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We present a procedure to construct tensor-network representations of many-body Gaussian states efficiently and with a controllable error. These states include the ground and thermal states of bosonic and fermionic quadratic Hamiltonians, which are essential in the study of quantum many-body systems. The procedure improves computational time requirements for constructing many-body Gaussian states by up to five orders of magnitude in the low and up to two orders of magnitude in the intermediate temperature regime, thus allowing simulations beyond the range of what was hitherto feasible. Our procedure combines ideas from the theory of Gaussian quantum information with tensor-network-based numerical methods, thereby opening the possibility of exploiting the rich toolkit of Gaussian methods in tensor-network simulations., acceptedVersion

We show that the addition of correlated phases to the recently developed method of randomized dynamical decoupling pulse sequences can improve its performance in quantum sensing. In particular, by correlating the relative phases of basic pulse units in dynamical decoupling sequences, we are able to improve the suppression of the signal distortion due to &pi, pulse imperfections and spurious responses due to finite-width &pi, pulses. This enhances the selectivity of quantum sensors such as those based on NV centers in diamond.

Dynamic nuclear polarization (DNP) is an important technique that uses polarization transfer from electron to nuclear spins to achieve nuclear hyperpolarization. Combining efficient DNP with optically polarized nitrogen-vacancy (NV) centers offers promising opportunities for novel technological applications, including nanoscale nuclear magnetic resonance spectroscopy of liquids, hyperpolarized nanodiamonds as magnetic resonance imaging contrast agents, and the initialization of nuclear spin���based diamond quantumsimulators. However, none of the current realizations of polarization transfer are simultaneously robust and sufficiently efficient, making the realization of the applications extremely challenging. We introduce the concept of systematically designing polarization sequences by Hamiltonian engineering, resulting in polarization sequences that are robust and fast. We theoretically derive sequences and experimentally demonstrate that they are capable of efficient polarization transfer from optically polarized NV centers in diamond to the surrounding 13C nuclear spin bath even in the presence of control errors,making the abovementioned novel applications possible., publishedVersion

In this work (multipartite) entanglement, discord, and coherence are unified as different aspects of a single underlying resource theory defined through simple and operationally meaningful elemental operations. This is achieved by revisiting the resource theory defining entanglement, local operations, and classical communication (LOCC), placing the focus on the underlying quantum nature of the communication channels. Taking the natural elemental operations in the resulting generalization of LOCC yields a resource theory that singles out coherence in the wire connecting the spatially separated systems as an operationally useful resource. The approach naturally allows us to consider a reduced setting as well, namely, the one with only the wire connected to a single quantum system, which leads to discordlike resources. The general form of free operations in this latter setting is derived and presented as a closed form. We discuss in what sense the present approach defines a resource theory of quantum discord and in which situations such an interpretation is sound—and why in general discord is not a resource. This unified and operationally meaningful approach makes transparent many features of entanglement that in LOCC might seem surprising, such as the possibility to use a particle to entangle two parties, without it ever being entangled with either of them, or that there exist different forms of multipartite entanglement., Facultad de Ciencias Exactas, Instituto de Física La Plata

Photosynthetic systems utilize adaptability to respond efficiently to fluctuations in their light environment. As a result, large photosynthetic yields can be achieved in conditions of low light intensity, while photoprotection mechanisms are activated in conditions of elevated light intensity. In sharp contrast with these observations, current theoretical models predict bacterial cell death for physiologically high light intensities. To resolve this discrepancy, we consider a unified framework to describe three stages of photosynthesis in natural conditions, namely light absorption, exciton transfer and charge separation dynamics, to investigate the relationship between the statistical features of thermal light and the Quinol production in bacterial photosynthesis. This approach allows us to identify a mechanism of photoprotection that relies on charge recombination facilitated by the photon bunching statistics characteristic of thermal sunlight. Our results suggest that the flexible design underpinning natural photosynthesis may therefore rely on exploiting the temporal correlations of thermal light, manifested in photo-bunching patterns, which are preserved for excitations reaching the reaction center., publishedVersion

We theoretically study a simple non-equilibrium quantum network whose dynamics can be expressed and exactly solved in terms of a time-local master equation. Specifically, we consider a pair of coupled fermionic modes, each one locally exchanging energy and particles with an independent, macroscopic thermal reservoir. We show that the generator of the asymptotic master equation is not additive, i.e. it cannot be expressed as a sum of contributions describing the action of each reservoir alone. Instead, we identify an additional interference term that generates coherences in the energy eigenbasis, associated with the current of conserved particles flowing in the steady state. Notably, non-additivity arises even for wide-band reservoirs coupled arbitrarily weakly to the system. Our results shed light on the non-trivial interplay between multiple thermal noise sources in modular open quantum systems., publishedVersion

