Quantum networks hold the potential to enable new applications, such as secure key distribution, high-precision distributed sensing, and distributed quantum computing. A central functionality of a quantum network is the distribution of entanglement between remote parties. Since experimental implementations remain in an early stage, it is important to understand both the capabilities and limitations of near-term architectures. However, characterising quantum network performance is challenging, due to the complex, stochastic nature of even simple architectures. Analytical studies can therefore play a crucial role: they not only reduce computational cost but also reveal fundamental relationships between performance, the choice of entanglement distribution protocols, and properties of quantum network hardware. In this thesis, we develop analytical methods to study quantumnetwork performance in several important scenarios.

We firstly analyse entanglement buffers, which are systems designed to generate and store high-quality entangled states to be consumed at any time. For this setting, we derive analytical expressions for two key performance metrics. The solutions are computationally efficient, make no restrictive assumptions about the entanglement purification protocol, and allow general insights: for example, that simple purification schemes can outperformmore complex ones previously considered “optimal” in different contexts.

Then,we turn to the problemof entanglement packet generation,where multiple entangled states of sufficient quality must be established simultaneously between network users. The fast generation of entanglement packets is an essential capability for many quantum network protocols. We obtain analytical results for the entanglement packet generation rate under a constant entanglement generation scheme and later extend the analysis to adaptive schemes, where entanglement parameters are tuned dynamically. Using parameter regimes motivated by current experiments, we show that adaptivity can enhance the entanglement packet generation rate by up to a factor of twenty.

Finally, we examine a standard assumption in performance analyses: that the initial states in a quantum repeater chain can be approximated by a symmetrised, or “twirled”, form. We investigate this assumption in the contexts of postselected and non-postselected entanglement swapping, where postselection is performed based on the Bell-state measurement outcomes at the repeaters. A central result is that, in many relevant cases, the twirled approximation is exact for non-postselected swapping. More generally, we provide a systematic framework to determine when the twirled approximation is valid for the initial states of a repeater chain.

The Quantum Internet is a complementary tool to the widely spread classical Internet, which has already revolutionized our everyday life. The promise is that the Quantum Internet will unlock new unprecedented capabilities and applications that span from secure communication, to distributed quantum computation and enhanced quantum sensing. The realization of such a powerful tool is the result of a joint effort among several fields, like computer science, physics, engineering, and materials science, which all rely on the fundamentals of quantum mechanics. The introduction of a new computational unit, the qubit, allows for the creation of superposition and entangled states, and the possibility of measuring such states. On a practical level, we can envision the Quantum Internet as a network of interconnected heterogeneous platforms aimed at solving different tasks, such as the processing of quantum information at the end nodes, and the storing and retrieval of quantum information in between end nodes to bridge long distances. The quantum information routing is governed and optimized by a dedicated software architecture that facilitates the user interface, removing the requirement of knowing the hardware’s physical principles for a general user.
In the hardware framework, the Nitrogen-Vacancy center in diamond represents a viable platform as processing end node, thanks to the high quality of its qubits and the capability of generating remote entanglement with other nodes in the network via its optical interface. These properties can be engineered to utilize the NV center as a test-bed for demonstrating crucial steps towards the Quantum Internet final goal.
We first employ a two-node NV quantum network in the laboratory to demonstrate the elementary building-blocks of distributed quantum computation: the generation of a distributed 4-partite Greenberger-Horne-Zeilinger state and the realization of a non-local Controlled-NOT gate between physically separated and non-interacting qubits.
In the long distance scenario, we use the NV center platform to study the photonic interface of solid-state qubits with time-bin qubits compatible with the emission from quantum memory platforms, such as Rubidium gas or Thulium-doped crystals. The interface is benchmarked with a quantum teleportation experiment. Quantum teleportation is the ultimate protocol that enables the transfer of quantum information from one physical point to another. We teleport a photonic time-bin qubit to the communication qubit of the NV center platform, establishing the primary form of communication between heterogeneous platforms in a quantum network.
Finally, the two-node NV network is used as reliable setup to demonstrate the first operating system for quantum network applications, QNodeOS. QNodeOS can schedule and manage quantum network applications in a multitasking fashion. It constitutes a software interface which enables facilitated access for users, boosting the research in quantum network applications and making a first step towards the deployment of such technology into society.

