Increasing ubiquity of computational resources has enabled simulation of complex electronic systems and modern materials. The PAOFLOW software package is a tool designed to construct and analyze tight binding Hamiltonians from the solutions of DFT calculations. PAOFLOW leverages localized basis sets to greatly reduce computational costs of post-processing QE simulation results, enabling efficient determination of properties such as electronic density, band structures in the presence of electric or magnetic fields, magnetic or spin circular dichroism, spin-texture, Fermi surfaces, spin or anomalous Hall conductivity (SHC or AHC), electronic transport, and more. PAOFLOW's broad functionality is detailed in this work, and several independent studies where PAOFLOW's capabilities directly enabled research on promising candidates for ferroelectric and spintronic based technologies are described. Today, Quantum computers are at the forefront of computational information science. Materials scientists and quantum chemists can use quantum computers to simulate interacting systems of fermions, without having to perform the iterative methods of classical computing. This dissertation also describes a study where the band structure for silicon is simulated for the first time on quantum hardware and broadens this concept for simulating band structures of generic crystalline structures on quantum machines.

This thesis investigates the impact noise has on Grover’s algorithm when being used to search for multiple items in a database. The main metric being looked at is the probability of the algorithm successfully finding a correct item. The Qiskit framework was used to implement and evaluate the algorithm’s performance in noise-free and noisy environments. Results from the experiments show significant findings. In noiseless tests, the algorithm performs effectively and as expected. However, with the introduction of a noise model, the algorithm’s performance declines noticeably. The probability of it finding a marked item was close to the probability of randomly selecting the same item from the database. This was the case regardless of how many items were marked or the database size. These unexpected outcomes illustrate the disabling effect of noise on Grover’s algorithm. Limitations of the study include noise completely disrupting the algorithm, challenges in accurately modelling quantum noise, and the use of relatively small databases. Further research is needed to explore noise mitigation strategies and assess the algorithm’s robustness in larger-scale scenarios. This research strengthens our understanding of noise’s impact on Grover’s algorithm, showcasing the challenges and limitations of its implementation. It highlights the importance of properly managing noise in quantum computing to fully utilize its potential in efficiently solving complex problems. / Denna avhandling undersöker effekten av brus på Grover’s algoritm för att söka efter flera markerade element i en databas. Huvudfokuset var att undersöka sannolikheten att algoritmen korrekt skulle hitta ett av flera markerade element i en databas. Qiskit-ramverket användes för att utvärdera algoritmens prestanda i brusfria och brusiga miljöer. Resultaten från experimenten var betydelsefulla. I brusfria tester presterar algoritmen effektivt och som förväntat. Men, med införandet av brus minskar algoritmens prestanda avsevärt. Sannolikheten för att algoritmen hittar ett markerat element liknar sannolikheten för att slumpmässigt välja ut samma element från databasen. Detta var fallet oavsett hur många element som var markerade och databasens storlek. Dessa oväntade resultat illustrerar brusets söndrande effekt på Grover’s algoritm. Begränsningar i studien inkluderar att bruset helt får algoritmen att sluta fungera, utmaningar med att noggrant modellera kvantbrus och användningen av relativt små databaser. Vidare forskning behövs för att undersöka strategier för att mitigera brus och bedöma algoritmens robusthet i storskaliga scenarier. Denna forskning stärker vår förståelse för brusets påverkan på Grover’s algoritm och betonar utmaningar och begränsningar vid dess implementering. Den betonar vikten av att hantera brus inom kvantdatorer för att kunna utnyttja deras potential för effektiv lösning av komplexa problem.

Previous work was successful at delineating reaction pathways for the photoactivated synthesis of an amine, [CztBu(PyriPr)(NH2−PyriPr)], by double intramolecular C−H activation and functionalization via irradiating a metal(II) azido complex, [CztBu(PyriPr)2NiN3. The present work seeks to expand upon earlier research, and to substitute the metal with iron or cobalt, and to expand the study to photocatalyzed intermolecular C−H activation and functionalization of organic substrates. Density functional theory (DFT) – B3LYP/6-31+G(d') and APFD/Def2TZVP – and time-dependent density functional theory (TDDFT) were used to propose a detailed pathway comprised of intermediates of low, intermediate, or high spin multiplicity and photo-generated excited states for the reaction of the azido complex, [CztBu(PyriPr)2MN3] to form the amine complex [CztBu(PyriPr)M(NH2−PyriPr)], M = Co, Ni or Fe, and the intermediates along the reaction pathway. For applications on quantum computing, the photophysical properties of photoactive d8 nickel(II) complexes are modeled. Such systems take advantage of a two-level system pathway between ground to excited state electronic transitions and could be useful for the discovery of successful candidates for a room temperature qubit, the analogue of a classical computational bit. A modified organometallic model, inspired by a nitrogen vacancy selective intersystem crossing model in diamond, was developed to take advantage of the formation of excited states. Tanabe-Sugano diagrams predict areas where these excited states may relax via phosphorescent emission. Under Zeeman splitting, these transitions create the conditions required for a two-level system needed to design a functional organometallic qubit.

