Before large-scale, robust quantum computers are developed, it is valuable to be able to classically simulate quantum algorithms to study their properties. To do so, we developed a numerical library for simulating quantum circuits via the matrix product state formalism on distributed memory architectures. By examining the multipartite entanglement present across Shor’s algorithm, we were able to effectively map a high-level circuit of Shor’s algorithm to the one-dimensional structure of a matrix product state, enabling us to perform a simulation of a specific 60 qubit instance in approximately 14 TB of memory: potentially the largest non-trivial quantum circuit simulation ever performed. We then applied matrix product state and matrix product density operator techniques to simulating one-dimensional circuits from Google’s quantum supremacy problem with errors and found it mostly resistant to our methods.

This thesis describes the measurement of direct CP asymmetry and branching fraction for the hadronic B decays B0 -> D0 pi0 an B+ -> D0 pi+. The study uses the full dataset of 711 fb^(-1) collected at the Y(4S) resonance by the Belle experiment at the KEKB accelerator in Tsukuba, Japan. Event reconstruction, background suppression and modelling are first studied using Monte Carlo simulations, before yield and direct CP asymmetry are extracted in a three-dimensional unbinned extended maximum likelihood fit. B+ -> D0 pi+ is measured first as the control mode to validate the methodology, before same techniques are used on B0 -> D0 pi0 . The measured branching fractions and direct CP asymmetries are: Br(B0 -> D0 pi0) = (2.69 +/- 0.06 +/- 0.09) x 10^(-4), A_CP(B0 -> D0 pi0) = (0.10 +/- 2.05 +/- 1.29) x 10^(-2), Br(B+ -> D0 pi+) = (4.53 +/- 0.02 +/- 0.14) x 10^(-3), A_CP(B+ -> D0 pi+) = (0.19 +/- 0.36 +/- 0.60) x 10^(-2), for B0 -> D0 pi0 and B+ -> D0 pi+ respectively, where the first uncertainty is statistical and the second is systematic. The represents the world’s first measurement of direct CP asymmetry for B0 -> D0 pi0. This measurement of branching fraction of B0 -> D0 pi0 and B+ -> D0 pi+, and direct CP asymmetry of B+ -> D0 pi+ are the most precise to date, and consistent with the current world average values.

Galaxy clusters are powerful probes of cosmology. Their abundance depends on the rate of structure growth and the expansion rate of the universe, making the density of clusters highly sensitive to dark energy. Galaxy clusters additionally provide powerful constraints on matter density, matter fluctuation amplitude, and the sum of neutrino masses. However, cluster cosmology is currently limited by systematic uncertainties in the cluster mass estimation. Generally, the cluster masses are estimated using observable-mass scaling relations where the observable can be optical richness, X-ray temperature etc. The observable-mass scaling relation depends on the complex cluster baryonic physics which is not well understood and any deviation in the baryonic physics will lead to uncertainties in the mass estimation. On the other hand, gravitational lensing offers one of the most promising techniques to measure cluster mass as it directly probes the total matter content of the cluster. Gravitational lensing can additionally be used to calibrate the observable-mass scaling relations. The gravitational lensing source can either be optical galaxies or the cosmic microwave background (CMB). My thesis focuses on developing statistical and mathematical tools to robustly extract the cluster lensing signal from CMB data. We develop a maximum likelihood estimator to optimally extract cluster lensing signal from CMB data. We find that the Stokes QU maps and the traditional EB maps provide similar constraints on mass estimates. We quantify the effect of astrophysical foregrounds on CMB cluster lensing analysis. While the foregrounds set an effective noise floor for temperature estimator, the polarisation estimator is largely unaffected. We use realistic simulations to forecast that CMB cluster lensing is expected to constrain cluster masses to 3-6%(1%) level for upcoming (next generation) CMB experiments. One of the standard ways to extract the CMB-cluster lensing signal is by using the quadratic estimator. The thermal Sunyaev-Zel'dovich effect (tSZ) acts as a major contaminant in quadratic estimator and induces significant systematic and statistical uncertainty. We develop modified quadratic estimator to eliminate the tSZ bias and to significantly reduce the tSZ statistical uncertainty. Using our modified quadratic estimator we constrain the mass of Dark Energy Survey year-3 cluster catalog. We also put constraints on the normalisation parameter of optical richness-mass scaling relation. In addition to removing the tSZ bias, modified quadratic estimator also reduces tSZ induced statistical uncertainty by 40% in future low noise CMB-surveys.

