Correcting errors in a quantum gate with pushed ions via optimal control

We analyze in detail the so-called pushing gate for trapped ions, introducing a time-dependent harmonic approximation for the external motion. We show how to extract the average fidelity for the gate from the resulting semiclassical simulations. We characterize and quantify precisely all types of errors coming from the quantum dynamics and reveal that slight nonlinearities in the ion-pushing force can have a dramatic effect on the adiabaticity of gate operation. By means of quantum optimal control techniques, we show how to suppress each of the resulting gate errors in order to reach a high fidelity compatible with scalable fault-tolerant quantum computing. ©2010 The American Physical Society