  This paper considers the communication over a quantum multiple-unicast
network where r sender-receiver pairs communicate independent quantum states.
We concretely construct a quantum network code for the quantum multiple-unicast
network as a generalization of the code [Song and Hayashi, arxiv:1801.03306,
2018] for the quantum unicast network. When the given node operations are
restricted to invertible linear operations between bit basis states and the
rates of transmissions and interferences are restricted, our code certainly
transmits a quantum state for each sender-receiver pair by n-use of the network
asymptotically, which guarantees no information leakage to the other users. Our
code is implemented only by the coding operation in the senders and receivers
and employs no classical communication and no manipulation of the node
operations. Several networks that our code can be applied are also given.
