  We study how dynamical decoupling (DD) pulse sequences can improve the
reliability of quantum computers. We prove upper bounds on the accuracy of
DD-protected quantum gates and derive sufficient conditions for DD-protected
gates to outperform unprotected gates. Under suitable conditions,
fault-tolerant quantum circuits constructed from DD-protected gates can
tolerate stronger noise, and have a lower overhead cost, than fault-tolerant
circuits constructed from unprotected gates. Our accuracy estimates depend on
the dynamics of the bath that couples to the quantum computer, and can be
expressed either in terms of the operator norm of the bath's Hamiltonian or in
terms of the power spectrum of bath correlations; we explain in particular how
the performance of recursively generated concatenated pulse sequences can be
analyzed from either viewpoint. Our results apply to Hamiltonian noise models
with limited spatial correlations.
