Quantum state transfer in spin chains via shortcuts to adiabaticity

Based on shortcuts to adiabaticity and quantum Zeno dynamics, we present a protocol to implement quantum state transfer (QST) in a quantum spin-$\frac{1}{2}$ chain. In the protocol, the complex Hamiltonian of an $N$-site system is simplified, and a simple effective Hamiltonian is present. It is shown that only the control of the coupling strengths between the boundary spins and the bulk spins are required for QST. Numerical simulations demonstrate that the protocol possesses high efficiency and is robust against the decay and the fluctuations of the control fields. The protocol might provide an alternative choice for transferring quantum states via spin chain systems.

Figure 1

Schematic of the spin chain system. The goal is to transfer the state of the sender qubit to the receiver qubit.

Figure 2

(a) Fidelities versus $t/T$ for spin chain lengths $N=4$, 6, and 8. (b) Fidelities versus $t/T$ for spin chain lengths $N=5$, 7, and 9.

Figure 3

Infideltiies $1-F\left(T\right)$ as a function of $J_{B}T$ with spin chain lengths $N=4$, 5, and 7.

Figure 4

The exchange couplings for the $N=5$ case with the parameters set as $\beta \left(T\right)=3\pi$ and ${\phi }_N\left(T\right)=-2.5\pi$.

Figure 5

The final fidelity $F\left(T\right)$ versus $\delta J_R/J_R$ and $\delta J_S/J_S$ with $J_{B}T=1000$.

Figure 6

The final fidelity $F\left(T\right)$ versus $\gamma /J_M$ with $J_{B}T=1000$.