Cryptography is used everywhere in our society, from simple internet searches to providing security and privacy for our banking systems. A key research area in this field is secure function evaluation, where multiple parties compute a function of their inputs, without revealing them to each other. However, as most cryptographic tasks, current implementations often rely on computational assumptions, which may become insecure in the future. Researchers have explored quantum communications to eliminate such computational assumptions since the 80s, but still challenges remain. For instance, many theoretical protocols using quantum communications rely on perfect single-photon sources. However, in practice, photon sources have a small probability of emitting multiple photons in one pulse, potentially leaking information to a dishonest party. Furthermore, a dishonest party could have secretly tampered the measurement device of the other party and potentially introduced a backdoor in it. The so-called “measurement device independent” setting has then been described, to provide security against this kind of attacks.
In this work, we investigate the possibility of achieving two secure function evaluation primitives - oblivious transfer and bit commitment - in the measurement device independent setting, using imperfect single-photon sources. We already know that under this setting, bit commitment is possible to achieve but oblivious transfer seems hard to achieve. It is still an open question if there exist a protocol to achieve oblivious transfer under this setting. If not, it would be interesting to find new achievable primitives other than oblivious transfer. Here, we study the existing protocols and provide some results towards answering these questions. We start by extending an existing result on the difficulty of achieving oblivious transfer by proving that even a weaker version of this primitive is difficult to achieve under such setting. We also shortly explore the possibility of using an existing reduction from oblivious transfer to bit commitment to see whether we can achieve oblivious transfer from the existing bit commitment protocol. Finally, we show that an existing bit commitment protocol can perform at a better rate by giving a slightly modified security proof.

As technology for implementing quantum networks advances, the challenge of efficiently managing entanglement generation under resource constraints becomes critical. In this thesis, a systematic methodology for selecting scheduling strategies in a centralised quantum network is proposed, and applied to a specific case for a quantum hub network utilising an entanglement generation switch. Using the NetSquid simulator, the first in, first out, on-demand, MaxWeight, earliest deadline first, earliest feasible deadline first and round-robin scheduling algorithms are evaluated across a wide range of metrics compiled in this thesis.
These metrics include measures of throughput, fairness, responsiveness, demand completion, and resource utilisation, among others. Varying network load conditions are simulated and two application-level use cases, quantum key distribution and blind quantum computing, are considered. The results offer detailed insight into how each scheduler performs under different demand patterns and operational contexts.
Based on these results, the earliest deadline first performs better in most metrics than the other schedulers within the context of this thesis. Additionally, the results indicate that classical optimality of a scheduler does not always translate to superior performance in quantum network scenarios. The findings presented and the framework described here can provide practical guidance for network operators seeking to balance multiple performance goals in near-term quantum networks.

Cryptographic primitives such as Bit Commitment (BC) and Oblivious Transfer (OT) are foundational building blocks for two-party Secure Function Evaluations. While unconditional security for BC is impossible in the quantum setting, it can be realised under additional physical assumptions. In particular, the bounded- and noisy-storage models provide a framework where security is guaranteed against adversaries with limited quantum memory. Recent work by Ribeiro and Wehner [1] introduced the first Measurement-Device-Independent (MDI) protocols for BC and OT in the bounded storage model. For the BC protocols, they consider a variant of BC that is called Randomised String Commitment (RSC). They give two MDI-RSC protocols using polarisation-encoded photon sources: one with perfect single-photon emission and another with multi-photon emissions. They also give an MDI-OT protocol using sources with perfect single-photon emission. However, the MDI security for OT using sources with multi-photon emissions remains an open problem.
This thesis investigates the feasibility of MDI-RSC protocols using sources with multi-photon emissions, such as weak coherent pulses (WCP) and spontaneous parametric down-conversion (SPDC) sources. First, we correct a practical error in the existing MDI-RSC protocol by bounding the relevant parameters, ensuring the validity of the original security claims. Second, we analyse the achievable committed string rates while using WCP and SPDC sources. We further consider heralded SPDC sources, which in principle enable single-photon emission, and discuss the impact of imperfect local detectors on their performance and the consequences that has on the protocol implementation. Finally, motivated by techniques from Twin-Field Quantum Key Distribution (TF-QKD), we give a phase-encoded MDI-RSC protocol using coherent states and provide a sketch of the security proof in the bounded-storage model. We also investigate extending the approach to OT. However, this is still a challenge due to the basis-dependent information leakage inherent in phase-encoded coherent states.

