Quantum computers have many desirable features but are physically challenging to build. They use quantum physics to solve practically motivated yet classically intractable problems, and because the experimental technology is still in its infancy, quantum mechanical devices are susceptible to errors that compromise data integrity. As a result, quantum error correction is necessary to protect important information from such undesirable influences, which inevitably increases the resource overhead to ensure a reliable quantum computation. In this thesis, we develop methods that are relevant to reducing the utilization of physical resources in a quantum computer. The core operations considered here are the so-called stabilizer operations, which have fault-tolerant constructions that are vital to achieving an error-resistant quantum computation. By applying our practices, we achieve small optimizations that have considerable value when implementing quantum algorithms in the near-term, when small quantum systems are much easier to manage than a single large quantum system. We cover two techniques to improve the efficiency of stabilizer operations applied to qubit states.

First, we introduce protocols that can probabilistically recreate an initial input qubit from the output qubit of specific quantum processes. These protocols are ideally suited for recovery purposes, and are designed with potentially many nested layers of stabilizer operations. We subsequently give a precise analysis on the effectiveness of the nested recovery. By integrating recovery at the optimal nesting depth, the resource usage of the relevant quantum processes can be reduced by up to half in expectation. Second, we define a new special arrangement of elementary stabilizer operations for realizing certain quantum computations, which we call a binary in-tree decomposition. We show that such implementations lead to a better process for lowering resource consumption. We then propose an efficient classical algorithm to assemble stabilizer operation sequences with such binary in-tree form. Finally, we demonstrate the merits of the binary in-tree structure on several examples.

Quantum computing seeks to use the powers of quantum mechanics to accomplish tasks that classical computers cannot easily accomplish. Adiabatic quantum computing is one flavor of quantum computing that slowly changes a system with time in such a way that the state remains close to the ground state for the entire evolution. An easy way to implement and study adiabatic computing is using stoquastic Hamiltonians with no-sign problem. These Hamiltonians can be readily simulated on classical computers using quantum Monte Carlo schemes; though, it is unknown whether such simulation captures the speed and power of the quantum computation.

In this work, I study stoquastic Hamiltonians, focusing on quantum mechanical tunneling through classically inaccessible regions and barriers. I study multi-qubit tunneling problems to determine what properties of the barrier make this problem quantum mechanically or classically hard or inefficient. I compare quantum adiabatic computing with a path-integral Quantum Monte Carlo algorithm, which is a classical algorithm designed to simulate the quantum mechanical dynamics of the adiabatic evolution. Limited numerical data shows strong correlation between adiabatic and Monte Carlo runtimes, but due to computational limits, only small system sizes could be sampled.

Additionally, I study the properties of the quantum adiabatic algorithm in both the asymptotic limit of a large number of qubits and long runtimes and more realistic finite system sizes and non-adiabatic conditions. I develop a modification of the existing Villain transformation that allows it to find the asymptotic running time of the quantum evolution for different barrier sizes. Furthermore, I compare this to finite system sizes and discover the extremely large numbers of qubits are needed for these asymptotics to be useful.

When the quantum dynamics are run faster than adiabatically, new behavior arises that could potentially lead to enhancements in the quantum runtimes. I explore these enhancements, discovering when they do and do not occur. I also develop a broad framework for determining the nature of the near-adiabatic behavior of any quantum evolution, using only information about the energy gap between the ground state and the first excited state.

Accurately representing the sources of important precursor gases for new particle formation and their chemical reactions in the atmosphere are critical for developing a robust understanding of the impacts of ultrafine particles on climate and health. Many types of compounds contribute to these nucleation and growth processes, including inorganic acids, bases and low-volatility organic compounds. Both formation of these compounds in the atmosphere and the processes by which they are converted to ultrafine particles depend greatly on their composition. Therefore, in this dissertation, these sources and processes were investigated using measurements of chemical composition, specifically chemical ionization mass spectrometry (CIMS). CIMS was used to measure important precursor gases for ultrafine particle formation and growth in controlled laboratory chamber studies for three separate chemical systems.

