<p> Randomized benchmarking is an experimental procedure intended to demonstrate control of quantum systems. The procedure extracts the average error introduced by a set of control operations. When the target set of operations is intended to be the set of Clifford operators, the randomized benchmarking algorithm is particularly easy to perform and its results have an important interpretation with respect to quantum computation. The aim of the benchmark is to provide a simple, useful parameter describing the quality of quantum control with an experiment that can be performed in a standard way on any prospective quantum computer. This parameter can be used to fairly compare different experiments or to mark improvement in a single experiment. </p><p> In this thesis I discuss first the original randomized-benchmarking procedure and the importance of the Clifford operators for its implementation. I develop the statistical analysis of the results and the physical assumptions that are required for the simplest analysis to apply. The original procedure does not extend in an obvious way to benchmarking of more than one qubit, so I introduce a standardized procedure for randomized benchmarking that applies to any number of qubits. This new procedure also enables the benchmarking of an individual control operation. I describe two randomized-benchmarking experiments I helped to design: one involved a single qubit and utilized a variation of the original procedure and the second involved two qubits and demonstrated the new procedure. I conclude with several potential extensions to the original and new procedures that give them reduced experimental overhead, the ability to describe encoded operations, and fairer comparisons between experiments.</p>

<p> Quantum Monte Carlo techniques stochastically evaluate integrals to solve the many-body Schr&ouml;dinger equation. QMC algorithms scale favorably in the number of particles simulated and enjoy applicability to a wide range of quantum systems. Advances in the core algorithms of the method and their implementations paired with the steady development of computational assets have carried the applicability of QMC beyond analytically treatable systems, such as the Homogeneous Electron Gas, and have extended QMC&rsquo;s domain to treat atoms, molecules, and solids containing as many as several hundred electrons.</p><p> FN-DMC projects out the ground state of a wave function subject to constraints imposed by our ansatz to the problem. The constraints imposed by the fixed-node Approximation are poorly understood. One key step in developing any scientific theory or method is to qualify where the theory is inaccurate and to quantify how erroneous it is under these circumstances.</p><p> I investigate the fixed-node errors as they evolve over changing charge density, system size, and effective core potentials. I begin by studying a simple system for which the nodes of the trial wave function can be solved almost exactly. By comparing two trial wave functions, a single determinant wave function flawed in a known way and a nearly exact wave function, I show that the fixed-node error increases when the charge density is increased. Next, I investigate a sequence of Lithium systems increasing in size from a single atom, to small molecules, up to the bulk metal form. Over these systems, FN-DMC calculations consistently recover 95% or more of the correlation energy of the system. Given this accuracy, I make a prediction for the binding energy of Li₄ molecule. Last, I turn to analyzing the fixed-node error in first and second row atoms and their molecules. With the appropriate pseudo-potentials, these systems are iso-electronic, show similar geometries and states. One would expect with identical number of particles involved in the calculation, errors in the respective total energies of the two iso-electronic species would be quite similar. I observe, instead, that the first row atoms and their molecules have errors larger by twice or more in size. I identify a cause for this difference in iso-electronic species. The fixed-node errors in all of these cases are calculated by careful comparison to experimental results, showing that FN-DMC to be a robust tool for understanding quantum systems and also a method for new investigations into the nature of many-body effects.</p>

<p> Laser cooling and trapping are central to modern atomic physics. It has been roughly three decades since laser cooling techniques produced ultracold atoms, leading to rapid advances in a vast array of fields and a number of Nobel prizes. Prior to the work presented in this thesis, laser cooling had not yet been extended to molecules because of their complex internal structure. However, this complexity makes molecules potentially useful for a wide range of applications. The first direct laser cooling of a molecule and further results we present here provide a new route to ultracold temperatures for molecules. In particular, these methods bridge the gap between ultracold temperatures and the approximately 1 kelvin temperatures attainable with directly cooled molecules (e.g. with cryogenic buffer gas cooling or decelerated supersonic beams). Using the carefully chosen molecule strontium monofluoride (SrF), decays to unwanted vibrational states are suppressed. Driving a transition with rotational quantum number <i>R</i>=1 to an excited state with <i> R'</i>=0 eliminates decays to unwanted rotational states. The dark ground-state Zeeman sublevels present in this specific scheme are remixed via a static magnetic field. Using three lasers for this scheme, a given molecule should undergo an average of approximately 100,000 photon absorption/emission cycles before being lost via unwanted decays. This number of cycles should be sufficient to load a magneto-optical trap (MOT) of molecules. In this thesis, we demonstrate transverse cooling of an SrF beam, in both Doppler and a Sisyphus-type cooling regimes. We also realize longitudinal slowing of an SrF beam. Finally, we detail current progress towards trapping SrF in a MOT. Ultimately, this technique should enable the production of large samples of molecules at ultracold temperatures for molecules chemically distinct from competing methods.</p>

