Quantum linear network coding for entanglement distribution in restricted architectures

• Published in: Quantum (Vienna, Austria) Vol. 4; p. 356
• Main Authors: Beaudrap, Niel de, Herbert, Steven
• Format: Journal Article
• Language: English
• Published: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 01.11.2020
• ISSN: 2521-327X; 2521-327X
• DOI: 10.22331/q-2020-11-01-356

In this paper we propose a technique for distributing entanglement in architectures in which interactions between pairs of qubits are constrained to a fixed network G . This allows for two-qubit operations to be performed between qubits which are remote from each other in G , through gate teleportation. We demonstrate how adapting quantum linear network coding to this problem of entanglement distribution in a network of qubits can be used to solve the problem of distributing Bell states and GHZ states in parallel, when bottlenecks in G would otherwise force such entangled states to be distributed sequentially. In particular, we show that by reduction to classical network coding protocols for the k -pairs problem or multiple multicast problem in a fixed network G , one can distribute entanglement between the transmitters and receivers with a Clifford circuit whose quantum depth is some (typically small and easily computed) constant, which does not depend on the size of G , however remote the transmitters and receivers are, or the number of transmitters and receivers. These results also generalise straightforwardly to qudits of any prime dimension. We demonstrate our results using a specialised formalism, distinct from and more efficient than the stabiliser formalism, which is likely to be helpful to reason about and prototype such quantum linear network coding circuits.