Perfect state transfer and efficient quantum routing: A discrete-time quantum-walk approach

We show that a perfect state transfer of an arbitrary unknown two-qubit state can be achieved via a discrete-time quantum walk with various settings of coin flips and extend this method to the distribution of an arbitrary unknown multiqubit entangled state between every pair of sites in the multidimensional network. Furthermore, we study the routing of quantum information on this network in a quantum-walk architecture, which can be used as quantum information processors to communicate between separated qubits.

Figure 1

Scheme of the state transfer in a 1D discrete-time QW architecture: (a) the walking direction corresponding to the resulting coin state, (b) the walking directions controlled by the biased coin flips, and (c) perfect transfer of the coin state $\alpha |0\rangle +\beta |1\rangle$ from position 0 to 3 after a five-step discrete-time QW. The red and blue arrows indicate the directions of the information flows of $\alpha$ and $\beta$, respectively. The protocol is shown in both (a) and (b) a tree diagram and (c) the number axis case.

Figure 2

Scheme in the two-dimensional case: (a) the walking direction corresponding to the resulting coin states and (b) perfect transfer of the coin state $\alpha |01\rangle +\beta |10\rangle$ from the original position (0,0) to the target position (1,3) after five steps. The first walker walks along the $x$ axis and the second walker walks along the $y$ axis. The red and blue arrows indicate the information flows of $\alpha$ and $\beta$, respectively.