Quantum technologies promise to impact on several aspects of society. Examples include quantum computing to perform certain calculations significantly faster than current classical computers, quantum cryptography for more secure communications, quantum sensing to make measurements with unprecedented sensitivity and resolution, and specialised quantum devices such as quantum hyperpolarisers for enhanced medical imaging. However, the field is still in its infancy and most quantum technologies have been realised only in delicate laboratory settings with little prospect for real-world applications (e.g. quantum sensors), or are many years away from being mature enough to make an impact (quantum computing). This thesis develops two applications of quantum technologies, in the direction of quantum hyperpolarisation on the one hand and quantum sensing on the other hand, which utilise a quantum system particularly suited for practical applications, the nitrogen-vacancy (NV) centre in diamond. This diamond spin defect can be operated in ambient conditions and the resulting quantum devices can be easily miniaturised for large scale deployment. Specifically, in the first part of this thesis (chapters 2 to 4), two new techniques to realise hyperpolarisation (HP) of nuclear spins are developed. Through effective HP, ensembles of nuclear spin can be polarised far beyond the normal Boltzmann level, which can be used to enhance the spin signal for nuclear magnetic resonance (NMR) and imaging (MRI). Chapter 2 and 3 focus on exploiting direct cross-relaxation (CR) between the NV spin and the nuclear spin. Chapter 2 investigates a CR-based protocol for sensing, and determines, through a study of the NV physics, under what regimes this protocol can be applied to nuclear spin detection. This study constructs a framework under which HP via CR can be realised. Chapter 3 continues in this direction and demonstrate that CR can be used to hyperpolarise external nuclear spins. A detailed understanding of the spin bath mechanics is explored and the impact of rogue uncontrolled NV spins on this spin bath is determined. Additionally, this protocol is compared with other HP techniques and shows a remarkable improvement in polarisation rate, however, it is particularly sensitive to magnetic field detuning. To overcome this issue, in chapter 4 a different technique is developed that relies on a dynamical decoupling protocol purposefully modified to achieve HP. This new technique has a slower polarisation rate than CR-based HP but is robust to the experimental errors that exist in scaling these hyperpolarisation techniques. The second part of this thesis (chapters 5 and 6) exploits the quantum sensing properties of ensembles of NV centres in diamond to develop multi-modal microscopic imaging, which is a promising tool for device diagnosis and the study of mesoscopic phenomena. Specifically, chapter 5 develops and implements a technique for imaging the electric field simultaneously with the magnetic field. The technique is applied to the study of electric fields that are intrinsic to interfaces and junctions. The functionality of electronic devices (such as transistors) are fundamentally dictated by these fields which have traditionally been opaque to probing except at the very surface. While the surface potential is crucial, a wealth of information is contained in the bulk structure which is the focus of this study. In chapter 6 the same sensing protocol is extended to image stress embedded in the diamond rather than electric fields. A series of different deformation sources is used to test and verify that the technique can determine the entire stress tensor with high sensitivity and micrometer spatial resolution. With these new imaging capabilities, extending the traditional magnetic field sensing to electric field and stress, multi-modal NV imaging is a promising example of quantum technology that may have an immediate impact in other fields of science.