Quantum computers allow us to solve certain problems that are unsolvable using classical computers. In this study we focus on solving the equality problem by simulating a three quantum computer network and using the communication complexity to determine if our theoretical quantum advantage is still there in practice. We want to know how the noise from realistic quantum networks that already exist affect this communication complexity. We found that we can beat the classical solution when simulating a laboratory setup in which the quantum computers are in close proximity to each other and when using only a small bit strings. However, when moving to setups in which there are kilometres between quantum computers instead of metres or when using larger bit strings as input to our problem we see that the noise becomes too much to simulate.

The development of a quantum internet is crucial for the advancement of quantum computing, enabling secure and distributed quantum computing capabilities. Despite significant progress in building small-scale quantum networks in lab environments, a fundamental barrier remained: the inability to communicate between quantum computers over metropolitan-scale distances. This thesis tackles this challenge and shows the development of a scalable quantum network hardware platform for long-distance deployment using existing internet fiber connections (Part I). To further widen the understanding of the future implications of a quantum internet, the second part of this thesis explores the social and business implications of future quantum networks (Part II). The results of thesis aim to accelerate the commercialization of a quantum internet and improve our understanding of its implications in business and society.

Quantum networks are expected to enable applications that are provably impossible with classical communication alone, such as generation of secret keys for secure communication and high-precision distributed sensing. A fundamental resource needed for many of these applications is shared entanglement among distant parties. Hence, the viability of an application relies on the underlying protocol for entanglement distribution. Existing protocols often suffer from long waiting times, as they rely on the success of multiple random events, each with a low probability of success. Moreover, pre-distribution of entanglement is difficult, since entanglement degrades over time when stored in memory, eventually becoming unusable. In this thesis, we address these challenges by designing efficient entanglement distribution protocols and architectures.

First, we focus on on-demand entanglement distribution, in which the entanglement distribution process is initiated only after some users request it. We find optimal protocols that minimize the waiting time for distributing entanglement among two users that are connected by a chain of two-way quantum repeaters. The performance of these protocols sets a benchmark for on-demand distribution of quantum states. We also study a multi-user network of one-way quantum repeaters, and we conclude that finite waiting times are only achievable when the users are at most a few kilometers apart from each other, irrespective of the number of repeaters available.

Next, we examine protocols for continuous entanglement distribution, in which the distribution process is initiated before any user requests. While these protocols can sometimes lead to resource wastage – as noise in memory renders the entanglement
unusable if distributed too early –, they offer the potential to reduce expected waiting times compared to on-demand methods. Surprisingly, we find that, when the time required to distribute entanglement follows a broad probability distribution, initiating the process preemptively can actually result in longer expected waiting times compared to an on-demand approach.

Lastly, we propose an architecture for buffering high-quality entanglement, ensuring it is readily available for use when needed. A key feature of this system is the use of purification subroutines to prevent the buffered entanglement from degrading over time due to quantum decoherence. Among other findings, we show that maximizing entanglement quality upon consumption requires frequent purification, even if this process often fails and results in the loss of high-quality buffered entanglement. The results presented in this dissertation were obtained mostly analytically, leveraging tools from performance analysis, including queueing theory and renewal theory, and supported by extensive discrete-event simulations. Our theoretical insights provide benchmarks and identify fundamental limitations of quantum networks, offering valuable guidance for the design of reliable entanglement distribution systems.

