High-fidelity fast quantum transport with imperfect controls

Effective transport of quantum information is an essential element of quantum computation. We consider the problem of transporting a quantum state by using a moving potential well while maintaining the encoded quantum information. In particular, we look at a set of cases where the input control defining the position of the potential well is subject to different types of distortion, each of which is motivated by experimental considerations. We show that even under these conditions, we are able to perfectly transfer the quantum information nonadiabatically over any given distance.

Figure 1

(Color online) Distortion of the transport function over time period $T=2\pi$. The thick (red) solid line is the transport function from Eq. (5), the dot-dashed (green) line is the $\dot{d}\left(t\right)$ model $(\alpha =1)$, the dashed (blue) line is the Fourier model (random coefficients in the range $[-1,1]$), and the dotted (black) line is the piecewise model with an exponential-type smoothing $(N=8)$.

Figure 2

(Color online) Trajectories through phase space in the frame of the moving potential of a transported particle over time period $T=2\pi$. See caption of Fig. 1 for key. For illustative purposes, the particle was given some initial momentum. The center circle is the trajectory of a freely oscillating particle with constant energy and the same initial momentum in a static potential.

Figure 3

(Color online) The evolution of the ground-state probability distribution from (a) an initial time $t=0$ to (f) the final time $T=2\pi$. See caption of Fig. 1 for key.

Figure 4

(Color online) The fidelity between the instantaneous ground state and the transported ground state over a time $T=2\pi$. See caption of Fig. 1 for key.