Wireless biomedical electronic implants are rapidly being developed to treat a variety of medical conditions. Current technologies include the pacemaker to treat arrhythmias, the cochlear implant to overcome hearing impairment and the deep brain stimulator to treat Parkinson’s disease. Researchers are aiming to create implants that are miniaturised, battery-free, and minimally invasive. This is to ensure that devices are simpler to implant, to avoid surgical battery replacement and to minimise the risk of infection. To meet these demands, future biomedical electronic implants need to be miniaturised and capable of wireless power and data transfer. This thesis explores and extends the capabilities of three different wireless power transfer technologies for biomedical electronic implants: inductive, capacitive and radiative power transfer. This thesis adopts a systems approach to extend the capabilities of wireless power transfer systems. Wireless inductive power transfer has received thorough attention in the literature and involves the use of time-varying magnetic fields to transmit power through biological tissue. Typically, inductive power transfer involves a single transmitter and single receiver. This thesis demonstrates many receiving devices can be operated from a single transmitter - without adding complicated electronics to each receiving device. Moreover, by tuning the receiving coil on each device carefully the transmitter can power individual devices, or multiple devices simultaneously, extending the capabilities of inductive power transfer systems. Optogenetics, a technique used to transfect cells to make them light sensitive, is used to provide biological validation of the multichannel inductive receiving topology. Human embryonic kidney cells are transfected to be sensitive to blue light and then a twin channel inductive receiver with a blue and yellow light is modulated to demonstrate a cell response and no cell response respectively. Inductive coupling is not always the most suitable power transfer scheme and wireless capacitive coupling is presented as an alternative. This is where time-varying electric fields transmit power through biological tissue via conductive plates. Stenting, a surgical procedure used to prevent blood vessels from closing, is used to validate the efficacy of capacitive coupling in a biological context. Stents are thin metal tubes resembling chicken wire made from nitinol - a conductive nickel titanium alloy. There is significant motivation to include intelligent sensors in stents as they are simple to implant via angiographic catheter. However, stents preclude the use of batteries as they cannot be removed after surgery so wireless power and data transfer is essential. The optimal frequency to use to transmit power to a stent via capacitive coupling is derived from first principles. Then, a miniaturised circuit board, capable of wireless power and data transmission is fabricated and placed between two stents. The wireless power and data transfer capabilities of the device are validated in-vitro in excised muscle tissue and in-vivo in a live ovine model. The results demonstrate that capacitive power and data transfer is viable for stent-based biomedical implants. An emerging area of study is wireless radiative power transfer through biological tissue. Such a technique is promising for powering miniaturised, deep tissue implants. Due to the dispersive nature of biological tissue, finite element analysis is essential to understanding how wireless radiative power transfer can power biomedical electronic implants efficiently. This thesis builds on efficient radiative power transfer schemes by proposing a new implant and antenna geometry. Long and thin implants show promise as they have the potential to be delivered by catheter or injection - reducing surgical risk and overhead. This thesis demonstrates a technique that uses near-field radiative power transfer to efficiently power a 20 mm long implant that is sub-millimetre in diameter. To power the device, optimised wide dipole transmitting antennas are simulated, designed, fabricated, tested and measured for various implant depths. Biological validation is provided by stimulating retinal ganglion cells wirelessly with the miniaturised device designed to power a small light. In summary, the work presented in this thesis demonstrates that by extending wireless powering schemes from the well known inductive coil to include capacitive and radiative power transfer, implants can be miniaturized and inserted in places in the body that might have not seemed previously possible. Therefore, wireless biomedical electronics implants are likely to become miniaturised, battery-free and ubiquitous. Whilst these techniques may offer significant economic and health benefits, there are also complicated ethical questions to consider. With the promise of pervasive, safe, minimally invasive and battery free biomedical electronic implants, humans will have the choice to enhance their abilities. Naturally, the question of what it means to be human will emerge.