Quantum networks promise exciting applications that are not possible with their classical counterparts, such as distributed quantum computation or fundamentally secure quantum communication. Optically active spins in solid states are among the prime candidates for realizing quantum network nodes, while photons are used to distribute entanglement between nodes. The nitrogen-vacancy (NV) center in diamond is a pioneering system with the demonstrations of teleportation of quantum states within a three-node network and metropolitan-scale heralded entanglement. However, scaling to more nodes or longer distances is limited by the low extraction of resonant photons, creating a high interest in optical resonators (cavities) to improve the optical interface. Moreover, the diamond tin-vacancy (SnV) center with better optical properties emerged as a promising alternative candidate for quantum network nodes.
This dissertation presents the building blocks and the experimental realization of an open, fiber-based, cryogenic Fabry-Pérot microcavity enabling the Purcell enhancement of diamond NV and SnV centers, incorporated into the microcavity via a diamond membrane. The background on color centers in the context of quantum networking (Chapter 2) and optical cavities for diamond color centers is summarized (Chapter 3). A novel laser-cutting patterning method is introduced, which can be used to fabricate micrometer-thin diamond devices with arbitrary lateral shapes in the range of tens to hundreds of micrometers (Chapter 4). Microdevices fabricated by this method are characterized by scanning cavity microscopy, revealing a high cavity finesse. Furthermore, SnV and NV centers in the microdevices maintain bulk-like optical properties, which are required for quantum networking. Next to the sample fabrication, the detailed design, construction, and operation of a cryogenic microcavity system is presented, reaching a reproducible cavity length stability level of around 25 picometer with a sample temperature of about 8 kelvin on the cavity mirror (Chapter 5), a prerequisite for the following cavity experiments. Two cavity quantum optics experiments are conducted, exploring the regimes of coherent cavity coupling and efficient photon extraction with the cavity. In the first experiment, a single SnV center is coupled to the cavity, achieving a coherent cooperativity of 0.7. This enables the observation of nonlinear quantum effects, such as the modulation of the cavity resonance by an individual SnV center and the altered photon statistics of light transmitted through the cavity (Chapter 6). In the second experiment, a single NV center is coupled to the cavity, and the Purcell enhancement combined with a high cavity outcoupling leads to a resonant photon extraction (end-to-end) efficiency of 0.5 %. The NV center’s electron spin qubit initialization, manipulation with an on-chip microwave stripline, and readout are utilized to generate spin-photon correlated states, a precondition for remote entanglement with a second color center (Chapter 7).
The presented platform combines an efficient optical interface with microwave control of the spin state and can be used for the exploration of optically active defects in solid states, as a bright source of single photons, and for cavity-enhanced quantum networking.

We perform a numerical optimisation of the hardware parameters of an atomic-ensemble-based single repeater setup. The setup operates on a real-life fiber network connecting the cities Delft and Eindhoven. Besides this network, the setup encompasses photon pair sources, quantum memories, single photon detectors, and 50:50 beam splitters. The corresponding hardware parameters we consider are the following;
- The detector efficiency, defined as the probability the photon detector correctly registers an incident photon.
-The detector dark count probability, defined as the probability that a detector registers a false detection event.
- The memory efficiency, defined as the maximum probability that an excitation is not lost in the quantum memory.
- The memory coherence time, defined as the characteristic time after which an excitation is lost in the quantum memory.
- The Hong-Ou-Mandel visibilty, which is a measure of the indistinguishability of the photons in the setup.
Additionally, the setup has the ability to be multiplexed. This means that the probabilistic processes essential for executing the repeater protocol are initiated $M$ times in parallel. This increases the performance of the protocol.

To achieve the optimisation, we introduce absolute minimal hardware requirements and minimal hardware requirements. An absolute minimal hardware requirement is defined as the least favourable hardware parameter that still allows the setup to reach a given target metric. This implies that all other hardware parameters are at their optimal value. Minimal hardware requirements are defined as the least favourable set of hardware parameters that still allow the setup to reach a given target metric.