In Chapter 2, the chemical composition of gasses emitted from vehicle brake wear were measured using both nitrate reagent ion (nitrate-CIMS) and iodide reagent ion (iodide-CIMS). Gases, coarse-mode particles and ultrafine particles were generated from a home-built brake dynamometer system, which simulated moderate and heavy braking conditions. The brake pad formulation (ceramic vs semi-metallic), degree of wear (new, gently worn, heavily worn), and temperature of the brake rotor influenced measured gaseous emissions. A critical temperature range was observed for ultrafine particle formation. These critical temperatures were found to be lower for ceramic brake pads (100-140 C) than semi-metallic brake pads (140-200 C), and increase as the brake pads became worn. High concentrations of sulfuric acid and sulfur trioxide were generated during heavy braking conditions at high temperatures, and were more abundantly emitted by the semi-metallic pads than the ceramic. Moderate braking conditions produced NOx, CO, inorganic nitrogen compounds HONO, N2O5, oxidized organics and organic acids. Emissions from different brake pad formulations and degrees of wear were highly variable, emphasizing the importance of representing brake-wear emissions over the lifetime of a brake pad for future control strategies.

In Chapter 3, the effects of monoterpene structure on nitrate radical-induced oxidation mechanism of four monoterpenes (a-pinene, b-pinene, d-carene, a-thujene) was investigated by conducting laboratory chamber experiments. Oxidized reaction products were measured with nitrate-CIMS. The major gas-phase species produced in each system were distinctly different, showing the effect of monoterpene structure on the oxidation mechanism and further elucidated the contributions of these species to particle formation and growth. Measured effective O:C ratio of reaction products were anti-correlated to new particle formation intensity and number concentration for each system; however, monomer:dimer ratio of products had a small positive trend. Gas phase yields of oxidation products correlated with particle number concentrations for each monoterpene system, with the exception of a-thujene, which produced a considerable amount of low volatility products but no particles. The lack of measurable new particle formation in spite of the presence of these dimers indicates a more complex relationship between highly oxidized organic compounds and new particle formation.

In Chapter 4, the formation of low-volatility gasses and new particle formation from ozonolysis of a-thujene was observed in laboratory chamber studies. This system was found to produce lower yields of particles at all mass loadings compared to s-pinene ozonolysis systems. The unique structure of a-thujene led to the competitive production of semi-volatile fragment compounds that reduced the overall volatility of the oxidized products. Theoretical growth rates (on the order of nm per min) calculated from volatility-parameterized organics underpredicted measured growth rates. However, the simple condensational growth model that was used did not account for the irreversible partitioning of semi-volatile organics, which were abundantly produced by this system.

There exist numerous proofs of Bell's theorem, stating that quantum mechanics is incompatible with local realistic theories of nature. Here the strength of such nonlocality proofs is defined in terms of the amount of evidence against local realism provided by the corresponding experiments. Statistical considerations show that the amount of evidence should be measured by the Kull-back-Leibler (KL) or relative entropy divergence. The statistical strength of the following proofs is determined: Bell's original proof and Peres' optimized variant of it, and proofs by Clauser, Horne, Shimony, and Holt (CHSH), Hardy, Mermin, and Greenberger, Horne, and Zeilinger (GHZ). The GHZ proof. is at least four and a half times stronger than all other proofs, while of the two-party proofs, the one of CHSH is the strongest.

The increasing number of positron-emission tomography (PET) tracers being developed to aid drug development and create new diagnostics has led to an increased need for radiosynthesis development and optimization. Current automated radiosynthesizers are designed for production of large clinical batches of radiopharmaceuticals. They are not well suited for reaction optimization or novel radiopharmaceutical development, since each data point involves significant reagent consumption, and contamination of the apparatus requires time for radioactive decay before the next use. Though with some radiosynthesizers it is possible to perform a few sequential radiosyntheses in a day, none allow for parallel radiosyntheses. To address these limitations, I developed a new platform for high-throughput experimentation in radiochemistry. This system contains an array of 4 heaters, each used to heat a chip containing an array of 16 reaction sites (hydrophilic patches) on a small Teflon-coated silicon chip, enabling 64 parallel reactions for the rapid optimization of conditions in any stage of a multi-step radiosynthesis process. As example applications, I studied the syntheses of several 18F-labeled radiopharmaceuticals, performing >800 experiments to explore the influence of parameters including base type, base amount, precursor amount, solvent, reaction temperature, and reaction time. The experiments were carried out within only 15 experiment days, and the small volume (~10 μL compared to the ~1 mL scale of conventional instruments) consumed ~100x less precursor per datapoint. This new method paves the way for more comprehensive optimization studies in radiochemistry and substantially shortening PET tracer development timelines. I also developed new methods and technologies to determine the reaction conversion when optimizing radiosynthesis processes. Radio-thin layer chromatography (radio-TLC) is commonly used to analyze purity of radiopharmaceuticals or to determine the reaction conversion. In applications where there are only a few radioactive species, radio-TLC is preferred over radio-high-performance liquid chromatography (radio-HPLC) due to its simplicity and relatively quick analysis time. However, with current radio-TLC methods, it remains cumbersome to analyze a large number of samples during reaction optimization. In a couple of studies, Cerenkov luminescence imaging (CLI) has been used for high-resolution reading TLC plates spotted with a variety of isotopes. We show that this approach can be extended to develop a high-throughput approach for radio-TLC analysis of many samples by spotting multiple samples in adjacent lanes and then separating and reading out all lanes in parallel. Finally, I worked on techniques to incorporate [19F]fluoride and [18F]fluoride into thioether molecules via electrochemical fluorination. Electrochemical fluorination and radiofluorination was performed under potentiostatic anodic oxidation using various types of electrochemical cells. I incorporated the concept of high throughput experimentation via microfluidics by using 96-ELISA-well plates with printed electrodes for the fast screening of parameters in electrochemistry for the radiofluorination of various thioether molecules, studying variables such as solvents, temperatures and electrolytes for the optimization of electrochemical labeling conditions. The use of high-throughput experimentation in radiochemistry can allow the exploration of various parameters in a fast manner and its combination with microfluidics makes the performance of various experimental parameters possible due to the minimal use of reagents. Both radiochemistry in droplets and electrochemistry for fluoride labeling in well plates showed the screening and optimization of synthesis parameters that could not be possible with conventional methods, moreover the methods presented in this dissertation can help with the exploration of novel PET tracers for preclinical research that otherwise would be expensive at macroscale.

