Optimizing electrically controlled echo sequences for the exchange-only qubit

Recently, West and Fong [New J. Phys. 14, 083002 (2012)] introduced an echo scheme for an exchange-only qubit, which relies entirely on the exchange interaction. Here, we compare two different exchange-based sequences and two optimization strategies, Uhrig dynamical decoupling and optimized filter function dynamical decoupling, which were introduced for a single spin qubit and are applied in this paper to the three spin exchange-only qubit. The calculation shows that the adaption of the optimization concepts can be achieved by straightforward calculation. We consider two types of noise spectra, Lorentzian and Ohmic noise. For both spectra, the results reveal a slight dependence of the performance on the choice of the echo sequence.