We investigate open- and closed-loop quantum optimal control in nitrogen-vacancy (NV) centre systems, using gate set tomography (GST) for pulse characterisation and calibration. Open-loop optimisation with GRAPE revealed a strong dependence of gate fidelity on pulse duration and the need for phase correction in echo-based gates.

Despite promising simulations of advanced pulse designs, experimental performance was consistently higher for a standard weak $\pi$ pulse, highlighting model limitations. Closed-loop optimisation with dCRAB improved performance but exhibited sensitivity to environmental drift, confirming magnet-induced variations.

GST identified dominant coherent error channels, notably ZZ, attributed to AC Stark-induced phase shifts. A novel gate design suppressed ZZ errors but introduced greater stochastic noise.

These results demonstrate the importance of integrating model-driven and data-driven approaches with advanced tomography protocols to achieve robust, high-fidelity quantum control in noisy intermediate-scale quantum (NISQ) devices.

The ability to send quantum information over long distances can enable fundamentally new applications, such as intrinsically secure communication, enhanced metrology, and distributed quantumcomputation. Entangled links serve as powerful resources for sending quantum information between nodes in a quantum network. However, generating entanglement in sufficient quantity and quality across a network, such that they can be used for applications, remains an open challenge.

In this thesis, we explore the use of color centers in diamond as network nodes. Their electron spin serves as a matter qubit with an optical interface, enabling the entanglement of two distant color centers, mediated by photons. The surrounding nuclear spins are used as memory qubits for local computation and entanglement storage. In this thesis, we investigate both the well-established nitrogen-vacancy (NV) center in diamond and the recently discovered tin-vacancy (SnV) center in diamond. The physics and control methods for both types of color centers are discussed in Chapter 2.

Remote entanglement between matter qubits can be achieved with many different entanglement protocols. In Chapter 3, we present a framework that explains and categorizes different protocols and quantum network hardware components. This framework is then used to compare the performance of various protocols while using similar hardware.

There have been many realisations of rudimentary network links between two network nodes using various quantum hardware. In Chapters 4 and 5, we realize the first entanglement-based three-node quantum network employing NV centers in diamond. In this network, we demonstrate fundamental network capabilities such as the creation of a remote three-party Greenberger–Horne–Zeilinger (GHZ) state and entanglement swapping to connect non-neighboring network nodes, as detailed in Chapter 4. These advancements are facilitated by storing an entangled state in a network node while generating a second entangled link. In Chapter 5 we demonstrate quantum teleportation between two non-neighboring network nodes by adding a fifth qubit to the network and utilizing the entangled link generated through the entanglement swapping.

The three-node network experimentswere enabled by the nuclear spin memory, emphasizing the importance of nuclear spin control for quantum networks based on color centers. In Chapter 6, we explore nuclear spin control with the SnV center in diamond. This recently discovered color center promises enhanced entanglement rates compared to the NV center due to its superior optical interface. We control single nuclear spins and show entanglement between the electron and nuclear spin. These experiments provide insights into the challenges and opportunities of controlling nuclear spins using an electron spin-1/2.

Electron-spin qubits associated to solid-state defects can exhibit exceptional optical and spin coherence. Additionally, magnetic interactions with surrounding spins presents a resource for multi-qubit registers. Combined, this makes such solid-state defect systems promising for quantum network applications. In this thesis, we first realize a toolbox to control electron-nuclear spin qubits surrounding an NV-center in diamond and investigate such spins as potential qubits by generating an entangled state shared amongst two spins. Secondly, we improve the robustness of a nuclear-spin memory qubit while emulating remote entanglement generation protocols. Ancillary (spectator) qubits subject to noise correlated to the memory qubit are measured and subsequent feedforward allows to mitigate this noise in real-time. Thirdly, we investigate spectral diffusion dynamics in commercially available silicon carbide and demonstrate (near-)Fourier linewidth limited optical transitions within a broad inhomogeneously broadened spectrum. Finally, an outlook on electron spin clusters and photonic integration of electron spins is presented.

The efforts to bring quantum states, fundamental building blocks of nature, from research labs into the outside world are intensifying. The generation and processing of remote quantum states between nodes in a network would allowfor new applications such as distributed quantum computing, quantumenhanced sensing and quantum communication. Various demonstrations of such a quantum network have been shown in a lab setting, such as the generation of a three node GHZ-state, device-independent quantum key distribution and memory enhanced quantumcommunication. Color centers in diamond have been at the forefront of these developments due to their optically active spin interface, long coherence times and nuclear spin registers. The Nitrogen Vacancy (NV-) center is the color center of choice in this thesis, which we describe in Chapter 2. We explain what an NV-center is, how to control it and how we can use them to generate remote entanglement.

