Protecting geometric gates by dynamical decoupling

Dynamical decoupling is a promising approach to protect quantum information from decoherence. It averages out the noise by flipping the qubits. In this paper, we demonstrate the protection of geometric gates by using dynamical decoupling with trapped ions. Specifically, a universal set of geometric gates is proposed with trapped ions and these gates are commutative with the decoupling group of the system. Our scheme combines the robust advantages of quantum holonomies and dynamical decoupling and hence can combat both control errors and decoherence. We also investigate the effects of dynamical decoupling pulse errors on the proposed geometric gates.

Figure 1

The two-step transition between the states $|00n\rangle$ and $|11n\rangle$, where $|0\rangle$ and $|1\rangle$ are qubit states and $|n\rangle$ is vibration state. Red solid lines and blue dashed lines respectively, represent transition states and intermediate states. Similar transition exists between the states $|01n\rangle$ and $|10n\rangle$.

Figure 2

Effects of flip-angle error and detuning error on logical gate $X_L$. Blue dashed lines and red solid lines represent flip-angle error and detuning error, respectively.

Figure 3

Effects of flip-angle error and detuning error on logical gate $Y_L$. Blue dashed lines and red solid lines represent flip-angle error and detuning error, respectively.

Figure 4

Effects of flip-angle error and detuning error on logical gate $e^{-i\frac{\pi }{4}{Y}_L\otimes Z_L}$. Blue dashed lines and red solid lines represent flip-angle error and detuning error, respectively.