Quantum linear network coding for entanglement distribution in restricted architecturesNiel de Beaudrap*

In many quantum hardware platforms, qubits are stored in immobile physical subsystems. Only particular pairs of spatially nearby physical qubits may directly interact, often arranged in some more-or-less periodic structure. We may describe the locations of the qubits, and the pairs which may interact, by the nodes and edges of a graph G. This raises the question of how best to perform 'remote' two-qubit operations, i.e., between qubits which are not adjacent in the graph G. 'Routing' consists of moving data physically by interchanging the data stored at various nodes in the graph; this requires many two-qubit operations, and an amount of time scaling as the distance between the nodes in the graph. If we realise two-qubit gates by gate teleportation, this reduces the problem of remote operations to the problem of entanglement swapping in the network G, which may be performed much more efficiently with fast classical processing of the teleporation measurement outcomes. However, this may still lead to bottlenecks in the graph G as one attempts to distribute multiple entangled pairs in parallel, across paths which cross in G. In this talk, I present techniques (developed with Steven Herbert) to distribute entanglement across well-structured graphs G, applying concepts from linear network coding to avoiding the problem of crossings.