  Many quantum computational tasks have inherent symmetries, suggesting a path
to enhancing their efficiency and performance. Exploiting this observation, we
propose representation matching, a generic probabilistic protocol for reducing
the cost of quantum computation in a quantum network. We show that the
representation matching protocol is capable of reducing the communication or
memory cost to almost minimum in various tasks, including remote execution of
unitary gate arrays, permutation gates and unitary conjugation, as well as the
storage and retrieval of unitary gates.
