Symmetry-enhanced performance of dynamical decoupling

We consider a system with general decoherence and a quadratic dynamical decoupling sequence (QDD) for the coherence control of a qubit coupled to a bath of spins. We investigate the influence of the geometry and of the initial conditions of the bath on the performance of the sequence. The overall performance is quantified by a distance norm $d$. It is expected that $d$ scales with $\tau$, the total duration of the sequence, as ${\tau }^{\min \{N_x,N_z\}+1}$, where $N_x$ and $N_z$ are the number of pulses of the outer and of the inner sequence, respectively. We show both numerically and analytically that the state of the bath can boost the performance of QDD under certain conditions: The scaling of QDD for a given number of pulses can be enhanced by a factor of 2 if the bath is prepared in a highly symmetric state and if the system Hamiltonian is SU(2) invariant.

Figure 1

Central spin model described by Eq. (1) with $M=4$. The solid lines represent the coupling between the central spin (qubit) and the spins of the bath, while the dashed lines represent the couplings between the spins of the bath.

Figure 2

The data of Tables and are graphically represented in panel (a) and in panel (b), respectively. The numbers are rounded to their first digit. Here we have introduced the notation $d\propto {\tau }^{\zeta }$, where $\zeta$ stands for the scaling exponents.

Figure 3

The data of Table (b) is graphically represented. The numbers are rounded to their first digit. The notation $\zeta$ refers to the scaling exponents of the norm distance $d\propto {\tau }^{\zeta }$.