  Refocusing of a quantum system in NMR and quantum information processing can
be achieved by application of short pulses according to the methods of spin
echo and dynamical decoupling. However, these methods are strongly limited by
the requirement that the evolution of the system between pulses be suitably
small. Here we show how refocusing may be achieved for arbitrary (but
time-independent) evolution of the system between pulses. We first illustrate
the procedure with one-qubit systems, and then generalize to $d$-dimensional
quantum systems. We also give an application of this result to quantum
computation, proving a new version of the Solovay-Kitaev theorem that does not
require inverse gates.