To evaluate the aforementioned target metric we conduct a numerical analysis. This analysis is based on the entanglement based version of quantum key distribution. We use Netsquid, a discrete event simulator for quantum networks, to carry out the numerical analysis. Utilising this, we formulate an optimisation problem that allows us to find absolute minimal hardware requirements and minimal hardware requirements for an atomic-ensemble-based single repeater setup.

We develop a method to solve this optimisation problem. This allows us to find absolute minimal hardware requirements and minimal hardware requirements for the hardware parameters listed above. We do this for different number of multiplexing modes, and different node placements on the existing fiber network. We consider both perfect photon pair sources and a model of a photon pair source based on Spontaneous Parametric Down Conversion (SPDC).

The quantum internet improves upon the classical internet with several new possibilities. However, to create such a quantum internet, metropolitan hubs (for this research we will use an Entanglement Generation Switch - EGS - as hub) are needed to avoid a scaling problem when connecting all end nodes individually with one another. These EGSs share resources for multiple end nodes. Hence, resource sharing protocols are needed to manage these resources. Unfortunately due to the probabilistic nature of end-to-end entanglement generation, classical resource sharing protocols will not suffice for implementation in a quantum network. Therefore the need to design quantum resource sharing protocols arises. These protocols, where we specifically investigate quantum schedulers, should be simple and predictable to provide a comprehensible addition to current research by incorporating more parameters into the current EGS model while still attempting optimal resource efficiency. In this research we have extended quantum network simulation software to be used in this research and following projects. We have implemented a classical Max Weight scheduler with a constant time window size to simulate the inefficiency of such a classical protocol in a quantum environment and improve upon this protocol by implementing a scheduler with a dynamic time window size which scales with the link length and the probability of a photon arriving at the EGS. We investigate the entanglement successes, idle time and entanglement rates when using these schedulers and compared these with each other and with a third scheduler without a time window size but using a cutoff timer instead, the Cutoff scheduler. These results show an optimality of entanglement successes, idle time and entanglement rates for the Cutoff scheduler over the Dynamic Time Window scheduler and for the Dynamic Time Window scheduler over the Max Weight scheduler with a constant time window size. Also a decrease in entanglement rate for all schedulers is shown when increasing the link length.

Distributed quantum computers hold great promise in the realization of scalable and fault-tolerant quantum computers. They contain multiple nodes with small quantum devices that can generate inter-node entanglement. Next to realizing distributed architectures on a single chip, these systems can be extended to large-scale quantum networks. Connecting the nodes based on the topology of a quantum error-correction code forms an intuitive path toward fault tolerance.

Performing error-detection measurements in distributed error-correction codes requires the generation and consumption of entangled states. We focus on systems that are capable of generating remote two-qubit entanglement between pairs of connected nodes—i.e., Bell pairs. Entangled states of higher weight—the so-called Greenberger-Horne-Zeilinger (GHZ) states—can be generated by fusing Bell pairs. On top of this, the quality of the generated entangled states can be increased with entanglement distillation. We implement dynamic programming to generate high-quality GHZ states by fusing and distilling Bell pairs.

The dynamic program allows us to optimize the quality of error-detection measurements for a specific distributed error-correction code: the (toric) surface code. We numerically evaluate the performance of this code with noise models based on experimental characterization of diamond color center hardware, including the typical behavior of memory decoherence in these devices. This leads to the identification of a threshold in the ratio between entanglement generation and the decoherence rates.

For a two-dimensional error-correction code like the surface code, performing error-detection over multiple time steps can be reinterpreted as measuring the qubits of a three-dimensional cluster state. This equivalence enables considering more general three-dimensional cluster states as fault-tolerant channels that transform the logical qubits of the underlying error-correction code. We use this idea to investigate distributed logical memory channels for general types of circuit-level and entanglement noise.

Our results show that efficient generation of high-quality entanglement and strategic design of error-correction channels are important aspects for developing noise-resilient distributed quantum computers.

