Analysis of measurement-based quantum network coding over repeater networks under noisy conditions

Abstract

Quantum network coding is an effective solution for alleviating bottlenecks in quantum networks. We introduce a measurement-based quantum network coding scheme for quantum repeater networks (MQNC), and analyze its behavior based on results acquired from Monte-Carlo simulation that includes various error sources over a butterfly network. By exploiting measurement-based quantum computing, operation on qubits for completing network coding proceeds in parallel. We show that such an approach offers advantages over other schemes in terms of the quantum circuit depth, and therefore improves the communication fidelity without disturbing the aggregate throughput. The circuit depth of our protocol has been reduced by 56.5% compared to the quantum network coding scheme (QNC) introduced in 2012 by Satoh, et al. For MQNC, we have found that the resulting entangled pairs' joint fidelity drops below 50% when the accuracy of local operations is lower than 98.9%, assuming that all initial Bell pairs across quantum repeaters have a fixed fidelity of 98%. Overall, MQNC showed substantially higher error tolerance compared to QNC and slightly better than buffer space multiplexing using step-by-step entanglement swapping, but not quite as strong as simultaneous entanglement swapping operations.

Towards Real‐World Quantum Networks: A Review

“…For instance, Satoh et al have proposed a protocol that works in quantum repeater networks, [247] and Matsuo et al further simplified this protocol by introducing measurement-based quantum computing. [248]…”

Transforming graph states to Bell-pairs is NP-Complete

“…The problem of transforming graph states to Bell-pairs using local operations is a problem with direct applications to the development of quantum networks or distributed quantum processors. Solutions to special cases of this problem have been considered in for example [2] and [5]. However, at least to our knowledge, the computational complexity of this problem was previously unknown.…”

“…Hence there is a need for fast algorithms to decide whether different entangled states can be converted into each other by local operations. In [5], measurement-based quantum network coding was introduced, where one step in the procedure includes transforming general graph states into Bell-pairs using single-qubit Clifford operations, single-qubit Pauli measurement and classical communication: LC + LPM + CC. However, the computational complexity of finding the correct operations or even Our main result is that we prove that the problem of deciding whether a given graph state can be converted into Bell Pairs using only LC + LPM + CC (BellVM) is in general NP-Complete.…”

Towards real-world quantum networks: a review

“…The concepts in quantum repeater network also give drive force to quantum network coding technology. For instance, T. Satoh et al have proposed a protocol that works in quantum repeater networks [244], and T. Matsuo et al further simplified this protocol by introducing measurement-based quantum computing [245].…”