Optimized Noise Filtration through Dynamical Decoupling

One approach to maintaining phase coherence of qubits through dynamical decoupling consists of applying a sequence of Hahn spin-echo pulses. Recent studies have shown that, in certain noise environments, judicious choice of the delay times between these pulses can greatly improve the suppression of phase errors compared to traditional approaches. By enforcing a simple analytical condition, we obtain sets of dynamical decoupling sequences that are designed for optimized noise filtration and are spectrum-independent up to a single scaling factor set by the coherence time of the system. We demonstrate the efficacy of these sequences in suppressing phase errors through measurements on a model qubit system, $^{9}$Be$^{+}$ ions in a Penning trap. Our combined theoretical and experimental studies show that in high-frequency-dominated noise environments this approach may suppress phase errors orders of magnitude more efficiently than comparable techniques can.
Comment: 4 pages, 3 figures version 2 - Different nomenclature to describe sequences - More detailed explanation contrasting feedback routine implemented here to that in previous work - Statements on the constraints on noise spectra which will allow improved error suppression added. - Typos corrected and other minor changes made