The brightest persistent astrophysical sources in the universe are quasars, a group of active galactic nuclei (AGN) that appear star-like and radiate across all wavelengths. The emitted radiation is believed to be powered by a supermassive black hole at the core of a galaxy. Matter that falls into the black hole is being fed onto the accretion disk, heating up the disk in the process due to friction. A wind emanating from the accretion disk, or a disk-wind, appears ubiquitous in these objects and acts as one effective way to generate the spectral lines observed in the quasar's spectrum. The broad spectral lines, originating from the broad line region (BLR), show diverse properties, specifically in velocity shift, line width, and degree of asymmetry. Yet, the exact structure of the BLR has remained perplexing due to its small size, which means it is unresolved even with the current astronomical instrumentation. Thus, simulations are important. By developing a model of the BLR, an informative analysis of the line profiles allows us to explore some of the key questions about the BLR, emphasising the shape of spectral lines, the disk-wind BLR, and the orientation. We simulate line profile modelling using a simple kinematical disk-wind model of the BLR with radiative transfer in the high velocity limit. The model provides a framework to explore the characteristics of the emission line profile induced by the different geometries and kinematics of the BLR, including the opening angle of the wind and the geometry of the line emitting region. The effect of orientation in these systems is also examined. As a first step, we use the model to simulate a narrow outflowing disk-wind, which has been described in the literature. The primary objective is to determine whether the observed emission line properties are consistent with a narrow wind scenario. We find that the line profiles are more blueshifted for a narrow polar wind model as opposed to intermediate and equatorial models. When viewing at pole-on angles, the simulated emission lines show a narrower line width, which is asymmetric and more blueshifted than that viewed edge-on. The blueward shift of the line profile increases as the line-of-sight and wind intersect. The model is also able to recover a shorter time delay in the red or blue side of the line profiles, consistent with observational evidence in reverberation mapping studies. The second part of the thesis considers the properties of broad absorption line quasars (BALQs). These objects are rare and often display a blueward absorption trough relative to the emission line. One interpretation of the velocity offsets is the unification based on orientation, whereby a BAL is viewed within a constrained narrow wind angle. In order to test whether the BALQs and non-BALQs can be distinguished by their emission features, we conduct statistical tests and machine learning on the two populations. We find that their continuum and emission features are qualitatively similar, which contradicts the narrow disk-wind model in the geometric unification. Therefore, we propose a model of the disk-wind comprising a wide wind opening angle with multiple dense radial streams, where the BAL is detected when the line-of-sight crosses these streams. These findings have lead us to the discovery of a novel orientation indicator of quasars in the ultraviolet-optical regime. We propose a simple yet robust angle-of-viewing probe using the correlation between the velocity shifts and line widths. Our idea is shown to be qualitatively consistent with other orientation proxies. We also perform a wide angle disk-wind simulation and successfully retrieve the predicted correlation with inclination. In addition, we extend our model to estimate the bias in the virial black hole mass due to the scale factor f, which is related to the unknown nature of the BLR. Using a wide disk-wind configuration, we retrieve the f factors for a range of inclination angle. The f factor shows significant dependence with orientation, characterisation of the line width, and location of the emission region in the wind. Therefore, using a constant f value biases the estimation of the mass of the black hole.

Understanding the nature of Dark Matter is a key goal in modern physics. The observed gravita-tional interactions of galaxies and galactic clusters, along with theories of structure formation in the early universe, indicate the existence of Dark Matter. Evidence of the specific nature of Dark Matter remains elusive however. Particle collider experiments search for evidence of Dark Matter production within energetic proton collisions. One strategy employed in this field is to make minimal assumptions about new particles and couplings to Standard Model particles, in order to explore the range of possibilities without being overly constrained by narrow assumptions. This thesis focuses on the assumption that Dark Matter couples strongly to the heavier quarks, which motivates searching for processes where it is produced in association with pairs of top quarks. An analysis is presented on the 2015 and 2016 “Run 2" dataset taken with the ATLAS detector, consisting of 36.1 fb -1 of proton-proton collisions at the Large Hadron Collider. This analysis studies the hypothesis of Dark Matter production in conjunction with hadronically decaying top quarks. No excess above the estimated Standard Model backgrounds is observed, and constraints on the allowed cross-sections are presented. When making minimal assumptions about the nature of Dark Matter, scalar mediator masses below 20 GeV are excluded. These results are then translated to more specific and complete Two Higgs Doublet models that feature for example in Supersymmetry that also predict the same final states, and constraints on the parameter space of these models are presented.

