Exact results on dynamical decoupling by π pulses in quantum information processes

The aim of dynamical decoupling consists in the suppression of decoherence by appropriate coherent control of a quantum register. Effectively, the interaction with the environment is reduced. In particular, a sequence of pi pulses is considered. Here we present exact results on the suppression of the coupling of a quantum bit to its environment by optimized sequences of pi pulses. The effect of various cut-offs of the spectral density of the environment is investigated. As a result we show that the harder the cut-off is, the better an optimized pulse sequence can deal with it. For cut-offs which are neither completely hard nor very soft we advocate iterated optimized sequences.