Quantum communication provides a plethora of new possibilities compared to the realm of classical communication. Since the channels used are noisy, losses are unavoidable, and quantum repeaters are needed to transmit a signal over longer distances to overcome these exponential losses. To increase the performance of these repeaters, cutoff times can be introduced. These cutoffs limit the amount of time a qubit can be stored in the quantum memory. Based on previous work done by Avis et al., this work analyzes how a variation in the initial coherence time, called a drift in coherence time, affects the optimal cutoff, the optimal secret key rate, and the loss in secret key rate. The main conclusions are that the greater the coherence time, the less the need for accurate cutoff times. This is due to losses in the secret key rate being inherently smaller at larger coherence times. Furthermore, the loss in secret key rate can be approximated using the derivations found in this thesis. Suggestions for further work are introduced; implementing these is beyond the scope of this thesis.

Benchmarks for quantum network systems currently are an underrepresented subject in the research field. This paper evaluates how informative a distributed CNOT gate application is, in recognizing errors in the total quantum system. The goal is to decide whether it should be included as a benchmark in a newly developed benchmark suite for quantum network systems. The application is simulated and its error rate on certain inputs is plotted against properties of the quantum network system. This way it is evaluated that the application is sensitive to certain parameters of the quantum link and quantum devices in the nodes. Additionally, a quantitative analysis on the results shows which inputs are most effective in reacting to errors in the total quantum system. That way it is possible to conclude that inputs in the x-basis are sensitive to the most parameters and that combining these results with the inputs |10⟩ or |11⟩ yields an optimal result. It can be included in a benchmark suite if it is sensitive to parameters to which non of the other applications in the suite are sensitive.

The rapid advancement of Quantum Network architectures necessitates a comprehensive and quantitative comparison to assess their effectiveness and performance. Unfortunately, there does not exist an implemented quantum network benchmark suite capable of determining the superior architecture. Hence, our study aims to establish the foundation for developing a benchmark suite by leveraging existing quantum network applications. However, the specific inclusion of quantum network applications in the suite remains to be determined. Therefore, to address this gap, our study will explore the potential inclusion of the Clauser-Horne-Shimony-Holt (CHSH) game based on its effectiveness in identifying errors within various properties of the quantum networking system. We use an exploratory research methodology involving experiments performed on simulated quantum networks utilizing SquidASM. Each experiment simulates multiple quantum networks, with a single property as the independent variable. For each value of the independent variable, we calculate both the success probability of the game and the number of successes per second. Subsequently, we employ the one-way ANOVA test to examine if there are significant variations in these performance metrics. Our results demonstrate that the CHSH game exhibits sensitivity to all properties affecting the quality of entanglement between nodes, execution time, and the error probability of both single-qubit gates and measure operations. Additionally, we compare the success probabilities based on different input combinations using the Root Mean Squared metric to uncover any underlying patterns within the data. As a result, we discovered a procedure for quantifying the difference between the error probabilities of measurements of zero and one. Based on the outcomes of our study, we consider the CHSH game to be a suitable addition to the benchmark suite if the testing requirements of the suite align with the qualities offered by the application. We anticipate that these results will aid the development of the benchmark suite and advance the understanding of quantum network architectures and their evaluation

Quantum networks provide numerous potential benefits over classical networks, such as enhanced security and faster computation, making their further development a lucrative prospect. As is the case with any technology, the advancement of quantum networks relies on the development of frameworks to test their quality, and compare different implementations of the technology. One such framework is a benchmarking suite for quantum network systems, that can identify areas for improvement in their implementation, by determining the erroneous properties of the system.
This paper examines the viability of using a specific quantum network application as a benchmark for quantum network systems. In order to quantify the application's ability to benchmark, we assess its sensitivity to changes in the properties of the system. These properties include link parameters, quantum gate properties, qubit coherence times, and measurement properties.
We use the BB84 protocol as the benchmarking application for this project, which is a Quantum Key Distribution scheme used to establish secure keys between two parties. In particular, we use the qubit error rate and the key generation rate as the performance metrics for the application. For the setup of the experiments, we prepare two system configurations: generic quantum device nodes with a depolarising error channel, and NV device nodes with a heralded link. In order to assess how the application behaves with changes to different system properties, we observe how the performance metrics change while individually varying system parameters and keeping all other parameters constant.
We find that the application is sensitive to changes in multiple parameters across both network configurations, such as link parameters, single qubit gate properties, and measurement properties. Contrarily, the application is not affected by changes to parameters such as two qubit gate properties and coherence times. We conclude that the BB84 protocol can be used as an individual localised test for the parameters it is sensitive to, and also in combination with other applications, in a more comprehensive benchmarking suite, that provide coverage for a broader range of parameters.