Ultra-thin layers of liquids on a surface behave differently from bulk liquids due to liquid-surface interactions. Some examples are significant changes in diffusion properties and the temperature at which the liquid-solid phase transition takes place. Indeed, molecular dynamics simulations suggest that thin layers of water on a diamond surface may remain solid even well above room temperature. However, because of the small volumes that are involved, it is exceedingly difficult to examine these phenomena experimentally with current technologies. In this context, shallow NV centres promise a highly sensitive tool for the investigation of magnetic signals emanating from liquids and solids that are deposited on the surface of a diamond. Moreover, NV centres are non-invasive sensors with extraordinary performance even at room-temperature. To that end, we present here a theoretical work, complemented with numerical evidence based on bosonization techniques, that predicts the measurable signal from a single NV centre when interacting with large spin baths in different configurations. In fact, by means of continuous dynamical decoupling, the polarization exchange between a single NV centre and the hydrogen nuclear spins from the water molecules is enhanced, leading to differences in the coherent dynamics of the NV centre that are interpreted as an unambiguous trace of the molecular structure. We therefore propose single NV centres as sensors capable to resolve structural water features at the nanoscale and even sensitive to phase transitions., publishedVersion

We show that the technique known as concatenated continuous dynamical decoupling (CCD) can be applied to a trapped-ion setup for a robust implementation of the quantum Rabi model in a variety of parameter regimes. These include the case where the Dirac equation emerges, and the limit in which a quantum phase transition takes place. We discuss the applicability of the CCD scheme in terms of the fidelity between different initial states evolving under an ideal quantum Rabi model and their corresponding trapped-ion realization, and demonstrate the effectiveness of noise suppression of our method., Video Abstract, publishedVersion

In this work, we combine an established method for open quantum systems—the time evolving density matrix using orthogonal polynomials algorithm—with the transfer tensors formalism, a new tool for the analysis, compression and propagation of non-Markovian processes. A compact propagator is generated out of sample trajectories covering the correlation time of the bath. This enables the investigation of previously inaccessible long-time dynamics with linear effort, such as those ensuing from low temperature regimes with arbitrary, possibly highly structured, spectral densities. We briefly introduce both methods, followed by a benchmark to prove viability and combination synergies. Subsequently we illustrate the capabilities of this approach at the hand of specific examples and conclude our analysis by highlighting possible further applications of our method., National Science Foundation (U.S.) (Grant No. CHE- 1112825), United States. Defense Advanced Research Projects Agency (Grant No. N99001-10-1-4063), MIT-Germany Seed Fund

We propose a set of techniques that enable universal quantum computing to be carried out using dressed states. This applies in particular to the effort of realizing quantum computation in trapped ions using long-wavelength radiation, where coupling enhancement is achieved by means of static magnetic-field gradient. We show how the presence of dressing fields enables the construction of robust single and multi-qubit gates despite the unavoidable presence of magnetic noise, an approach that can be generalized to provide shielding in any analogous quantum system that relies on the coupling of electronic degrees of freedom via bosonic modes., publishedVersion

We propose an all-optical scheme to prolong the quantum coherence of a negatively charged nitrogen-vacancy (NV) center in diamond at cryogenic temperatures. Optical control of the NV spin suppresses energy fluctuations of the ground states and forms an energy gap protected subspace. By optical control, the spectral linewidth of magnetic resonance is much narrower and the measurement of the frequencies of magnetic field sources has higher resolution. The optical control also improves the sensitivity of the magnetic field detection and can provide measurement of the directions of signal sources., publishedVersion

Environmental noise usually hinders the efficiency of charge transport through coherent quantum systems; an exception is dephasing-assisted transport (DAT). We show that linear triple quantum dots in a transport configuration and subjected to pure dephasing exhibit DAT if the coupling to the drain reservoir exceeds a threshold. DAT occurs for arbitrarily weak dephasing and the enhancement can be directly controlled by the coupling to the drain. Moreover, for specific settings, the enhanced current is accompanied by a reduction of the relative shot noise. We identify the quantum Zeno effect and long-distance tunnelling as underlying dynamic processes involved in dephasing-assisted and -suppressed transport. Our analytical results are obtained by using the density matrix formalism and the characteristic polynomial approach to full counting statistics., publishedVersion