Solid-state defects in diamond and silicon carbide have emerged as a promising platform for exploring various quantum technologies, such as distributed quantum computing, quantum simulations of many-body physics, and nano-scale nuclear magnetic resonance. The noise environment surrounding such defects, consisting of magnetic and electrical impurities, directly impacts the spin and optical coherence, posing a key challenge for advancing quantum technologies. Systematic study of these spins and charges is crucial for mitigating their noise contribution. In some cases, establishing control over the environment can even convert it into a resource, to be used for storing, or processing (quantum) information. In this thesis, we develop experimental and analytical tools that enable a more detailed study of the defect spin and charge environment, and can be exploited to manipulate its microscopic configuration.

Solid-state defect centers, such as the nitrogen-vacancy centers in diamond, represent a promising and versatile platform for quantum technologies. This thesis focuses on overcoming the challenge of noise in diamond to facilitate its practical use in various quantum technology applications.

Random walks have been used in a number of different fields for a long time. With the rise of of quantum random walks a lot of these applications have been made more efficient. Recently there have been a lot of improvements in the realization of these quantum random walks in real world systems.
In this research, the effect of uncertainty in the measurement time and measurement frequency are studied on three problems that make use of a quantum random walk. These problems are the network centrality problem, the graph isomorphism problem and the spatial search problem.
These effects are studied by first looking at the theory behind these problems after which the theoretical results of these three problems are calculated. These theoretical results will then be compared to simulated results that have a certain level of uncertainty in the measurement time or frequency.
For both the network centrality problem and the spatial search problem we concluded that only a small error is made when uncertainties are introduced in the system. This implies that these problems are solvable in realizations of the quantum random walk in real world systems. For the Graph isomorphism problem we saw that the error that is made when uncertainties are introduced was large which implies that this problem would only be solvable for small uncertainties.

We introduce a method of designing NMR pulse sequences, with a specific focus toward complete decoupling of carbon-13 spin qubits coupled to a nitrogen-vacancy (NV) center in diamond. Using Average Hamiltonian Theory, we calculate different intermediate Hamiltonians corresponding to different rotations implemented by NMR pulses. Two novel pulse sequences are obtained containing 24 and 12 evolution periods respectively. Assuming ideal and instantaneous pulses, performance for both sequences is better than the WAHUHA + echo sequence for total evolution times of less than 5 ms and comparable for greater evolution times. Analysis of sensitivity points toward non-robustness for angle errors in the applied pulses when the direction of pulses is not taken into account, however this can be corrected for using chirality sums. Suggestions for further research include the study of non-globally applied pulses and application of the design method to non-zero effective Hamiltonians.

The development of quantum computers is a monumental challenge for modern physics. One proposed pathway toward a fully scalable and fault-tolerant quantum computer involves the development of a quantum network. Such a network would have applications ranging from distributed quantum computation to fundamentally secure quantum communication. The building blocks of such a network, the nodes, require optical links with which to generate entanglement with other nodes, as well as memory and data qubits to improve the entanglement between nodes and perform computations.

In this thesis, we study the dynamics of spin pairs surrounding nitrogen-vacancy
(NV) centres in diamond - a promising proposed node for a quantum network. We build on previous work that has successfully detected and controlled pairs of strongly coupled 13C nuclear spins using the NV centre as a probe, and investigate how these spin pairs can be individually addressed using radio frequency pulses.

Next, we consider pairs of P1 centres and demonstrate the detection and control of the electron spins of this pair. We show that dynamical decoupling sequences can be used to initialise and readout the electron pair of the P1 centres with high fidelity (∼94 − 96%), and measure natural dephasing times of ∼ 50 ms with the NV centre in the m s = 0 state. The control we demonstrate over pairs of electron spins in P1 centres is an important proof-of-concept that electronic spin defects in diamond can be coherently controlled, and used as memory or data qubits in a future quantum network node.

Due to its long spin coherence and coherent spin-photon interface the nitrogen vacancy (NV) center in diamond has emerged as a promising platform for quantum science and technology, including quantum networks, quantum computing and quantum sensing. In recent years larger quantum systems have been demonstrated by using optical entanglement links between distant NV centers. These systems were based on high-quality NV centers that exhibit good optical coherence. State-of-the-art experiments with such systems have shown deterministic delivery of entanglement across a two-node quantum network as well as genuine multi-partite entanglement across a three-node quantum network. The additional capability to create larger quantum registers by direct magnetic coupling between high-quality NV centers and to other nearby defects would provide new opportunities for quantum memories in quantum networks but also for enhanced sensing protocols and spin chains for quantum computation architectures. In this thesis, we investigate methods to create larger quantum registers based on magnetic coupling and develop techniques to address and control individual defects in a system consisting of multiple defects. The results provide new insights for extended quantum registers based on magnetically coupled defects...