Radiopharmaceuticals labeled with short-lived positron-emitting or gamma-emitting isotopes are injected into patients just prior to performing a positron emission tomography (PET) or single photon emission computed tomography (SPECT) scan. These imaging modalities are widely used in clinical care, as well as in the development and evaluation of new therapies via clinical trials. Unlike ordinary pharmaceuticals, the short lifetime of radiopharmaceuticals requires that they be produced in relatively small batches close to the geographical location where the patient is scanned.

Since PET tracers are classified as drugs by regulatory agencies, they must pass stringent quality control (QC) tests after their production to ensure patient safety prior to injection. Performing and documenting these tests is cumbersome and time-consuming, and requires an array of expensive analytical chemistry equipment and significant dedicated lab space, and there is considerable interest in the development of automated and lower-cost approaches.

By replacing conventional techniques with lab-on-a-chip technologies, it may be possible to achieve further reductions in the size, cost, and complexity of automated QC testing platforms. While some advances have been made for some of the many QC tests, high-resolution miniaturized methods suitable for assessment of chemical or radiochemical identity and purity are notably missing. We have been exploring microchip capillary electrophoresis (MCE) as a potential means to fill this gap. We have shown the potential to perform chemical identity and purity analysis by successful separation of the PET tracer [18F]FLT from all of its side products, with comparable limit of detection as HPLC. More recently, we demonstrated first-in-field work to add radiation detection to the MCE system, using a high-resolution positron detector to perform the radiochemical identity analysis of PET tracers.

Microfluidic systems are also useful for the synthesis of radiopharmaceuticals such as radiolabeled peptides and antibody fragments, which provide a means to image disease-specific targets with extremely high specificity. To substantially reduce the high cost of radiolabeling, we have explored the feasibility of using a microdroplet reactor approach. As an example, a thiol-containing RGD peptide was labeled with fluorine-18 in a site-specific manner via the maleimide-based prosthetic group, [18F]FBEM on a microfluidic chip. We have also explored the site-specific radiofluorination of engineered antibody fragments (diabody) for ImmunoPET imaging via this microfluidic approach.

These studies, and other work on small-molecule synthesis, have shown that there are advantages in performing radiochemistry in microdroplets. Active means of manipulating microdroplets, such as electrowetting-on-dielectric (EWOD) provides more flexibility of reaction implementation than passive methods, but EWOD devices are well known to suffer from a charging effect and the dielectric and hydrophobic layers have been found to suffer defects during harsh chemical reactions. Therefore, a novel droplet actuation mechanism, electro-dewetting, has been developed to address these challenges. Electro-dewetting uses an electric field formed inside a droplet to manipulate the adsorption of ionic surfactant molecules on the solid surface to change the contact angle. The underlying mechanism of this pheromone has been elucidated.

We believe that all the work described here shows the potential for dramatic miniaturization of the complete PET tracer production process, and ultimately increasing the availability of diverse PET tracers for research use, further development, and clinical translation via lowering the cost and complexity of tracer production.