In the development of any new technology, it is essential to have methods to assess the quality of a system, to compare different systems to one another, and to compare different versions of the same system, to see if changes to the system can actually be classified as improvements. For quantum networks, this is no different. To further develop quantum networks, we need a benchmarking suite to judge the quality of such systems.

The aim of this research is to determine the effectiveness of blind quantum computation - a quantum network algorithm - as a benchmark. We determine what changes to the system affect the results of executing this application, and we use this to determine whether it would be effective to use this application as part of a larger benchmarking suite. We do this by simulating a quantum network, and manually varying system parameters one by one, to see if they have an effect on the results.

What we observed from these experiments is that blind quantum computation is sensitive to almost all system parameters. This means that introducing an imperfection into almost any system parameter will negatively affect the results of the application. This means the application is useful as a full-system benchmark, because it is affected by almost the entire system. However, it also means that the application is less useful as a benchmark for individual parameters.

This means that to make the most useful benchmarking suite, blind quantum computation would have to be combined with other quantum network applications that are more suitable for benchmarking individual system parameters.

The goal of quantum application scheduling is to enable the execution of applications on a quantum network. As the final step in the application scheduling process, program scheduling locally schedules execution of blocks of instructions on each node by defining so-called node schedules. In this thesis, we present a formal definition of program scheduling and propose success metrics to evaluate the quality of node schedules. We implement program scheduling using the framework of Resource-Constrained Project Scheduling Problem (RCPSP) and and simulate the execution of node schedules. By evaluating the performance of program scheduling on datasets with diverse quantum applications including quantum key distribution and blind quantum computing, we observe that heuristic-driven approaches achieve comparable results to optimal program scheduling while requiring fewer computational resources. Our work offers valuable insights into the translation of classical scheduling problems into the quantum domain, contributing to the advancement of quantum application scheduling.

Quantum networks offer more capabilities than classical networks. For example, quantum networks can solve certain problems faster than classical networks and they can even solve problems which cannot be solved with classical networks. One well-known quantum network application is blind quantum computing (BQC). In a BQC application, a client node sends a computation to a server node in the network. The server node performs this computation without knowing the details about the actual input or computation being performed and returns the result of the computation to the client node. Quantum applications are often repeated many times due to randomness that is involved in the result of executing a quantum application. When a server node performs BQC repeatedly with multiple client nodes, there arises an interesting problem of how all corresponding instructions can be scheduled for the server optimally, given that certain types of instructions referred to as entanglement instructions can only be scheduled at given moments by a so-called network schedule. One classical metric used to assess the quality of a schedule is makespan, which is the time that it takes to complete all instructions. A quantum-oriented metric involved is success probability, which indicates what fraction of executions yield a desired result when repeatedly executing an application. In this thesis, an experimental demonstration is given of the use of constraint programming (CP) for the scheduling of instructions of quantum network applications. This demonstration focuses on scheduling instructions that the server node should execute when performing BQC repeatedly with a small number of client nodes at the same time. Different CP models are presented that assign start times to tasks that the server node should execute. By comparing the CP models to a baseline scheduler that schedules tasks as soon as possible, it was found that CP can be used to reduce the makespan when BQC is performed by the server node with multiple clients at the same time, while preserving a similar success probability. A main drawback that followed from the CP approach is scalability. Future work is to be done on studying how CP can be used for larger quantum networks.