  Over the past decade we have seen an explosion of demonstrations of quantum
coherence in atomic, optical, and condensed matter systems. These developments
have placed a new emphasis on the production of robust and optimal quantum
control techniques in the presence of environmental noise. We discuss the use
of dynamical decoupling as a form of open-loop quantum control capable of
suppressing the effects of dephasing in quantum coherent systems. We introduce
the concept of dynamical decoupling pulse-sequence construction as a
filter-design problem, making connections with filter design from control
theory and electrical engineering in the analysis of pulse-sequence performance
for the preservation of the phase degree of freedom in a quantum superposition.
A detailed mathematical description of how dephasing and the suppression of
dephasing can be reduced to a linear control problem is provided, and used as
motivation and context for studies of the filtration properties of various
dynamical decoupling sequences. Our work then takes this practical perspective
in addressing both "standard" sequences derived from nuclear magnetic resonance
and novel optimized sequences developed in the context of quantum information.
Additionally, we review new techniques for the numerical construction of
optimized pulse sequences using the filter-design perspective. We show how the
filter-design perspective permits concise comparisons of the relative
capabilities of these sequences and reveals the physics underlying their
functionality. The use of this new analytical framework allows us to derive new
insights into the performance of these sequences and reveals important limiting
issues, such as the effect of digital clocking on optimized sequence
performance.