The Compact Linear Collider (CLIC) is a 3 TeV linear electron-positron collider which is proposed to operate with loaded accelerating gradients up to 100 MV/m. These high gradients are accompanied by high field phenomena which limit the operation of the accelerating structures. Achieving reliable operation at these accelerating gradients requires an in-depth understanding of these phenomena and their effects on CLIC. This thesis investigates the phenomenology of high fields in CLIC accelerating structures through tests performed at the CERN's high gradient testing facilities. The commissioning of a novel RF test stand will be presented. Using a unique RF pulse weaving method in combination with RF pulse compression, the new test stand offered the ability to test multiple accelerating structures in situ and at repetition rates up to 200 Hz. This offered a significant increase in the high gradient testing capacity at CERN. Using the new test stand, as well as existing infrastructure, four unique accelerating structures underwent conditioning to high gradients. These accelerating structures included a CLIC baseline design prototype, a structure with high order mode damping material, and two structures fabricated through novel machining and joining technologies. Three of the four structures were able to reliably operate at unloaded accelerating gradients of at least 100 MV/m with low breakdown rates. Concurrent to the high gradient testing of accelerating structure, was an investigation into the radiation within the testing facilities, which was known to be the result of field emission capture. A series of measurements and simulations characterised the radiation produced during high power testing. A particular focus for the investigation was how the field emission capture varies with phase velocity. A model to describe the dependency of the capture of field emitted electrons on the phase velocity is presented. Measurements on the X-band test stands at CERN demonstrated that the capture increased ~20% for a 1 MHz increase in the RF driver frequency. These results were corroborated using a three dimensional RF and particle simulation.

This project aims to develop a data-driven technique for the estimation of the dominant background contribution in the inclusive search for new physics signals where equally charged lepton pairs are featured in the final state and where an hadronically decaying tau lepton can be found in a pair. The studies presented in this thesis were performed with data collected by the ATLAS experiment. A data driven technique has been developed for the abundant background of jets originated from the hadronisation of quarks or gluons which are mis-identified as hadronically decaying tau leptons. Mis-identification weighting factors have been measured for the extrapolation of this background into the signal region of the analysis and have been validated using a selection independent with respect to the the signal region. Systematic uncertainties have also been estimated. The work presented in this thesis will be incorporated in a general extrapolation technique within the ATLAS experiment aiming to be used by all ATLAS searches featuring hadronic tau decays in the final state.

Globular clusters (GCs), compact stellar systems orbiting in and around galaxies, are natural laboratories to study a diverse range of astrophysical processes. The current stellar population of the oldest GCs in our Galaxy is the manifestation of more than 12 billion years of combined stellar, dynamical and hydrodynamical evolution, whose interplay is responsible for enhanced presence of star exotica such as millisecond pulsars, blue stragglers and black hole (BH) binaries. GCs have also been indicated as possible formation sites of intermediate-mass black holes (IMBHs), which might represent the missing link between the wellknown populations of stellar BHs (few tens times the Sun’s mass) and supermassive BHs (more than a million times the Sun’s mass). Despite recent efforts, a clear evidence of their existence is still missing, therefore identifying multiple signatures of their presence has become critical. In the first part of this thesis, we address two main issues that may affect a possible IMBH detection. The first issue is represented by the systematic uncertainties in classical observational techniques (e.g., integrated-light IFU spectroscopy). In particular, we use state-of-the-art numerical simulations to produce realistic mock observations considering different setups in order to assess under which conditions the presence of an IMBH can be successfully recovered. The second issue is related to the IMBH wandering off-center, which is fundamental to take into account, especially when the presence of IMBHs is constrained through dynamical modeling of stellar kinematics. Guided by the simulation results, we developed a basic yet accurate model that can be used to estimate the average IMBH radial displacement in terms of structural quantities, which can be constrained by the observations. In the second part of the thesis, we present a new set of cutting-edge direct Nbody simulations, which have been specifically designed to study the dynamical influence of BHs on the long-term evolution of GCs. We combined our numerical simulations with analysis techniques from high-resolution observations of GCs with the aim of identifying key indicators that correlate with the black hole mass fraction. Our results offer novel approaches to indirectly characterise black hole populations in star clusters, which in turn can constrain theories of globular cluster formation and estimates of dynamically-induced gravitational wave merging rates.

