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We present rigorous performance bounds for the quadratic dynamical decoupling(QDD) pulse sequence which protects a qubit from general decoherence, and forits nested generalization to an arbitrary number of qubits. Our bounds applyunder the assumption of instantaneous pulses and of bounded perturbingenvironment and qubit-environment Hamiltonians such as those realized by bathsof nuclear spins in quantum dots. We prove that if the total sequence time isfixed then the trace-norm distance between the unperturbed and protected systemstates can be made arbitrarily small by increasing the number of appliedpulses.

Rigorous Performance Bounds for Quadratic and Nested Dynamical Decoupling