We implement a set of simulation experiments in NetSquid specifically designed to estimate the end-to-end fidelity across a path of quantum repeaters or quantum switches. The switch model includes several generalizations that are not currently available in other tools and are useful for gaining insight into practical and realistic quantum network engineering problems: an arbitrary number of memory registers at the switches, simplicity in including entanglement distillation mechanisms, arbitrary switching topologies, and routing protocols. An illustrative case study is presented, namely a comparison in terms of performance between a repeater chain where repeaters can only swap sequentially and a single switch equipped with multiple memory registers that is able to handle multiple swapping requests.
We implement a set of simulation experiments in NetSquid specifically designed to estimate the end-to-end fidelity across a path of quantum repeaters or quantum switches. The switch model includes several generalizations that are not currently available in other tools and are useful for gaining insight into practical and realistic quantum network engineering problems: an arbitrary number of memory registers at the switches, simplicity in including entanglement distillation mechanisms, arbitrary switching topologies, and routing protocols. An illustrative case study is presented, namely a comparison in terms of performance between a repeater chain where repeaters can only swap sequentially and a single switch equipped with multiple memory registers that is able to handle multiple swapping requests.
Entanglement-based networks (EBNs) enable general-purpose quantum communication by combining entanglement and its swapping in a sequence that addresses the challenges of achieving long-distance communication with high fidelity associated with quantum technologies. In this context, entanglement distribution refers to the process by which two nodes in a quantum network share an entangled state, serving as a fundamental resource for communication. In this paper, we study the performance of entanglement distribution mechanisms over a physical topology comprising end nodes and quantum switches, which are crucial for constructing large-scale links. To this end, we implemented a switch-based topology in NetSquid and conducted a series of simulation experiments to gain insight into practical and realistic quantum network engineering challenges. These challenges include, on the one hand, aspects related to quantum technology, such as memory technology, gate durations, and noise; and, on the other hand, factors associated with the distribution process, such as the number of switches, distances, purification, and error correction. All these factors significantly impact the end-to-end fidelity across a path, which supports communication between two quantum nodes. We use these experiments to derive some guidelines towards the design and configuration of future EBNs.
We evaluate the performance of two-way quantum repeater chains with sequential entanglement swapping. Within the analysis we consider memory decoherence, gate imperfections, and imperfect link-level entanglement generation. Our main results include closed-form expressions for the average entanglement fidelity of the generated end-to-end entangled states. We generalize previous findings for the one-shot fidelity analysis and study the case where repeater chains serve end-to-end requests continuously. We provide solutions to the continuous request scenario by combining results from quantum information theory and queuing theory. Finally, we apply the formulas obtained to analyze the impacts of hardware parameters, i.e., coherence times and gate fidelity, and distance on the entanglement fidelity and secret key rate of homogeneous quantum repeater chains.
When built, quantum repeater networks will require classical network protocols to control the quantum operations. However, existing work on repeaters has focused on the quantum operations themselves, with less attention paid to the contents, semantics, ordering and reliability of the classical control messages. In this work we define and describe our implementation of the classical control protocols. The state machines and packet sequences for the three protocol layers are presented, and operation confirmed by running the protocols over simulations of the physical network. We also show that proper management of the resources in a bottleneck link allows the aggregate throughput of two end-to-end flows to substantially exceed that of a single flow. Our layered architectural framework will support independent evolution of the separate protocol layers. Networks of quantum repeaters utilize three concepts to execute a distributed algorithm that creates entangled quantum states between nodes that are far apart: a basic entanglement mechanism which depends on the physical implementation, error management (in this work, we study a method known as purification), and finally a quantum state propagation layer (here we implement entanglement swapping, which builds multi-hop connections from single-hop connections). Some researchers are investigating approaches that are substantially different from entanglement swapping [30, 24, 19]. Here we focus on swapping, but the layered architecture approach is broadly applicable, allowing other implementations to replace only a single layer in the protocol stack. Previous work primarily focused on the physical and mathematical tools for building repeaters. Classical information is also needed to enable teleportation and swapping, as many quantum operations are not deterministic, and results of quantum measurements need to be reported to distant partners before further operations can proceed. Also, operations in the middle of the network must be coordinated to route and swap properly. This requires classical messages to make operations robust, but message propagation times penalize performance. Even though this delay is usually included in repeater simulations, prior work has not defined the protocols in detail, especially with respect to how all of the nodes make consistent decisions in a timely fashion. In this work, we introduce a protocol stack for networks of quantum repeaters that considers all the necessary classical messages and which can be easily adapted for different approaches at all three protocol layers. We run simulations of competing flows on a dumbbell topology in order to increase our confidence in the behavior of our network protocols. By adjusting the fidelity thresholds required for entanglement