We study the problem of quantum multi-unicastcommunication over the butterfly network in a quantum-walk architecture,where multiple arbitrary single-qubit states are transmitted simultaneouslybetween multiple source-sink pairs. Here, by introducing quantum walks, wedemonstrate a quantum multi-unicast communication scheme over the butterflynetwork and the inverted crown network, respectively, where the arbitrarysingle-qubit states can be efficiently transferred with both the probabilityand the state fidelity one. The presented result concerns only the butterflynetwork and the inverted crown network, but our techniques can be applied toa more general graph. It paves a way to combine quantum computation andquantum network communication.
Figure 1
(Color online) The butterfly network and its corresponding graph. (a) The butterfly network and (b) 6-cycle. The six nodes connected by blue lines consist of a 6-cycle. $A_1~$ and $A_2~$ are source nodes. Target nodes $B_1 $ and $B_2~$, and intermediate nodes $C_{1}$ and $C_{2}$.
Figure 2
(Color online) Probability (a) and fidelity (b) the QW from $A_1$ to $B_1$ at the butterfly network. The number of steps $t~=~\left(~{N~/~2}\right)~+ n\times~N,N~=~6,n~=~0,1,2,3,\ldots$, and $\alpha$ is the amplitude of the initial coin state $\left|~{\psi~_0~}\right\rangle =~\alpha~\left|~0~\right\rangle~+~\beta~\left|~1~\right\rangle~$.
Figure 3
(Color online) The inverted crown network and its corresponding graph. (a) The inverted crown network.protectłinebreak (b) The corresponding graph. $~A_{1}$, $A_{2}$ and $A_{3}$ are the source nodes. The target nodes are $B_{1}$, $B_{2}$ and $B_{3}$, and the intermediate nodes are $C_{1}$ and $C_{2}$. A cycle is composed of the edges with the same roughness.
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