Quantum repeaters have promised efficient scaling of quantum networks for over two decades. Despite numerous platforms proclaiming functional repeaters, the realization of large-scale networks remains elusive, indicating that the resources required to do so were thus far underestimated. Here, we investigate the dependence of the resource scaling of networks on realistic experimental errors. Using a nested repeater protocol based on the purification protocol by Bennett [], we provide an analytical approximation of the polynomial degree of the resources consumed by entanglement routing. Our error model predicts substantially stricter thresholds for efficient network operation than previously suggested, requiring two-qubit gate errors below 1.3% for resource scaling with polynomial degree below 10. The analytical model presented here provides insight into the reason why previous experimental implementations of quantum repeaters failed to scale efficiently and inform the development of truly scalable systems, highlighting the need for high-fidelity local two-qubit gates. We employ our analytical approximation of the scaling exponent as a figure of merit to compare different platforms and find that trapped ions and color centers in diamond currently provide the best route towards large-scale networks.
Quantum repeaters have promised efficient scaling of quantum networks for over two decades. Despite numerous platforms proclaiming functional repeaters, the realization of large-scale networks remains elusive, indicating that the resources required to do so were thus far underestimated. Here, we investigate the dependence of the resource scaling of networks on realistic experimental errors. Using a nested repeater protocol based on the purification protocol by Bennett [], we provide an analytical approximation of the polynomial degree of the resources consumed by entanglement routing. Our error model predicts substantially stricter thresholds for efficient network operation than previously suggested, requiring two-qubit gate errors below 1.3% for resource scaling with polynomial degree below 10. The analytical model presented here provides insight into the reason why previous experimental implementations of quantum repeaters failed to scale efficiently and inform the development of truly scalable systems, highlighting the need for high-fidelity local two-qubit gates. We employ our analytical approximation of the scaling exponent as a figure of merit to compare different platforms and find that trapped ions and color centers in diamond currently provide the best route towards large-scale networks.
A large scale quantum network requires the distribution of high-fidelity end-to-end entanglement. To overcome the range limitations inherent to terrestrial fiber, a leading architecture has emerged: satellite-based sources transmitting entanglement to quantum repeaters on the ground. By bridging the gap between abstract analytical frameworks and computationally heavy numerical simulations, this paper provides the first quantitative answer to the question of such a network's achievable performance with current and near-term space technology, while accounting for entanglement swapping and purification. This is achieved by integrating a detailed physical model of a satellite-to-ground link into an analytical entanglement resource estimation framework for quantum repeaters, enabling an optimization of the end-to-end entanglement rate. Our analysis, performed across leading quantum hardware platforms, shows that Low Earth Orbit satellite constellations combined with quantum repeaters employing Neutral Atom or Nitrogen and Silicon Vacancy qubits, could enable a global quantum network, distributing entanglement over distances up to 20,000 km, sufficient for connecting any two points on Earth. This work highlights the major bottlenecks in space and quantum hardware technologies, which need to be addressed, thereby guiding informed investments necessary for enabling a large scale quantum network.
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.
Developing and deploying advanced Quantum Repeater (QR) technologies will be necessary to scale quantum networks to 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 networks, or a specific regime of operational parameters. We perform theoretical analysis and simulations of quantum repeaters and networks to investigate the relative performance and resource requirements of different quantum network paradigms. Our results will help guide the optimization of quantum hardware and components and shed light on the role of a robust control plane. We present our research findings on theoretical analysis and simulations of memory-based first-generation trapped-ion quantum repeaters and networks, and all-photonic entanglement-based quantum repeaters and networks. We study the relative performance in terms of entanglement generation rate and fidelity, as well as the resource requirements of these two different quantum network paradigms.
This paper presents a comprehensive study on the scalability challenges and opportunities in quantum communication networks, with the goal of determining parameters that impact networks most as well as the trends that appear when scaling networks. We design simulations of quantum networks comprised of router nodes made up of trapped-ion qubits, separated by quantum repeaters in the form of Bell State Measurement (BSM) nodes. Such networks hold the promise of securely sharing quantum information and enabling high-power distributed quantum computing. Despite the promises, quantum networks encounter scalability issues due to noise and operational errors. Through a modular approach, our research aims to surmount these challenges, focusing on effects from scaling node counts and separation distances while monitoring low-quality communication arising from decoherence effects. We aim to pinpoint the critical features within networks essential for advancing scalable, large-scale quantum computing systems. Our findings underscore the impact of several network parameters on scalability, highlighting a critical insight into the trade-offs between the number of repeaters and the quality of entanglement generated. This paper lays the groundwork for future explorations into optimized quantum network designs and protocols.
Efficient classical simulation of large-scale quantum networks frequently relies on noise approximations, which consider a restricted set of operators to describe noisy channels and operations. In this work, we demonstrate how such simplified error models, such as Pauli twirling or reset channels, can lead to severe quantitative and qualitative discrepancies in protocol performance predictions. We analyze, in particular, how small differences can accumulate in iterative and sequential protocols such as entanglement purification, entanglement swapping, and repeater chains. Our results reveal that neglected error contributions can lead to important performance under- and over-estimations, measurement-outcome dependency, and oscillations in the fidelity, which are entirely overlooked by the simplified error model approximations. These results show that rigorous validation of complete noise architectures is indispensable for accurately predicting operational thresholds in future quantum technologies.
A fully-quantum network implies the creation of quantum entanglement between a given source node and some other destination node, with a number of quantum repeaters in between. This paper tackles the problem of quantum entanglement distribution by solving the routing problem over an infrastructure based on quantum repeaters and with a finite number of pairs of entangled qubits available in each link. The network model considers that link purification is available such that a nested purification protocol can be applied at each link to generate entangled qubits with higher fidelity than the original ones. A low-complexity multi-objective routing algorithm to find the shortest path between any two given nodes is proposed and assessed for random networks, using a fairly general path extension mechanism that can fit a large family of particular technological requirements. Different types of quantum protocols require different levels of fidelity for the entangled qubit pairs. For that reason, the proposed algorithm identifies the shortest path between two nodes that assures an end-to-end fidelity above a specified threshold. The minimum requirements for the end-to-end entanglement fidelity depend on the whole extension of the paths, and cannot be looked at as a local property of each link. Moreover, one needs to keep track not only of the shortest path, but also of longer paths holding more entangled qubits than the shorter paths in order to satisfy the fidelity criterion. Thus, standard single parameter shortest-path algorithms do not necessarily converge to the optimal solution. The problem of finding the best path in a network subject to multiple criteria (known as multi-objective routing) is, in general, an NP-hard problem due to the rapid growth of the number of stored paths. This work proposes a metric that identifies and discards paths that are objectively worse than others. By doing so, the time complexity of the proposed algorithm scales near-to-linearly with respect to the number of nodes in the network, showing that the shortest-path problem in quantum networks can be solved with a complexity very close to the one of the classical counterparts. That is analytically proved for the case where all the links of a path have the same fidelity (homogeneous model). The algorithm is also adapted to a particular type of path extension, where different links along a path can be purified to different degrees, asserting its flexibility and near-to-linearity even when heterogeneous fidelities along the sections of a path are considered.