes.
