Robustness of dynamical decoupling sequences

Active protection of quantum states is an essential prerequisite for the implementation of quantum computing. Dynamical decoupling (DD) is a promising approach that applies sequences of control pulses to the system in order to reduce the adverse effect of system-environment interactions. Since every hardware device has finite precision, the errors of the DD control pulses can themselves destroy the stored information rather than protect it. We experimentally compare the performance of different DD sequences in the presence of an environment that was chosen such that all relevant DD sequences can equally suppress its effect on the system. Under these conditions, the remaining decay of the qubits under DD allows us to compare very precisely the robustness of the different DD sequences with respect to imperfections of the control pulses.

Figure 1

Decay of the magnetization of the ${}^1$H spin system under free evolution and in a Hahn spin-echo (HE) sequence.

Figure 2

Dynamical decoupling pulse sequences tested in this work.

Figure 3

Time evolution of the spin-system magnetization under the application of a CPMG sequence. The black solid line shows the evolution of the magnetization, and the blue squares mark the echo amplitude at the end of a CPMG cycle. We use the echo maxima for measuring the CPMG decay time. The cycle time was ${\tau }_c=$ 32 ms.

Figure 4

Average decay times as a function of the delay $\tau$ between pulses for different DD sequences.

Figure 5

Normalized spin magnetization as a function of the evolution time for short delays ($\tau =100\mu$s) between the pulses for an XY8(s) sequence. Pulse errors dominate here, inducing a multiexponential decay. The red solid line is a fit to Eq. (2).

Figure 6

Fitted decay times for the double-exponential decay.

Figure 7

Average error per pulse for different DD sequences with delay $\tau =$100 $\mu \text{s}$.