Emerging communication systems are expected to integrate new types of communication networks including quantum networks. In contrast to classical networks, the communication in quantum networks is accomplished with qubits and their attribute entanglement. Entanglement is a type of correlation between multiple qubits with no counterpart in classical communication. With the help of entanglement new protocols are developed to perform classical and quantum network tasks more efficiently. The main task of quantum networks is to share entanglement to distant communication partners with the help of intermediate nodes and repeated entanglement swapping, the so called Repeater Protocol. Due to the decoherence of quantum states, establishing entanglement has to be accomplished with minimal delay to preserve the states of qubits. This paper proposes a new Repeater Protocol FRP, which reduces delay by up to 51% and on average by 13% in establishing end-to-end entanglement compared with the direct approach CRP. Additionally, the provided solution lowers hardware requirements for quantum routers. Both protocols, CRP and FRP are evaluated in terms of end-to-end delay and fidelity in extensive simulations with a parameter search on 3 different topologies.
Emerging communication systems are expected to integrate new types of communication networks including quantum networks. In contrast to classical networks, the communication in quantum networks is accomplished with qubits and their attribute entanglement. Entanglement is a type of correlation between multiple qubits with no counterpart in classical communication. With the help of entanglement new protocols are developed to perform classical and quantum network tasks more efficiently. The main task of quantum networks is to share entanglement to distant communication partners with the help of intermediate nodes and repeated entanglement swapping, the so called Repeater Protocol. Due to the decoherence of quantum states, establishing entanglement has to be accomplished with minimal delay to preserve the states of qubits. This paper proposes a new Repeater Protocol FRP, which reduces delay by up to 51% and on average by 13% in establishing end-to-end entanglement compared with the direct approach CRP. Additionally, the provided solution lowers hardware requirements for quantum routers. Both protocols, CRP and FRP are evaluated in terms of end-to-end delay and fidelity in extensive simulations with a parameter search on 3 different topologies.
Future communication systems are expected to integrate quantum networks to enable highly secure communication and enhance computational capabilities. In quantum networks, communication is accomplished by sharing entanglement between remote locations, which is the basis for most known quantum protocols. Entanglement is a correlation between qubits that is not reproducible with classical means. However, as entanglement is susceptible to noise limiting its range, quantum repeaters can enable entanglement over more considerable distances. Using the entanglement swapping protocol, quantum repeaters can be placed between remote locations to establish entanglement. This requires each repeater to first generate entanglement with its neighboring nodes, named entanglement generation. However, as the size of current quantum networks is limited, the development and evaluation of quantum networks and quantum protocols is based on simulations. To simulate quantum networks accurately, accurate and high-performance models of the entanglement generation process must be employed. This paper proposes two new models for generating entanglement in simulations and develops quantum protocols for generating and purifying entanglement. The protocols are evaluated in thorough simulations under perfect and realistic conditions regarding delay and fidelity. Furthermore, the accuracy and runtime of the models are evaluated. The results show the models are accurate, with delay primarily influenced by the source duration, while longer coherence times significantly enhance fidelity. The model runtimes are consistently shorter than the simulation runtimes across all protocols, averaging about 2% of the total simulation time.
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.
With the emergence of the Quantum Internet, the need for advanced quantum networking techniques has significantly risen. Various models of quantum repeaters have been presented, each delineating a unique strategy to ensure quantum communication over long distances. We focus on repeaters that employ entanglement generation and swapping. This revolves around establishing remote end-to-end entanglement through repeaters, a concept we denote as the “quantum-native” repeaters (also called “first-generation” repeaters in some literature). The challenges in routing with quantum-native repeaters arise from probabilistic entanglement generation and restricted coherence time. Current approaches use synchronized time slots to search for entanglement-swapping paths, resulting in inefficiencies. Here, we propose a new set of asynchronous routing protocols for quantum networks by incorporating the idea of maintaining a dynamic topology in a distributed manner, which has been extensively studied in classical routing for lossy networks, such as using a destination-oriented directed acyclic graph or a spanning tree. The protocols update the entanglement-link topology asynchronously, identify optimal entanglement-swapping paths, and preserve unused direct-link entanglements. Our results indicate that asynchronous protocols achieve a larger upper bound with an appropriate setting and significantly higher entanglement rate than existing synchronous approaches, and the rate increases with coherence time, suggesting that it will have a much more profound impact on quantum networks as technology advances.
Emerging experimental quantum network deployments are based on collaborations between research institutions and rely on telecommunications fiber infrastructure. Currently, such networks consist of mostly Dual Input Repeaters (DIRs) and can be viewed as composed of (mostly) line graphs. In order to evaluate the performance of such networks (e.g., in terms of Entangled Pair Rate, EPR, and average Fidelity) we developed a custom quantum network simulation platform that takes into account both the quantum and classical network components. To support the verification of the simulation results, we develop a novel approach for performance analysis of DIRs. We compare the simulation results to the analytical results for DIRs and to prior results for repeaters with more than two inputs. We observe that although the expected memory utilization cannot be bounded, \emph{a small DIR memory size is sufficient and leads to minimal performance degradation}. For line networks with a single repeater and 3 repeaters, we explore the dependency of incoming and outgoing memory size requirements on the number of nodes (network size), their connectivity (fiber length) and various quantum error settings (amplitude damping and phase flip channels). We evaluate the \emph{EPR} and the \emph{average Fidelity} for a sub-network of a deployed network with 3 repeaters, using two alternative paths. We show that as the number of nodes increases or when the fiber lengths between nodes differ significantly, additional node memory is needed to maintain the same EPR (qubits are stored for longer duration to allow completion of entanglement across the network). We also show that the memory size should be above some minimum threshold to allow EP creation (EPR >0) as pair selection and swapping completion propagate across the network.
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.
Quantum internet offers a variety of applications that either enhance or surpass its classical counterpart. Quantum repeaters are imperative to a quantum network as they connect between two quantum nodes, and create quantum entanglement between two targeted nodes with entanglement swapping protocol which require resource from both connections. As a quantum state has a finite decoherent time, it is crucial that a connection protocol is performed efficiently and within suitable time interval, so that two end-to-end matter qubits are entangled. We simulate a second generation network of quantum repeaters, one that is capable of quantum error correction, to estimate the waiting time needed to establish connection between distant nodes. Simulations are performed for a linear chain of nodes with unequal path lengths, and loss rates. We find that asymmetry of path lengths contributes to the waiting time of physical qubits. By simply adjusting the photon generation rate from one of its nodes, the waiting time is reduced while the time to complete quantum state tomography remains unaffected. This simple adjustment can play important roles in compensating for distance asymmetry when a quantum repeater is not stationary.