The detection of a nuclear spin in an individual molecule represents a key challenge in physics and biology whose solution has been pursued for many years. The small magnetic moment of a single nucleus and the unavoidable environmental noise present the key obstacles for its realization. In this paper, we demonstrate theoretically that a single nitrogen-vacancy center in diamond can be used to construct a nano-scale single-molecule spectrometer that is capable of detecting the position and spin state of a single nucleus and can determine the distance and alignment of a nuclear or electron spin pair. The proposed device would find applications in single-molecule spectroscopy in chemistry and biology, for example in determining the protein structure or in monitoring macromolecular motions, and can thus provide a tool to help unravel the microscopic mechanisms underlying bio-molecular function., publishedVersion

An autonomous quantum thermal machine comprising a trapped atom or ion placed inside an optical cavity is proposed and analysed. Such a machine can operate as a heat engine whose working medium is the quantised atomic motion or as an absorption refrigerator that cools without any work input. Focusing on the refrigerator mode, we predict that it is possible with state-of-the-art technology to cool a trapped ion almost to its motional ground state using a thermal light source such as sunlight. We nonetheless find that a laser or a similar reference system is necessary to stabilise the cavity frequencies. Furthermore, we establish a direct and heretofore unacknowledged connection between the abstract theory of quantum absorption refrigerators and practical sideband cooling techniques. We also highlight and clarify some assumptions underlying several recent theoretical studies on self-contained quantum engines and refrigerators. Our work indicates that cavity quantum electrodynamics is a promising and versatile experimental platform for the study of autonomous thermal machines in the quantum domain., publishedVersion

The Kibble-Zurek mechanism is applied to the spontaneous formation of vortices in a harmonically trapped thermal gas following a temperature quench through the critical value for Bose-Einstein condensation. Whereas in the homogeneous scenario, vortex nucleation is always expected, we show that it can be completely suppressed in the presence of the confinement potential whenever the speed of the spatial front undergoing condensation is lower than a threshold velocity. Otherwise, the interplay between the geometry and the causality leads to different scaling laws for the density of vortices as a function of the quench rate, as we also illustrate for the case of a toroidal trapping potential. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. EPSRC/EP/E058256 Alexander-von-Humboldt Professorship EU STREP

