Network coding for distributed quantum computation over cluster and butterfly networks

TL;DR

This paper explores how network coding can enable distributed quantum computation over specific network topologies, demonstrating the implementability of certain unitary operations with limited quantum communication.

Contribution

It introduces methods for implementing quantum unitaries over cluster and butterfly networks, connecting quantum network coding with classical network structures.

Findings

Any two-qubit unitary is implementable over butterfly and grail networks.

Quantum communication is limited to qubit transmission, but classical communication is unrestricted.

Probabilistic implementations of unitaries over cluster networks are analyzed.

Abstract

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.