  To apply network coding for quantum computation, we study the distributed
implementation of unitary operations over all separated input and output nodes
of quantum networks. We consider a setting of networks where quantum
communication between nodes is restricted to sending just a qubit, but
classical communication is unrestricted. We analyze which N-qubit unitary
operations are implementable over cluster networks by investigating
transformations of a given cluster network into quantum circuits. We show that
any two-qubit unitary operation is implementable over the butterfly network and
the grail network, which are fundamental primitive networks for classical
network coding. We also analyze probabilistic implementations of unitary
operations over cluster networks.
