Universal dynamical decoherence control of noisy single- and multi-qubit systems

In this paper, we develop, step by step, the framework for universal dynamical control of two-level systems (TLS) or qubits experiencing amplitude or phase noise (AN or PN) due to coupling to a thermal bath. A comprehensive arsenal of modulation schemes is introduced and applied to either AN or PN, resulting in completely analogous formulae for the decoherence rates, thus underscoring the unified nature of this universal formalism. We then address the extension of this formalism to multipartite decoherence control, where symmetries are exploited to overcome decoherence.