Quantum many-body models describing natural systems or materials and physical systems assembled piece by piece in the laboratory for the purpose of realizing quantum information processing share an important feature: intricate correlations that originate from the coherent interaction between a large number of constituents. In recent years it has become manifest that the cross-fertilization between research devoted to quantum information science and to quantum many-body physics leads to new ideas, methods, tools, and insights in both fields. Issues of criticality, quantum phase transitions, quantum order and magnetism that play a role in one field find relations to the classical simulation of quantum systems, to error correction and fault tolerance thresholds, to channel capacities and to topological quantum computation, to name but a few. The structural similarities of typical problems in both fields and the potential for pooling of ideas then become manifest. Notably, methods and ideas from quantum information have provided fresh approaches to long-standing problems in strongly correlated systems in the condensed matter context, including both numerical methods and conceptual insights.Focus on quantum information and many-body theory ContentsTENSOR NETWORKSHomogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems M Rizzi, S Montangero, P Silvi, V Giovannetti and Rosario FazioConcatenated tensor network states R Hübener, V Nebendahl and W DürEntanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms G Evenbly and G VidalFinite-size geometric entanglement from tensor network algorithms Qian-Qian Shi, Román Orús, John Ove Fjærestad and Huan-Qiang ZhouCharacterizing symmetries in a projected entangled pair state D Pérez-García, M Sanz, C E González-Guillén, M M Wolf and J I CiracMatrix product operator representations B Pirvu, V Murg, J I Cirac and F VerstraeteSIMULATION AND DYNAMICSA quantum differentiation of k-SAT instances B Tamir and G OrtizClassical Ising model test for quantum circuits Joseph Geraci and Daniel A LidarExact matrix product solutions in the Heisenberg picture of an open quantum spin chain S R Clark, J Prior, M J Hartmann, D Jaksch and M B PlenioExact solution of Markovian master equations for quadratic Fermi systems: thermal baths, open XY spin chains and non-equilibrium phase transition Tomaž Prosen and Bojan ŽunkovičQuantum kinetic Ising models R Augusiak, F M Cucchietti, F Haake and M LewensteinENTANGLEMENT AND SPECTRAL PROPERTIESGround states of unfrustrated spin Hamiltonians satisfy an area law Niel de Beaudrap, Tobias J Osborne and Jens EisertCorrelation density matrices for one-dimensional quantum chains based on the density matrix renormalization group W Münder, A Weichselbaum, A Holzner, Jan von Delft and C L HenleyThe invariant-comb approach and its relation to the balancedness of multipartite entangled states Andreas Osterloh and Jens SiewertEntanglement scaling of fractional quantum Hall states through geometric deformations Andreas M Läuchli, Emil J Bergholtz and Masudul HaqueEntanglement versus gap for one-dimensional spin systems Daniel Gottesman and M B HastingsEntanglement spectra of critical and near-critical systems in one dimension F Pollmann and J E MooreMacroscopic bound entanglement in thermal graph states D Cavalcanti, L Aolita, A Ferraro, A García-Saez and A AcínEntanglement at the quantum phase transition in a harmonic lattice Elisabeth Rieper, Janet Anders and Vlatko VedralMultipartite entanglement and frustration P Facchi, G Florio, U Marzolino, G Parisi and S PascazioEntropic uncertainty relations—a survey Stephanie Wehner and Andreas WinterEntanglement in a spin system with inverse square statistical interaction D Giuliano, A Sindona, G Falcone, F Plastina and L AmicoAPPLICATIONSTime-dependent currents of one-dimensional bosons in an optical lattice J Schachenmayer, G Pupillo and A J DaleyImplementing quantum gates using the ferromagnetic spin-J XXZ chain with kink boundary conditions Tom Michoel, Jaideep Mulherkar and Bruno NachtergaeleLong-distance entanglement in many-body atomic and optical systems Salvatore M Giampaolo and Fabrizio IlluminatiQUANTUM MEMORIES AND TOPOLOGICAL ORDERThermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes Stefano Chesi, Daniel Loss, Sergey Bravyi and Barbara M TerhalTopological color codes and two-body quantum lattice Hamiltonians M Kargarian, H Bombin and M A Martin-DelgadoRENORMALIZATIONLocal renormalization method for random systems O Gittsovich, R Hübener, E Rico and H J Briegel, publishedVersion

This thesis investigates the origin of mechanically decoupled quantum emitters in hexagonal Boron Nitride and uses this emitter type for random number generation experiments. Furthermore, Nitrogen- and Silicon-vacancy centers in diamond integrated in laser-written diamond waveguides are employed for magnetometry and on-chip single photon experiments.

Quantum physics currently provides our deepest description of nature. To understand precisely how it differs from classical physics is not only of foundational interest, but also important to advance technology: the advent of quantum information has led to the insight that certain quantum phenomena, e.g., entanglement and coherence, are resources which enable us to solve practical tasks that are unsolvable within the realm of classical physics. But how can we quantify quantum resources and how do we decide which resource is relevant for a specific operational advantage in quantum cryptography, quantum computation, or quantum metrology? How can we employ these resources optimally? Addressing these questions is the motivation for the development of quantum resource theories, a mathematically rigorous framework that allows us to investigate a specific quantum phenomenon as a resource. Formally, such theories emerge from restrictions which are imposed in addition to the laws of quantum mechanics. A prominent example is the restriction to local operations and classical communication, which singles out entanglement as a resource. Typically, such theories describe the value of quantum states, i.e., static resources. An important question in such theories concerns their structure as determined by the restriction under consideration, which is analyzed for coherence theory on qubits in this thesis. Only recently, so-called dynamical resource theories that quantify the value of operations were proposed, which are advantageous for several reasons: they include resource theories of states as special cases, allow us to quantify additional quantum properties such as the detection or usage of static resources, which will be a main topic of this thesis, and are more natural from an operational perspective. But are different types of dynamical resources present in quantum operations related? For the case of dynamical coherence and entanglement, it will be shown that there is not only a quantitative, but also a qualitative connection.