Abstract Iris The power of quantum computing lies in its ability to perform certain calculations and solve complex problems exponentially faster than classical computers. This potential has profound implications for a wide range of fields, including particle physics. This thesis lays a fundamental foundation for understanding quantum computing. Particular emphasis is placed on the intricate process of quantum gate decomposition, an elementary lynchpin that underpins the development of quantum algorithms and plays a crucial role in this research. In particular, this concerns the implementation of quantum algorithms designed to simulate the dynamic evolution of multi-particle quantum systems - so-called Hamiltonian simulations. The concept of quantum gate decomposition is introduced and linked to quantum circuit optimisation. The decomposition of quantum gates plays a crucial role in fault-tolerant quantum computing in the sense that an optimal implementation of a quantum gate is essential to efficiently perform a quantum simulation, especially for near-term quantum computers. Part of this thesis aims to propose a new explicit tensorial notation of quantum computing. Two notations are commonly used in the literature. The first is the Dirac notation and the other standard formalism is based on the so-called computational basis. The main disadvantage of the latter is the exponential growth of vector and matrix dimensions and the fact that it hides some relevant quantum properties of the operations by increasing the apparent number of independent variables. A third possible notation is introduced here, which describes qubit states as tensors and quantum gates as multilinear or quasi-multilinear maps. Some advantages for the detection of separable and entangled systems and for measurement techniques are also shown. Finally, this thesis demonstrates the advantage of quantum computing in the description of multi-particle quantum systems by proposing a quantum algorithm to simulate collective neutrino oscillations. Collective flavour oscillations of neutrinos due to forward neutrino-neutrino scattering provide an intriguing many-body system for time evolution simulations on a quantum computer. These phenomena are of particular interest in extreme astrophysical settings such as core-collapse supernovae, neutron star mergers and the early universe. A detailed description of the physical phenomena and environments in which collective flavor oscillations occur is first reported, and the derivation of the Hamiltonian governing the evolution of flavor oscillations is detailed. The aim is to reproduce this evolution using a quantum algorithm. To manage the computational complexity, we use the Trotter approximation of the time evolution operator, which mitigates the exponential growth of circuit complexity. The quantum algorithm was designed to work on a trapped-ion based testbed (the theory of which is presented in detail). After machine-aware optimisation, the quantum circuit implementing the algorithm was run on the real quantum machine 'Quantinuum', and the results are presented and discussed.

Quantum information technologies include secure quantum communications and ultra precise quantum sensing that are significantly more efficient than their classical counterparts. To enable such technologies, we need a scalable quantum platform in which qubits are con trollable. Color centers provide controllable optically-active spin qubits within the coherence time limit. Moreover, the nearby nuclear spins have long coherence times suitable for quantum memories. In this thesis, I present a theoretical understanding of and control protocols for various color centers. Using group theory, I explore the wave functions and laser pumping-induced dynamics of VSi color centers in silicon carbide. I also provide dynamical decoupling-based high-fidelity control of nuclear spins around the color center. I also present a control technique that combines holonomic control and dynamically corrected control to tolerate simultaneous errors from various sources. The work described here includes a theoretical understanding and control techniques of color center spin qubits and nuclear spin quantum memories, as well as a new platform-independent control formalism towards robust qubit control. / Doctor of Philosophy / Quantum information technologies promise to offer efficient computations of certain algorithms and secure communications beyond the reach of their classical counterparts. To achieve such technologies, we must find a suitable quantum platform to manipulate the quantum information units (qubits). Color centers host spin qubits that can enable such technologies. However, it is challenging due to our incomplete understanding of their physical properties and, more importantly, the controllability and scalability of such spin qubits. In this thesis, I present a theoretical understanding of and control protocols for various color centers. By using group theory that describes the symmetry of color centers, I give a phenomenological model of spin qubit dynamics under optical control of VSi color centers in silicon carbide. I also provide an improved technique for controlling nuclear spin qubits with higher precision. Moreover, I propose a new qubit control technique that combines two methods - holonomic control and dynamical corrected control - to provide further robust qubit control in the presence of multiple noise sources. The works in this thesis provide knowledge of color center spin qubits and concrete control methods towards quantum information technologies with color center spin qubits.

