We conduct a numerical investigation of fiber-based entanglement distribution over distances of up to 1600 km using a chain of processing-node quantum repeaters. We determine minimal hardware requirements while simultaneously optimizing over protocols for entanglement generation and entanglement purification, as well as over strategies for entanglement swapping. Notably, we discover that through an adequate choice of protocols the hardware improvement cost scales linearly with the distance covered. Our results highlight the crucial role of good protocol choices in significantly reducing hardware requirements, such as employing purification to meet high-fidelity targets and adopting a swap as soon as possible policy for faster rates. To carry out this analysis, we employ an extensive simulation framework implemented with NetSquid, a discrete-event-based quantum-network simulator, and a genetic-algorithm-based optimization methodology to determine minimal hardware requirements.@en

In blind quantum computing (BQC), a user with a simple client device can perform a quantum computation on a remote quantum server such that the server cannot gain knowledge about the computation. Here, we numerically investigate hardware requirements for verifiable BQC using an ion trap as server and a distant measurement-only client. While the client has no direct access to quantum-computing resources, it can remotely execute quantum programs on the server by measuring photons emitted by the trapped ion. We introduce a numerical model for trapped-ion quantum devices in NetSquid, a discrete-event simulator for quantum networks. Using this, we determine the minimal hardware requirements on a per-parameter basis to perform the verifiable BQC protocol. We benchmark these for a five-qubit linear graph state, with which any single-qubit rotation can be performed, where client and server are separated by 50 km. Current state-of-the-art ion traps satisfy the minimal requirements on a per-parameter basis, but all current imperfections combined make it impossible to perform the blind computation securely over 50 km using existing technology. Using a genetic algorithm, we determine the set of hardware parameters that minimises the total improvements required, finding directions along which to improve hardware to reach our threshold error probability that would enable experimental demonstration. In this way, we lay a path for the near-term experimental progress required to realise the implementation of verifiable BQC over a 50 km distance.@en

We perform a numerical study of the distribution of entanglement on a real-world fiber grid connecting the German cities of Bonn and Berlin. The connection is realized using a chain of processing-node quantum repeaters spanning roughly 900 kilometers. Their placement is constrained by the fiber grid we consider, resulting in asymmetric links. We investigate how minimal hardware requirements depend on the target application, as well as on the number of repeaters in the chain. We find that requirements for blind quantum computing are markedly different than those for quantum key distribution, with the required coherence time being around two and a half times larger for the former. Further, we observe a trade-off regarding how target secret-key rates are achieved when using different numbers of repeaters: comparatively low-quality entangled states generated at a high rate are preferred for higher numbers of repeaters, whereas comparatively high-quality states generated at a lower rate are favored for lower numbers of repeaters. To obtain our results we employ an extensive simulation framework implemented using NetSquid, a discrete-event simulator for quantum networks. These are combined with an optimization methodology based on genetic algorithms to determine minimal hardware requirements.@en

We numerically study the distribution of entanglement between the Dutch cities of Delft and Eindhoven realized with a processing-node quantum repeater and determine minimal hardware requirements for verifiable blind quantum computation using color centers and trapped ions. Our results are obtained considering restrictions imposed by a real-world fiber grid and using detailed hardware-specific models. By comparing our results to those we would obtain in idealized settings, we show that simplifications lead to a distorted picture of hardware demands, particularly on memory coherence and photon collection. We develop general machinery suitable for studying arbitrary processing-node repeater chains using NetSquid, a discrete-event simulator for quantum networks. This enables us to include time-dependent noise models and simulate repeater protocols with cut-offs, including the required classical control communication. We find minimal hardware requirements by solving an optimization problem using genetic algorithms on a high-performance-computing cluster. Our work provides guidance for further experimental progress, and showcases limitations of studying quantum-repeater requirements in idealized situations.

