Quantum linear network coding for entanglement distribution in restricted architectures

Niel de Beaudrap1 and Steven Herbert1,2

1Department of Computer Science, University of Oxford, UK
2Riverlane, 1st Floor St Andrews House, 59 St Andrews Street, Cambridge, UK

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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 $\textit{quantum linear network coding}$ 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.

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[1] Michael Beverland, Vadym Kliuchnikov, and Eddie Schoute, "Surface Code Compilation via Edge-Disjoint Paths", PRX Quantum 3 2, 020342 (2022).

[2] Niel de Beaudrap and Steven Herbert, "Fast Stabiliser Simulation with Quadratic Form Expansions", Quantum 6, 803 (2022).

[3] Steven Herbert, "Quantum Monte Carlo Integration: The Full Advantage in Minimal Circuit Depth", Quantum 6, 823 (2022).

[4] Cheeranjiv Pandey, Sanidhya Gupta, Rimon Ranjit Das, and Ankur Raina, 2023 National Conference on Communications (NCC) 1 (2023) ISBN:978-1-6654-5625-8.

[5] Mark Webber, Vincent Elfving, Sebastian Weidt, and Winfried K. Hensinger, "The impact of hardware specifications on reaching quantum advantage in the fault tolerant regime", AVS Quantum Science 4 1, 013801 (2022).

[6] Steven Herbert, "Increasing the classical data throughput in quantum networks by combining quantum linear network coding with superdense coding", Physical Review A 101 6, 062332 (2020).

The above citations are from Crossref's cited-by service (last updated successfully 2024-06-18 12:29:18) and SAO/NASA ADS (last updated successfully 2024-06-18 12:29:19). The list may be incomplete as not all publishers provide suitable and complete citation data.