Linear Algebraic Techniques for Quantum Dynamical Decoupling

Suppressing decoherence is one of the most challenging problems in the control of quantum dyamical systems. Dynamical Decoupling is an open loop decoherence control technique based on high-frequency and high-amplitude periodic controls. Here, we reformulate the effects of the basic strategy in terms of linear, symmetric matrix equations. Such a reformulation proves to be useful both in the analysis and in the synthesis of the needed unitary control actions. A general framework is provided, and simple, but significant, particular cases are studied in detail.