Models of quantum gravity imply a fundamental revision of our description of position and momentum. This revision manifests in modifications of the canonical commutation relations. Experimental tests of such modifications remain an outstanding challenge. In recent years, tabletop experiments to test for quantum gravity have been proposed. This thesis address two main challenges to such experiments. The first contribution is related to the recent proposal to use cavity-optomechanical systems to test for these deformations [Nat. Phys. 8, 393-397 (2012)]. Improving the achievable precision of such devices represents a major challenge that we address with our present work. More specifically, we develop sophisticated paths in phase-space of such optomechanical systems to obtain significantly improved accuracy and precision under contributions from higher-order corrections to the optomechanical Hamiltonian. An accurate estimate of the required number of experimental runs is presented based on a rigorous error analysis that accounts for uncertainty in mean photon number, which can arise from classical fluctuations or from quantum shot noise in measurements. Furthermore, we propose a method to increase precision by using squeezed states of light. Finally, we demonstrate the robustness of our scheme to experimental imperfection, thereby improving the prospects of carrying out tests of quantum gravity with near-future optomechanical technology. The second contribution is based on the fact that the deformations in the canonical commutator scale with the mass of test particles, which motivates experiments using macroscopic composite particles. Here we consider a challenge to such tests, namely that quantum gravity corrections of canonical commutation relations are expected to be suppressed with increasing number of constituent particles. Since the precise scaling of this suppression is unknown, it needs to be bounded experimentally and explicitly incorporated into rigorous analyses of quantum gravity tests. We analyse this scaling based on concrete experiments involving macroscopic pendula and provide tight bounds that exceed those of current experiments based on quantum mechanical oscillators. Furthermore, we discuss possible experiments that promise even stronger bounds. Thus, the work in this thesis brings rigorous and well-controlled tests of quantum gravity closer to reality.

Nuclear magnetic resonance (NMR) is an established method for non-invasive and non-destructive imaging and spectroscopy. The nitrogen vacancy (NV) center in diamond has emerged as a promising sensor for NMR signals at the nanoscale due to the possibility to initialize and manipulate its spin at room temperature combined with the electron spin properties that allow to measure different signals. This thesis presents improvements for two main aspects of NV-NMR, advanced NV-hyperpolarization techniques that allow to improve the signal-to-noise ratio of NMR applications, and improved NV-sensing protocols. The work on hyperpolarization techniques includes various improvements, adaptations, and applications of the PulsePol sequence. Modifications and alternative sequence designs that overcome different experimental challenges are shown, including designs that allow to generate nuclear-nuclear gates, designs without neighbouring pulses, an adaptation for usage in cavities and a pulse design that is more robust to NV-NV interactions. We investigate the behaviour under various conditions analytically and numerically. We further show that pulsed polarization sequences can be applied to other systems than NV-centers, for example to Parahydrogen-induced polarization. The second part on improved NV-sensing protocols presents and investigates extensions of recently developed heterodyning schemes. We show that an array of nuclear spins can be used to transform the problem of measuring a constant magnetic field to measuring the frequency of an oscillation with the NV center and compare this protocol to other methods. We further adapt heterodyning protocols such that they are sensitive to frequency differences by analyzing the effect of the pulse phases on the readout probability and discuss under which conditions this allows to overcome magnetic field fluctuations that would render conventional NMR signals unusable. In summary, this work investigates two essential aspects of NV-NMR. We present and improve pulsed polarization protocols as a robust and efficient tool to achieve nuclear hyperpolarization and develop tools for the ideal detection of the NMR signal from nuclear spins with the NV center.

During the last decade, nitrogen-vacancy (NV) centers in diamond have gained a prominent role within the field of quantum technologies. These color defects inside the diamond lattice have been proved to be an extraordinary platform that assists in many of the current challenges that cutting-edge research is facing. The application of these novel tools exceeds the borders of quantum physics and reaches fields such as medicine, biology or chemistry. This thesis is focused on the development of novel theoretical schemes that intend to open new ways of understanding the NV centers as a quantum tool and sensor with direct applications. The manipulation of NV centers has become relatively easy in these last years. Moreover, via a proper control, the environment of an NV center may be overridden. In this thesis, we treat the NV center as a tool for enhancing the performance of nuclear magnetic resonance (NMR). Since the resolution of NMR is largely limited by the poor polarization of certain organic molecules, we here create and develop a theoretical frame that uses the NV center as a tool to transfer polarization toward organic samples in an efficient and controllable manner. In addition, this theoretical effort is supported by extensive numerical simulations and, moreover, all the predictions are confirmed by experimental evidence. Therefore, we demonstrate polarization transfer to external molecules at room-temperature paving the way for high-resolution NMR. Motivated by the success of the NV center as a polarization tool, we have further extended our analysis aiming to develop a phase transition sensor. In particular, we propose the NV center as a tool to assist current research on chemical reactions and molecular dynamics occurring at solid-liquid interfaces. These processes occur at a nanometric scale and thus, a nanometric sensor is desirable. In this context, the NV center is introduced as an ideal platform to investigate exotic phases of water when deposited onto diamond surface at room-temperature. In fact, recent studies predict that ultra-thin layers of water behave differently from bulk water due to interactions between water molecules and carbon atoms in the diamond surface. Through this thesis, we provide a theoretical and numerical work that predict how the NV center spin will behave in the presence of different phases of water, and hence, we reveal the NV center as a high-resolution sensor able to determine internal structures.

