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

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 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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One-way quantum repeaters where loss and operational errors are counteracted by quantum error-correcting codes can ensure fast and reliable qubit transmission in quantum networks. It is crucial that the resource requirements of such repeaters, for example, the number of qubits per repeater node and the complexity of the quantum error-correcting operations are kept to a minimum to allow for near-future implementations. To this end, we propose a one-way quantum repeater that targets both the loss and operational error rates in a communication channel in a resource-efficient manner using code concatenation. Specifically, we consider a tree-cluster code as an inner loss-tolerant code concatenated with an outer 5-qubit code for protection against Pauli errors. Adopting flag-based stabilizer measurements, we show that intercontinental distances of up to 10,000 km can be bridged with a minimized resource overhead by interspersing repeater nodes that each specialize in suppressing either loss or operational errors. Our work demonstrates how tailored error-correcting codes can significantly lower the experimental requirements for long-distance quantum communication.

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We study the performance (rate and fidelity) of distributing multipartite entangled states in a quantum network through the use of a central node. Specifically, we consider the scenario where the multipartite entangled state is first prepared locally at a central node and then transmitted to the end nodes of the network through quantum teleportation. As our first result, we present leading-order analytical expressions and lower bounds for both the rate and fidelity at which a specific class of multipartite entangled states, namely, Greenberger-Horne-Zeilinger (GHZ) states, are distributed. Our analytical expressions for the fidelity accurately account for time-dependent depolarizing noise encountered by individual quantum bits while stored in quantum memory, as verified using Monte Carlo simulations. As our second result, we compare the performance to the case where the central node is an entanglement switch and the GHZ state is created by the end nodes in a distributed fashion. Apart from these two results, we outline how the teleportation-based scheme could be physically implemented using trapped ions or nitrogen-vacancy centers in diamond.

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The future quantum internet promises to create shared quantum entanglement between any two points on Earth, enabling applications such as provably-secure communication and connecting quantum computers. A popular method for distributing entanglement is by sending entangled photons through optical fiber. However, the probability of successful transmission decreases exponentially with the fiber length. This makes it challenging to realize large fiber-based quantum networks that create shared entanglement, let alone the construction of a quantum internet. Quantum repeaters have been proposed as a solution to mitigate losses by acting as intermediary nodes that divide long optical fibers into smaller segments. The required technology, however, is still under development. In this thesis we aim to expedite the realization of fiber-based quantum networks by identifying shortcuts towards that end. One way in which we look for shortcuts is by identifying the technological advances that are required to build such networks. To achieve this we translate performance demands on the network to requirements on individual components, such as quantum repeaters. This way we are not only able to indicate how much development current-day technology still requires before functional quantum networks can be built, but also what specific set of improvements could be applied to state-of-the-art hardware to get there as soon as possible. A specific promising shortcut that we investigate in this thesis is the construction of quantum networks using existing fiber infrastructure. As deploying optical fiber is costly, an economical method for building quantum networks would be to incorporate fiber that has already been placed in the field. Existing infrastructure however imposes restrictions on quantum networks, in particular on the possible locations where quantum hardware could be installed. An important question to answer is then how severe the effects of these restrictions are. We address this question by investigating the performance degradation caused by displacing nodes from their optimal location, and the increase in required technological advances when restrictions are taken into account. Additionally, we provide tools for choosing where to deploy quantum repeaters when subject to placement restrictions. Finally, we also address the fact that quantum networks may need to provide entanglement to more than just two parties. When a network has many end nodes that require bipartite entanglement between different pairs of them, it is important that it is designed such that every end node is sufficiently connected to every other end node. We provide conditions to judge whether this is the case and a method to ensure the conditions are met. Alternatively end nodes could require multipartite entangled states shared by more than two of them, in which case specialized nodes may need to be included in the network. We investigate what such a node could look like and perform a thorough performance analysis.@en

We consider the problem of deploying a quantum network on an existing fiber infrastructure, where quantum repeaters and end nodes can only be housed at specific locations. We propose a method based on integer linear programming (ILP) to place the minimal number of repeaters on such an existing network topology, such that requirements on end-to-end entanglement-generation rate and fidelity between any pair of end-nodes are satisfied. While ILPs are generally difficult to solve, we show that our method performs well in practice for networks of up to 100 nodes. We illustrate the behavior of our method both on randomly-generated network topologies, as well as on a real-world fiber topology deployed in the Netherlands.

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