Owing to its exceptional spin properties and bright spin-photon interface, the nitrogenvacancy (NV) center in diamond has emerged as a promising platformfor quantum science and technology, including quantum communication, quantum computation and quantum sensing. In this thesis we develop novel methods for atomic-scale imaging and high-fidelity control of complex nuclear-spin systems coupled to the electron spin of an NV center in diamond. This well-controlled quantum system provides new opportunities in quantum sensing, quantum information processing, and may also form the building block of a large-scale quantum network, one of the key goals in quantum technology.

In this thesis, networks of coupled quantum harmonic oscillators are studied. The dynamics of these networks are determined by single-frequency vibrations of the entire network called normal modes. We study the behavior of the nor- mal modes when the network is coupled to a thermodynamical heat bath by looking at the Lindblad Master Equation of the system. From this equation, we determine the rate at which the normal modes decay. Certain normal modes decay very slowly, and some do not decay at all. These normal modes are called quasi-noiseless and noiseless clusters respectively. We determine what happens to the noiseless clusters when the network pa- rameters are very slightly perturbed. We have found that two distinct types of noiseless clusters can be identified. The first type disappears with even the slightest perturbation, making it useless in practice. The second type instead be- comes quasi-noiseless, making it a viable candidate for applications. We show how to determine the degree to which these noiseless clusters become quasi- noiseless by looking at the other normal modes of the network. We also explain how a network of oscillators, including an optional heat bath, can be simulated with an optical setup as described in [3]. We suggest this setup can be used to verify our findings.

The Hamiltonian of the NV center contains unknown parameters, such as the zero-field splitting and the magnetic field. Knowing how the frequency measurements depend on the parameters will give greater understanding
of the NV center. Including the nitrogen nuclear spin gives us the opportunity to find more parameters such as the quadrupole splitting. Analytically finding expressions for all of these parameters is very time consuming to do, and therefore the method of second order perturbation is used in this report
to find approximations. With this method, estimations of the eigenvalue differences and parameters were found, including new estimations for the quadrupole splitting. As we don't exactly know whether the quadrupole splitting is positive or negative, there are two estimates found given by Δ_Q⁺ = 4949.25(2) kHz and Δ_Q^- = -4949.11(1) kHz.

Quantum networks play an important role in the fields of quantum information and quantum computation. One of the current problems for these networks concerns nonlocality. Characterizing and detecting nonlocality is relevant to the implementation of quantum networks and quantum repeaters, where Bell inequalities can be used to test if configurations are prepared correctly.
This report contains an overview of an iterative method to find Bell inequalities for networks. Starting from a given network, this method constructs a new Bell inequality for a network containing one additional source and one additional party. We use this procedure to find new Bell inequalities for specific network structures and analyse how these can be used to detect nonlocality within a network.
In the first part the Bell inequalities are considered from a more theoretical point of view. We focus on star-shaped networks and discuss violations predicted by quantum mechanics. We look for quantitative bounds describing a set of states that lead to violation, giving an indication of the required quality of the sources.
Finally this method is applied to a setup similar to the one described by Bernien et al. We consider a network consisting of three parties and two sources. The effect of errors during preparation of an entangled pair of photons on the ability to detect nonlocality is evaluated. The same is done for the effect of measurement errors. Using numerical computations we show that violation of the Bell inequality can be improved by choosing different measurement angles.

The NV-center in diamond is a promising system for quantum information processing. The typical qubits are the electron spin in the NV-center and the surrounding 13C nuclear spins. Fast and precise control of many 13C spins is desirable but challenging due to crosstalk. Crosstalk is the unwanted effect of a control pulse on the other qubits. The coupled NV-13C system is explored, and numerical techniques to optimize the control of multiple and single qubits are used. In this report the effect of the Bloch-Siegert shift in the weak driving regime is investigated first. This is done by studying the effect of a π-pulse when two carbon qubits are driven at the same time on resonance. It turns out that in this weak driving regime the effect of the off resonance is very small, and changes the fidelity not more than 0.3%. Furthermore the effect of a square πpulse on 4 nearby qubits is studied. If the pulse is not optimized (thus square), the pulse cannot be done in less than 100µs while retaining at least 99% fidelity. By optimizing the envelope of the driving field using constrained optimization the pulse can be done in 22µs while retaining at least 99% fidelity.