This thesis provides also a detailed stepwise guideline on the data analysis for scanning X-ray diffraction experiments at a modern synchrotron radiation source. / Halbleiterbasierte Spin-Qubits in elektrostatischen Quantenpunkten haben vor Kurzem ein technologisches Niveau erreicht, welches lange Kohärenzzeiten und hohe Fidelitäten ermöglicht. Diese Eigenschaften sind wichtig, um eine große Anzahl von Qubits zu realisieren, welche durch adiabatische Ladungstransporte miteiander verbunden werden sollen. Allerdings können lokale Fluktuationen der Gitterverspannung im aktiven Material die Spinzustände stören, da sie das elektrostatische Potential beeinflussen. Diese Arbeit untersucht die Gitterverspannung in funktionalen Loch-Spin-Qubits und in Bauelementen für kohärenten Elektronentransport, welche auf epitaktischen Ge/Si0.20Ge0.80 und Si/Si0.66Ge0.34 Heterostrukturen mit metallischen Elektroden basieren. Die experimentelle Herausforderung besteht darin, zugleich eine hohe Sensitivität für die Gitterdeformation und eine räumliche Auflösung auf der Nanometerskala zu erreichen. Dies wird durch rasternde Röntgenbeugungsmikroskopie an der Strahllinie ID01/ESRF ermöglicht, welche eine Abbildung des Verspannungstensors mit einer lateralen Auflösung von ≤ 50 nm in bis zu 10 nm-dünnen epitaktischen Quantentöpfen ermöglicht. Die Untersuchung von vier verschiedenen Quantenbauteilen zeigt Modulationen der Gitterverspannung von 10−4 − 10−3 auf, welche durch die Elektroden und die plastische Entspannung der Heterostruktur verursacht sind. Diese Modulationen werden in räumliche Fluktuationen der Bandkantenniveaus von einer Größenordnung von mehreren meV übersetzt, die damit ähnlich zu den Abständen der orbitalen Energieniveaus der Quantenpunkte sind. Folglich stellt diese Arbeit wichtige Informationen für die Realisierung eines skalierbaren Quantenprozessors durch eine Berücksichtigung der lokalen Materialeigenschaften bereit / Semiconductor spin qubits featuring gate-defined electrostatic quantum dots have recently reached a maturity level enabling long spin coherence times and high fidelity. These characteristics are of paramount importance in the realization of large arrays of qubits interconnected by adiabatic charge shuttling. However, spin coherence can be strongly affected by local fluctuations of the lattice strain in the active material, since they impact the electrostatic potential. This work explores strain fluctuations in functional hole spin qubits and coherent electron shuttling devices based on epitaxial Ge/Si0.20Ge0.80 and Si/Si0.66Ge0.34 heterostructures with metallic electrodes. The main experimental challenge is to simultaneously achieve high sensitivity to the lattice deformation together with nanoscale spatial resolution. These requirements are met by Scanning X-ray Diffraction Microscopy at the synchotron beamline ID01/ESRF, which allows spatial mapping with ≤ 50 nm lateral resolution of the strain tensor in quantum well layers as thin as 10 nm. The analysis of four different devices highlights local modulations of the strain tensor components in the range of 10−4 − 10−3 induced by the gate electrodes and the plastic relaxation of the heterostructure. By means of band perturbation calculations, these strain fluctuations are translated into spatial modulations of the band edge energy levels. These perturbations are found to be of a few meV and thus on a similar magnitude as the orbital energy of the quantum dots. As such, this work provides important information for the realization of a scalable quantum processor with coherent interconnects by considering local material properties.