Biochemical processes are conducted by interactions of individual molecules that comprise cells. It is the transient physical shape of proteins that dictates their specific functionality. However, imaging individual instances of single molecular structures is one of the notable challenges in structural biology. Presently available protein structure reconstruction techniques, Nuclear Magnetic Resonance (NMR) spectroscopy, X-ray crystallography and cryogenic Electron microscopy (cryo-EM), cannot provide images of individual molecules. Despite their power and their complementary capabilities, said techniques produce only average molecular information. They achieve this by sampling large ensembles of molecules in nearly identical conformational states. As a result, individual instances of a generic, inhomogeneous or unstable atomic structures presently remain beyond reach. We seek to address this problem in a novel way by leveraging quantum technologies. In quantum computing, qubits are usually arranged in grids and coupled to one another in a highly organised manner. However, what if a qubit was coupled to an organic cluster of nuclear spins instead, e.g. that of a single molecule? What can be done with such a system in the context of quantum control and 3D imaging of individual molecular systems? What are its ultimate limits and possibilities? We explore those questions in stages throughout the chapters of this thesis. We begin in Chapter 2 by investigating dipole-dipole interactions present between the nuclear spins in a target molecule, on one side, and between an electron-spin based qubit and each of the nuclear target spins on the other. We consider the Nitrogen Vacancy (NV) centre in diamond as an example of a suitable qubit with an active community interest as a biocompatible nano-magnetometer. Our intention is to lay down foundations that will help us advance from magnetometry to 3D molecular imaging. Our inspiration comes from drawing parallels between the single molecule sensing in the qubit-target system and the clinical Magnetic Resonance Imaging (MRI). An MRI machine directly images a single, specific sample in its native state regardless of its characteristics. That is precisely what we would like to achieve on the molecular level. In Chapter 3, we develop a framework that allows a spin qubit to serve as a platform for 3D atomic imaging of molecules with Angstrom resolution. It uses an electron spin qubit simultaneously as a detector and as a gradient field provider for MRI-style imaging. We develop a theoretical quantum control methodology that allows dipole-dipole decoupling sequences used in solid-state NMR to be interleaved with the gradient field provided by the qubit. In Chapter 4, we propose group-V donors in silicon as a novel qubit platform for bioimaging. Actively researched for quantum computing purposes, such qubits have not been considered in the biological context. A prime example of this class of qubits is the phosphorus donor in silicon (Si:P). We show how its specific set of properties, including long coherence times, large wave function and low operational temperatures can be leveraged for the purposes of atomic level imaging. Finalising the work in Chapter 5, we simulate the imaging process for one transmembrane protein of the influenza virus embedded in a lipid membrane. This demonstration highlights the potential of silicon spin qubits in the future development of in situ single molecule imaging at sub-Angstrom resolution.

The discovery of the Higgs boson in 2012 has opened up a new sector of particle physics to measurements of yet undiscovered couplings. Measurements of the numerous couplings of the Higgs boson - primarily through studies of bosonic decays - have consistently confirmed the Standard Model of Particle Physics. The measurement of fermionic Yukawa couplings, which is a free parameter of the Standard Model, is a critical test of the origin of mass in the Standard Model and serves as a probe for a wide array of new physics models. This thesis presents a measurement, search and feasibility study of couplings of the Higgs boson to the third generation lepton, the tau . A measurement is presented of the H -> tau tau cross-section which is performed using 36.1 inverse fb of sqrt(s) = 13 TeV collision data collected at the Large Hadron Collider by the ATLAS detector. A 6.4 sigma excess over the background-only hypothesis was observed in combination with sqrt(s) = 7, 8 TeV which constitutes a discovery of the final remaining coupling to third generation fermions. The total cross-section was measured as 3.70 +- 0.58(stat) +0.89-0.75(syst) pb, consistent with the expectation from the Standard Model. Several new physics models predict phenomena which can probed in supressed Higgs boson decays: one such phenomena is lepton flavour violation. A search for lepton flavour violating Higgs boson decays to e,mu and mu,e final states, using a new multivariate approach, is also detailed. This search used the same dataset as for the H -> tau tau cross-section. No excess is observed and upper limits on the branching ratio for H -> mu tau and H -> e tau of 0.47% and 0.28% are set, respectively. The limit on H -> e tau is now the new global limit. Finally a feasibility study for measuring the state of the Higgs boson using decays to two tau leptons is demonstrated. At tree-level, the H -> tau tau decays are sensitive to CP admixture couplings to a Higgs boson. One of the promising decay channels, where the tau lepton decays to three charged pions, is shown to be viable thanks to development of a robust neural network approach.