swapping, we show that some configurations boost the aggregate throughput for multiple flows significantly above the maximum for a single flow, taking advantage of resources that would otherwise sit idle. The operation of such complex networks and such delicate tuning of the system without formal protocol definitions would not be possible. Previous work has also concentrated almost exclusively on the dedicated use of a single line or chain of repeaters, delivering Bell pairs only to the two nodes at the ends of the chain. Networks, however, typically have more than two end points, and allow any pair of these end nodes to communicate. More topologically complex networks, with numerous end nodes, are obviously much more scalable than connecting every possible pair of nodes using a dedicated line of repeaters. we investigate how classical multiplexing schemes translate to the domain of quantum repeaters, in order to manage shared resources and active communication flows of data from different stations. We simulate four sharing protocols in a complex network with competing traffic. Circuit switching gives any individual flow the best performance, but makes poor use of the overall network and is inflexible. We use circuit switching as our baseline case to compare time division multiplexing, buffer space multiplexing, and statistical multiplexing, and show that all multiplexing schemes are better than circuit switching. For the particular network simulated, we find that statistical multiplexing outperforms time division multiplexing by 28% and buffer space multiplexing by 13%. We find that all three multiplexing schemes are fair; each flow is penalized a similar percentage of its throughput as the the total number of users in the network increases. Finally, statistical multiplexing requires no network-wide coordination of the use of quantum memory or channels, and is easier to implement than a robust, scalable scheme for the other protocols. Our current results suggest that the best strategy for quantum repeater networks is statistical multiplexing. (This is in fact the quantum analogue of the basis on which the Internet works.) However, our current simulations are done with no degradation of memory over time, using the assumption of quantum error-corrected memory at each repeater; inclusion of decoherence and a finite qubit lifetime remains as future work.
Developing and deploying advanced Quantum Repeater (QR) technologies will be necessary to scale quantum networks at longer distances. Depending on the error mitigation mechanisms adopted to suppress loss and errors, QRs are typically classified into “memory-based” or “all-photonic” QRs, and each type of QR may be best suited for a specific type of underlying quantum technology, a particular scale of quantum network, or a specific regime of operational parameters. Modeling and simulation of quantum repeaters and networks can help in understanding the relative performance and resource requirements of different types of QRs, identify tradeoffs of alternative quantum network architectures, optimize quantum hardware, and assist in the design of a robust control plane. This paper introduces a quantum repeater simulation toolkit based on NetSquid, which includes component models and protocols to study advanced quantum repeater networks. We present our initial research findings on modeling and simulation of “allphotonic” entanglement-based QRs and “memory-based” first generation trapped ion QRs. We study the relative performance and resource requirements of these two different types of QRs and networks. The performance metrics include entanglement generation rate and fidelity between the endpoints of the network. For fair comparison of resource requirements of different types of QRs, entanglement generation rate is normalized by the total number of matter qubits involved.
The distribution of high-quality entanglement over long distances remains a challenge due to losses in quantum channels. As a solution, quantum repeater protocols generate entanglement over short segments and progressively extend its range using entanglement swapping, while using distillation to compensate for entanglement degradation. Numerous studies analyze repeater protocols through tailored tools that are tied to specific protocol types and network assumptions. In this work, we propose a formal language to specify quantum repeater protocols in a unified manner, modeling the concurrent distribution of entanglement across multiple pairs of network nodes. We consider delays arising from failures and contention for resources, and account for the effects of noise and decoherence on the quality of entanglement. Furthermore, we provide a prototype tool based on our language to precisely track the rate and fidelity of the distributed entangled pairs, supporting heterogeneous hardware configurations and constraints on available quantum memories. Finally, we demonstrate the effectiveness of our approach by expressing common protocols from the literature and evaluating their performance.
In this work we consider a quantum network consisting of multiple interconnected quantum repeaters. In this network, data plane of communication is achieved by photon transmission over fibre cables, while the control plane which transmits results of measurements and control information is implemented over classical Internet. Important part of the control plane is the server which distributes connection requests and entanglement resources to nodes involved in the path. Together, data and control plane establish reliable multi hop links over the network deploying purification and swapping operations. We analyze the performance of such a network using probabilistic model of communication time between repeaters, rather than slotted time. We consider random arrivals of connection requests to each repeater and variable path lengths. We model a single repeater using theory ofM[x]/G/m+rqueues where each batch request encompasses heralding, purification, and swapping times pertaining to a single repeater node. To model the network, we have used the concept of Jackson's network over repeater nodes in the path. This model allows derivation of end-to-end entanglement delivery time as random distribution and calculation of probability of decoherence of qubits stored in quantum memories over the path. We considered different numbers of entanglements per request and different types of quantum memories. Results of this analysis are useful for dimensioning capacities of quantum repeaters, memories and links in order to avoid decoherence of quantum memories.