<p> Superconducting qubits and resonators with quality factors exceeding 10⁷ are of great interest for quantum information processing applications. The improvement of present devices necessarily involves the consideration of participation ratios, which budget the influence of each physical component in the total energy decay rate. Experiments on compact resonators in which participation ratios were varied has demonstrated the validity of this method, yielding a two-fold improvement in quality factor. Similar experiments on compact transmon qubit devices led to a three-fold improvement over previous transmons, validating the method of participation ratios for qubits as well. Through the use of a 3D cavity, a further minimization of the participation of surface components combined with the removal of unnecessary components, produced an additional ten-fold increase in coherence times. Finally, the fluxonium qubit was redesigned in a similar minimalist environment with an improved superinductance, thus combining the advantages of the 3D architecture with the natural insensitivity to dissipation of the fluxonium, resulting in <i>another</i> tenfold increase in relaxation times. This large increase in relaxation and coherence times enables experiments that were previously impossible, thus preparing the field of quantum information to advance on other fronts.</p>

<p>Beauty quarks are pair-produced by strong interactions in multi-TeV proton-proton (pp) collisions at the CERN Large Hadron Collider (LHC). Such interactions allow for a test of perturbative Quantum Chromodynamics (QCD) in a new energy regime. The primary beauty-antibeauty quark b<span style="text-decoration:overline"> b</span> pair production mechanisms in perturbative QCD are referred to as flavor creation, flavor excitation, and gluon splitting. These three mechanisms produce b<span style="text-decoration:overline">b</span> pairs with characteristic kinematic behavior, which contribute differently to the shape of the differential b<span style="text-decoration:overline"> b</span> production cross section with respect to the difference in the azimuthal angle &Delta;&phis; and the combined separation variable &Delta;<i> R</i> = [special characters omitted] between the beauty and antibeauty quarks (b and <span style="text-decoration:overline">b</span>, respectively); with &Delta;&eta; being the change in the pseudorapidity &eta; = &mdash; ln (<i>tan</i> (&thetas;/2)), &thetas; being the polar angle. These &Delta;&phis; and &Delta;^R variables are collectively referred to as angular correlation variables and hence forth referred to as &Delta;<i> A</i>. By measuring the shape and absolute normalization of the differential production cross section distributions with respect to &Delta;<i>A</i> a test of the predictions of perturbative QCD can be performed. </p><p> This dissertation describes a measurement of the differential production cross sections with respect to the &Delta;<i>A</i> between two hadronic jets arising from the hadronization and decay of b or <span style="text-decoration:overline">b</span> (referred to as <i>b</i> hence forth) produced in pp collisions at the LHC observed with the Compact Muon Solenoid (CMS) detector. Hadronic jets are identified as originating from b quarks, i.e. b-tagged, based on the presence of high impact parameter tracks with respect to the primary pp interaction point in events in which a muon is also produced. The study presented in this dissertation corresponds to an integrated luminosity of 3 pb^-1 collected in 2010 by the CMS experiment at a center-of-mass energy of 7 TeV. </p><p> The visible kinematic phase-space of the differential production cross sections probed in this study is given by the requirement of two b-tagged hadronic jets with [special characters omitted] > 30 GeV and &par;&eta;^jet&par; &lt; 2.4, with an angular separation of &Delta;R > 0.6 between them, one of these jets has a muon within its constituents with [special characters omitted] > 8 GeV and &par;&eta;^&mu;&par; &lt; 2.1. The results obtained in data are compared with predictions based on perturbative QCD calculations given by CASCADE, MADGRAPH/MADEVENT, and PYTHIA Monte Carlo event generators. The predictions of perturbative QCD are found to be in agreement the measured differential cross sections within uncertainties. </p>