In the works leading to this thesis the aim was to give a clear operational interpretation of different aspects of non-classicality. Doing so, enables to see the different properties as different aspects of the same underlying question, namely whether there is a classical explanation of the measurements at hand. If one incorporates the additional assumptions in the setting (such as locality by the separation of the two parties in entanglement theory), the question of whether some system is classical, boils down to ask whether one can simulate everything one can possibly observe by classical variables governed by a stochastic process. This new perspective allows to characterise dynamic properties of non-classicality, and also to connect them to more static types of non-classicality such as entanglement. Indeed we unify entanglement, discord and coherence from one single perspective. We do this by restricting our setting such that the operations have a clear classical interpretation and hence incorporating natural restrictions of classical systems, if the initial state of the system is not entangled does not have discord or does not have coherence. If the initial state of the system is different, we see the magic of quantum mechanics happening again. For instance we show for one specific quantum algorithm, which is thought to be better than any classical algorithm for its task, that the precision of the algorithm scales with the coherence present at its start. In other words, it is these resources (coherence, discord and entanglement) that make the magic possible and with our perspective we can interpret the role of the different resources and analyse how they are linked to each other. This does not give an explanation of the magic of quantum mechanics, but it does make the mechanisms more transparent allowing for new explanations and there are some examples already in this thesis. Finally we also look at the dual of when states are non-classical, asking, and answering, in a specific setting, what makes measurements non-classical.

Quantum systems and tensors share the property that the complexity of their description grows exponentially with the number of physical subsystems or tensor indices. This thesis discusses efficient methods for tensor reconstruction, quantum state estimation and verification, as well as quantum state and process tomography. The methods proposed here can be efficient in the sense that the resource requirements scale only polynomially instead of exponentially with the number of physical subsystems or tensor indices. In numerical and analytical calculations, matrix product state (MPS)/tensor train (TT), projected entangled pair state (PEPS), and hierarchical Tucker representations are used. The reconstruction and estimation methods are discussed in principle, their performance is evaluated with numerical simulations, and the quantum state in an ion trap quantum simulator experiment is estimated and verified.

A Dissertation on open quantum systems, containing a general review of the current standing of the field, in particular regarding systems interacting with Gaussian environments, as well as original analytical and numerical results. The problem of the impact of a variation in the environmental properties on the reduced dynamics of an open system is investigated analytically, and a new computational technique for the simulation of non-perturbative, non-Markovian open quantum system dynamics based on devising error-certified effective environments is presented.

The dynamics of any quantum device is altered by its interaction with the surrounding environment. This thesis discusses the impact of noise in a scenario of quantum frequency estimation and techniques to control the dynamics between interacting quantum systems, as well as a method to tailor memory effects in the dynamics of an experimentally relevant system. In particular, we exploit a quantum metrology setting where N two level systems are employed as probes to estimate the amplitude of a field which alters their level splitting in a linear fashion. There, we explore the fundamental limits of the estimation precision we can achieve using quantum strategies. Furthermore, we apply newly developed quantum control methods to nitrogen-vacancy centers in diamond. These techniques are focused on the interpretation of frequency spectra, the creation of high fidelity two-qubit gates via specifically designed dynamical decoupling sequences and the control of memory effects in the open quantum system dynamics of the nitrogen-vacancy center.

Trapped atomic ions are one of the leading platforms for quantum simulations. Recently, they have also established themselves as a testbed for classical statistical mechanics and mesoscopic systems. The challenges in this field are twofold at the moment. In the endeavor to simulate systems which are beyond the simulation capabilities of currently available conventional computers, trapped-ion experiments have constantly become more complex. The precise interrogation of the dynamics of the ever more complex experiments remains a challenge. It is therefore desirable to develop new schemes for the study of the dynamics of crystals of trapped ions which can be realized with state-of-the-art technology. On the other hand, there is a demand for simulation protocols that can be implemented in current experiments and, at the same time, are able to simulate physics which cannot be simulated efficiently on conventional computers. In this thesis we address both of these issues.