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The future quantum internet promises to enable users all around the world to, among other applications, generate shared secure keys and perform distributed quantum computations. To do so, entanglement must be distributed between remote users. One way of doing this is by sending photons through optical fiber, which allows for reusing some existent classical infrastructure. However, the probability of photons being absorbed in optical fiber grows exponentially with the distance covered, rendering entanglement generation at larger-than-metropolitan scales unfeasible. One possible approach to enable distributing entanglement over larger distances is to employ quantum repeaters, devices that can in theory mitigate the effects of fiber loss by splitting the total distance to be covered into smaller segments. Despite recent advances, the required technology is still under development. In this dissertation we aim to contribute to a swifter realization of fiber-based quantum-repeater networks. To this end, we introduce a methodology combining quantum-network simulations and genetic-algorithm-based optimizations that allows for determining hardware requirements for quantum repeaters. Using this methodology we translate quantum-network-application-derived performance metrics into specific requirements on the quantum repeaters used to implement the quantum network. This indicates not only how good hardware must be in order to enable given applications, but also in what specific ways state-of-the-art hardware must be improved to do so. We also investigate the effects of using existing fiber infrastructure for the deployment of near-term quantum networks. Doing so would be a cost-effective way of constructing quantum networks. However, existing infrastructure also imposes constraints, namely on where quantum hardware can be placed. We quantify to what extent such constraints affect quantum-network performance, as well as how these effects can be mitigated by optimizing repeater placement. Finally, we contribute to answering the question of how to extract the best possible performance out of imperfect hardware. For a given hardware quality, making the right choices with regards to what protocols are executed by the nodes and where nodes are placed can result in significant boosts in performance. We perform a joint hardware-protocol optimization and find that good hardware choices can significantly relax hardware requirements, as well as highlight multiple possible paths to functional quantum-repeater networks. We also provide tools for the discovery of entanglement generation protocols. @en

Quantum network protocols offer new functionalities such as enhanced security to communication and computational systems. Despite the rapid progress in quantum hardware, it has not yet reached a level of maturity that enables execution of many quantum protocols in practical settings. To develop quantum protocols in real world, it is necessary to examine their performance considering the imperfections in their practical implementation using simulation platforms. In this paper, we consider several quantum protocols that enable promising functionalities and services in near-future quantum networks. The protocols are chosen from both areas of quantum communication and quantum computation as follows: quantum money, W-state based anonymous transmission, verifiable blind quantum computation, and quantum digital signature. We use NetSquid simulation platform to evaluate the effect of various sources of noise on the performance of these protocols, considering different figures of merit. We find that to enable quantum money protocol, the decoherence time constant of the quantum memory must be at least three times the storage time of qubits. Furthermore, our simulation results for the w-state based anonymous transmission protocol show that to achieve an average fidelity above 0.8 in this protocol, the storage time of sender’s and receiver’s particles in the quantum memory must be less than half of the decoherence time constant of the quantum memory. We have also investigated the effect of gate imperfections on the performance of verifiable blind quantum computation. We find that with our chosen parameters, if the depolarizing probability of quantum gates is equal to or greater than 0.05, the security of the protocol cannot be guaranteed. Lastly, our simulation results for quantum digital signature protocol show that channel loss has a significant effect on the probability of repudiation.

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Long-distance quantum communication via entanglement distribution is of great importance for the quantum internet. However, scaling up to such long distances has proved challenging due to the loss of photons, which grows exponentially with the distance covered. Quantum repeaters could in theory be used to extend the distances over which entanglement can be distributed, but in practice hardware quality is still lacking. Furthermore, it is generally not clear how an improvement in a certain repeater parameter, such as memory quality or attempt rate, impacts the overall network performance, rendering the path toward scalable quantum repeaters unclear. In this work we propose a methodology based on genetic algorithms and simulations of quantum repeater chains for optimization of entanglement generation and distribution. By applying it to simulations of several different repeater chains, including real-world fiber topology, we demonstrate that it can be used to answer questions such as what are the minimum viable quantum repeaters satisfying given network performance benchmarks. This methodology constitutes an invaluable tool for the development of a blueprint for a pan-European quantum internet. We have made our code, in the form of NetSquid simulations and the smart-stopos optimization tool, freely available for use either locally or on high-performance computing centers.

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