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Quantum control is an important prerequisite for quantum devices. A
major obstacle is the fact that a quantum system can never completely be
isolated from its environment. The interaction with the environment
causes decoherence. Optimal control theory is a tool that can be used to
identify control strategies in the presence of decoherence. I will show
how to adapt optimal control theory to quantum information tasks for
open quantum systems and present examples for cold atoms and
superconducting qubits. In particular, I will discuss how
non-Markovianity of the open system time evolution can be exploited for
control.
The perspective on decoherence only as the adversary of quantum control
is nevertheless too narrow. There exist a number of control tasks, such
as cooling and measurement, that can only be achieved by an interplay of
control and dissipation. I will show how to utilize optimal control
theory to derive efficient cooling strategies when the timescales of
coherent dynamics and dissipation are very different. Our approach can
be generalized to quantum reservoir engineering, opening up new avenues
for control.
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