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.
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.
Quantum repeater networks have attracted attention for the implementation of long-distance and large-scale sharing of quantum states. Recently, researchers extended classical network coding, which is a technique for throughput enhancement, into quantum information. The utility of quantum network coding (QNC) has been shown under ideal conditions, but it has not been studied previously under conditions of noise and shortage of quantum resources. We analyzed QNC on a butterfly network, which can create end-to-end Bell pairs at twice the rate of the standard quantum network repeater approach. The joint fidelity of creating two Bell pairs has a small penalty for QNC relative to entanglement swapping. It will thus be useful when we care more about throughput than fidelity. We found that the output fidelity drops below 0.5 when the initial Bell pairs have fidelity F<0.90, even with perfect local gates. Local gate errors have a larger impact on quantum network coding than on entanglement swapping.
Quantum network coding can effectively improve the aggregate throughput of quantum networks and alleviate bottlenecks caused by topological constraints. Most of previous schemes are dedicated to the efficient teleportation of unknown quantum states in a quantum network. Herein a proposal for transmission of deterministic known states over quantum repeater network based on quantum measurements. We show that the new protocol offers advantages over three aspects. Firstly, the senders in our protocol obtain the knowledge of the quantum state to be transmitted, which enables the autonomy of quantum network transmission. Secondly, we study the quantum repeater network coding for long-distance deterministic quantum state communication. Quantum repeater network initialization requires entanglement distribution only among neighboring nodes, greatly saving entanglement resources, channel overhead and storage costs. Thirdly, based on Pauli measurements and local complementation, new protocol realizes parallel coding operations to mitigate latency issues sufficiently. Combining quantum network coding and quantum remote state preparation technology, our protocol provides an important solution for deterministic known states transmission over large-scale quantum network in the future.
Network coding is an effective means to enhance the communication efficiency. The characterization of network solvability is one of the most important topic in this field. However, for general network, the solvability conditions are still a challenge. In this paper, we consider the solvability of general quantum k-pair network in measurement-based framework. For the first time, a detailed account of measurement-based quantum network coding(MB-QNC) is specified systematically. Differing from existing coding schemes, single qubit measurements on a pre-shared graph state are the only allowed coding operations. Since no control operations are concluded, it makes MB-QNC schemes more feasible. Further, the sufficient conditions formulating by eigenvalue equations and stabilizer matrix are presented, which build an unambiguous relation among the solvability and the general network. And this result can also analyze the feasibility of sharing k EPR pairs task in large-scale networks. Finally, in the presence of noise, we analyze the advantage of MB-QNC in contrast to gate-based way. By an instance network [Formula: see text], we show that MB-QNC allows higher error thresholds. Specially, for X error, the error threshold is about 30% higher than 10% in gate-based way. In addition, the specific expressions of fidelity subject to some constraint conditions are given.
In quantum networks an important goal is to reduce resource requirements for the transport and communication of quantum information. Quantum network coding presents a way to do this by distributing entangled states over a network that would ordinarily exhibit contention. In this work, we study measurement-based quantum network coding (MQNC), which is a protocol particularly suitable for noisy intermediate-scale quantum devices. In particular, we develop techniques to adapt MQNC to state-of-the-art superconducting processors and subsequently demonstrate successful teleportation of quantum information, giving new insight into MQNC in this context after a previous study was not able to produce a useful degree of entanglement. The teleportation in our demonstration is shown to occur with fidelity higher than could be achieved via classical means, made possible by considering qubits from a polar cap of the Bloch sphere. We also present a generalization of MQNC with a simple mapping onto the heavy-hex processor layout and a direct mapping onto a proposed logical error-corrected layout. Our work provides some useful techniques to test and successfully carry out quantum network coding.
Quantum repeaters are essential for scalable long-distance quantum networking. As quantum information processing moves toward fault-tolerant and error-corrected operations, it becomes increasingly important to study quantum repeaters that also move beyond raw physical entanglement and towards logical entanglement. In this paper, we implement and simulate the quantum repeater with encoding and classical error correction (QRE-CEC) protocol in SeQUeNCe, a discrete-event simulator of quantum networks. The protocol distributes logical Bell pairs, performs encoded entanglement swapping, and uses classical error correction for the decoding of entanglement swapping measurement outcomes to determine Pauli-frame corrections. For this study, we extend SeQUeNCe with a stabilizer-based backend, add support for CSS code-based encoded operations, and integrate gate, measurement, idle decoherence, and state-initialization noise models. Our simulation results show that QRE-CEC suppresses all modeled errors to the second order. Also, QRE-CEC can distribute logical Bell pairs with 0.91 fidelity over a distance of 2000 km under the parameter regimes we study. Beyond protocol-level performance evaluation, our implementation exposes practical simulator and control-plane challenges that are typically abstracted away in theoretical studies.
Abstract Quantum network coding (QNC) aims at alleviating quantum communication congestion in quantum networks. Although several QNC protocols have been presented, they cannot meet the practical requirements that part of source nodes intend to transmit their quantum states with same or different qubit numbers via the bottleneck network simultaneously. Here, the study presents a flexible QNC protocol by using quantum multiplexing. First, the entangled pairs are generated between adjacent nodes in a heralded way by using quantum multiplexing. Then the quantum memories of the source nodes and the ones of the corresponding target nodes are entangled when the intermediate nodes execute multiple rounds of entanglement swapping operations on their quantum memories. Finally, the quantum states are transmitted from the source nodes to their corresponding target nodes by means of quantum teleportation. Compared with the existing protocols, the protocol allows an arbitrary part of the source nodes to transmit their quantum states with same or different qubit numbers via the bottleneck network simultaneously, thereby exhibiting its flexibility.