Robust quantum state transfer inspired by Dzyaloshinskii-Moriya interactions

Quantum state transfer (QST) is a fundamental problem in quantum mechanics and is important for quantum information processing. In this paper we explore a fast, robust, and efficient QST in spin-based quantum dots. Differing from the usual method that only uses the exchange interactions to control the evolution of the spin system, here we treat the non-negligible Dzyaloshinskii-Moriya (DM) interactions that can be electrically and thermally controlled in quantum dots as an assisted driving to accelerate the population transfer. We demonstrate that the DM interactions are not an error source, but are beneficial for population evolution under certain condition because they can sufficiently eliminate the undesirable quantum transitions among adiabatic passages and strictly maintain the population evolution in a designed passage with high efficiency. We give a generic $N$-spin anisotropic Heisenberg spin model to describe the population evolution and take specific two- and three-spin systems as examples to demonstrate the advantages of the DM interactions for QST.

Figure 1

(a) Spin interaction sequence for QST. The population evolution goes along the passage $|+\rangle$ with coupling shapes $J\left(t\right)=J_0{e}^{-{(t/T)}^2}$ and $b\left(t\right)=-b_{0}t/T$. The DM interaction $D\left(t\right)$ is small enough to be treated as a perturbation term. (b) Spin energies of this interaction sequence, with the direction of population evolution marked by the arrows. Also shown is the population transfer (c) without the DM interaction $D\left(t\right)$ and (d) with the DM interaction.

Figure 2

(a) Intuitive order of exchange interactions. In this case, the magnetic field is linearly varied with time and is used to separate the degenerate spin state. The DM interactions are small enough to be treated as perturbation terms. (b) Spin energies of the intuitive interaction order. Like the interaction sequence shown in (a), the population evolution goes along the arrows. (c) The QST from the initial state $|\downarrow \uparrow \uparrow \rangle$ to the target state $|\uparrow \uparrow \downarrow \rangle$ in the case of ignoring the DM interactions. (d) The QST considering the DM interactions. The given spin $|\downarrow \rangle$ in particle 1 is efficiently moved to the target particle 3 inspired by the DM interactions $D_{12}, D_{23}$, and $D_{13}$.

Figure 3

(a) Counterintuitive order of exchange interactions. For the population transfer along the passage, $|{\lambda }_0\rangle$ is independent of the magnetic field $b\left(t\right)$ and the mixing angle $\varphi$; the parameters $b\left(t\right), D_{12}$, and $D_{23}$ are all ignored in our numerical solution. (b) Spin energies of the counterintuitive interaction order, with the population evolution along the passage $|{\lambda }_0\rangle$ marked by arrows. Also shown is the population transfer (c) without the DM interaction $D_{13}$ and (d) with the DM interaction $D_{13}$. The population is also spurred by the DM interaction and there is no population in the state $|\uparrow \downarrow \uparrow \rangle$ in (d).

Figure 4

(a) Efficiency with different decay rates for the two-spin system. The dynamics goes along the adiabatic passage $|+\rangle$ from the initial state $|\uparrow \downarrow \rangle$ to the target one $|\downarrow \uparrow \rangle$ with the same parameters as in Fig. 1. (b) Efficiency for the three-spin system. The dynamics goes along the adiabatic passage $|{\lambda }_{+}\rangle$ from the state $|\downarrow \uparrow \uparrow \rangle$ to the state $|\uparrow \uparrow \downarrow \rangle$ with the parameter $J_0=1/T$. Here the red and blue lines depict the results with and without DM interactions, respectively.