<p dir="ltr">Quantum information science and technology has been at the forefront of science and technology since MIT mathematician Peter Shor discovered a quantum algorithm to factor large numbers in 1994. Advancement in quantum theory also advances practical technological applications. Quantum technology can be applied both in civilian society and the military field from encryption, artificial intelligence, sensing, to communications. This multi-purpose applicability, therefore, has the potential to alter international security as scientifically advanced nation-states vie for quantum supremacy. This research examines the applications of quantum science and how these applications can potentially impact international security. Because nation-states fund and support quantum science research, sources of method will include academic journals and online resources as well as government reports. Practical applications of quantum technology, including quantum computing, quantum sensing, and quantum communication, will constitute the primary scope of this research.</p>

Quantum computing is a form of computation that exploits quantum mechanical phenomena for information processing, with promising applications (among others) in optimization and machine learning. Indeed, quantum machine learning is currently one of the most popular directions of research in quantum computing, offering solutions with an at-least-theoretical advantage compared to the classical counterparts. Nevertheless, the quantum devices available in the current Noisy Intermediate-Scale Quantum (NISQ) era are limited in the number of qubits and significantly affected by noise. An interesting alternative to the current prototypes of general-purpose quantum devices is represented by quantum annealers, specific-purpose quantum machines implementing the heuristic search for solving optimization problems known as quantum annealing. However, despite the higher number of qubits, the current quantum annealers are characterised by very sparse topologies. These practical issues have led to the development of hybrid classical-quantum schemes, aiming at leveraging the strengths of both paradigms while circumventing some of the limitations of the available devices. In this thesis, several hybrid classical-quantum algorithms for optimization and machine learning are introduced and/or empirically assessed, as the empirical evaluation is a fundamental part of algorithmic research. The quantum computing models taken into account are both quantum annealing and circuit-based universal quantum computing. The results obtained have shown the effectiveness of most of the proposed approaches.

Micro– and subsequently nano–scale fabrication techniques have reshaped our world more drastically than almost any other development of the last half-century. Spurred by the invention of the transistor at Bell Labs in 1947, monolithic integrated circuits—or microchips in the colloquial lexicon—were developed in ’59, kickstarting the modern digital age as we know it. More recently, the maturation of classical computing technology and significant advancements in materials science have led to a boom of interest in and progress by the quantum sector on both computation and communication fronts. The explosive growth currently underway in the field of quantum information science (QIS) marks the dawning of a new age, which will undoubtedly transform our world in ways we have yet to imagine. This dissertation seeks to leverage advanced nanofabrication approaches, atomically thin materials, and state of the art microscopy techniques to develop room-temperature single photon sources for QIS applications. A basic overview of 2D materials is provided in Chapter 1. Particular emphasis is placed on the optical properties of tungsten diselenide (WSe2), which is followed by a brief discussion of quantum emitters in 2D and other material systems. Chapter 2 describes the scanning near-field optical microscopy (SNOM) technique we use to investigate the photoluminescence (PL) response of strained WSe₂ with resolution well below the classical diffraction limit. The third chapter is dedicated to the various fabrication methods explored and developed to produce the plasmonic substrates necessary for near-field optical studies. The first section focuses on the creation of extremely flat metallic surfaces, while the second deals with extremely sharp metallic stressors. These two platforms enable the investigations of nanobubbles—touched upon in Chapter 2—and nanowrinkles, which are the subject of discussion in Chapter 4. The strain confinement provided by these wrinkles leads to highly localized quantum dot-like states that exhibit excitation power saturation at room temperature. Together, these studies lay the groundwork for achieving high-temperature quantum emission in atomically thin semiconducting van der Waals materials.

We explore the paradigm shift in quantum computing and quantum information science, emphasizing the synergy between hardware advancements and algorithm development. Only now have the recent advances in quantum computing hardware, despite a century of quantum mechanics, unveiled untapped potential, requiring innovative algorithms for full utilization. Project 1 addresses quantum applications in radiative reactions, overcoming challenges in many-fermion physics due to imaginary time evolution, stochastic methods like Monte Carlo simulations, and the associated sign problem. The methodology introduces the Electromagnetic Transition System and a general two-level system for computing radiative capture reactions. Project 2 utilizes Variational Quantum Eigensolver (VQE) to address the difficulties in adiabatic quantum computations, highlighting Singular Value Decomposition (SVD) in quantum computing. Results demonstrate an accurate ground state wavefunction match with only a 0.016% energy error. These projects advance quantum algorithm design, error mitigation, and SVD integration, showcasing quantum computing’s transformative potential in computational science.