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Articles on this Page
- 12/31/15--16:00: _A precision measure...
- 12/31/15--16:00: _Squeezed states for...
- 12/31/15--16:00: _A precision measure...
- 12/31/92--16:00: _Threshold electrodi...
- 12/31/15--16:00: _Fluid dynamics in a...
- 12/31/16--16:00: _Quantum gas microsc...
- 12/31/16--16:00: _Probing local group...
- 12/31/16--16:00: _Characterization of...
- 12/31/16--16:00: _Electroweak physics...
- 12/31/16--16:00: _Photonics for techn...
- 12/31/66--16:00: _Observations of sev...
- 12/31/55--16:00: _Pion production in ...
- 12/31/40--16:00: _Forced oscillations...
- 12/31/77--16:00: _Study of the electr...
- 12/31/16--16:00: _A spatially resolve...
- 12/31/16--16:00: _Detectability of dy...
- 12/31/16--16:00: _Quantum signal proc...
- 12/31/16--16:00: _Top mass determinat...
- 12/31/16--16:00: _Strongly interactin...
- 12/31/17--16:00: _Practical fault-tol...
- 12/31/15--16:00: Squeezed states for advanced gravitational wave detectors
- 12/31/15--16:00: Fluid dynamics in action
- 12/31/16--16:00: Quantum gas microscopy of strongly correlated fermions
- 12/31/40--16:00: Forced oscillations of electromagnetic cavity resonators
- 12/31/16--16:00: Quantum signal processing by single-qubit dynamics
- 12/31/16--16:00: Top mass determination using Effective Field Theories
- 12/31/16--16:00: Strongly interacting photons via Rydberg-Rydberg interactions
- 12/31/17--16:00: Practical fault-tolerant quantum computation
A precision measurement of the cosmic ray positron fraction on the International Space Station
Krafczyk, Matthew Scott
AMS-02 is a precision particle physics experiment in space aiming to study dark matter, antimatter, and properties of cosmic rays to the TeV energy scale. This thesis presents a study of the cosmic ray positron fraction in AMS-02 data covering an energy range of 0.5 GeV to 500 GeV, and identifies 10.3 x 106 electron and 650 x 101 positron events. The results show that the positron fraction increases with energy and reaches a maximum at 275 ± 32 GeV.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2016.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 118-128).
Squeezed states for advanced gravitational wave detectors
Oelker, Eric Glenn
Quantum vacuum fluctuations impose strict limits on precision displacement measurements, those of interferometric gravitational-wave detectors among them. Introducing squeezed states into an interferometer's readout port can improve the sensitivity of the instrument, leading to richer astrophysical observations. In recent years, this technique has been used to improve the sensitivity of the GEO600 [1011 and the Initial LIGO detector at Hanford, WA . Squeezed states could be employed in advanced gravitational-wave detectors, such as Advanced LIGO, to further push the limits of the observable gravitational wave universe. To maximize the benefit from squeezing, environmentally induced disturbances such as back scattering and angular jitter need to be mitigated. Also, optomechanical interactions dictate that the quadrature of the squeezed vacuum state must rotate by 900 at around 50 Hz in order to achieve a broadband sensitivity improvement for Advanced LIGO. In this thesis we describe a series of experiments that lead to a ultra-high vacuum (UHV) compatible, low phase noise, and frequency-dependent squeezed vacuum source required for Advanced LIGO and future gravitational-wave detectors. In order to develop the required technology, two proof-of-principal experiments were conducted. In the first experiment, we built a UHV compatible squeezed vacuum source and homodyne readout and operated them in UHV conditions. We also commissioned a control scheme that achieved a record low 1.30-7 mrad of phase noise. This is a nearly tenfold improvement over previously reported measurements with audio-band squeezed vacuum sources. In the second experiment we used a 2-m-long, high-finesse optical resonator to produce frequency-dependent squeezed quadrature rotation around 1.2kHz. This demonstration of audio-band frequency-dependent squeezing uses technology and methods that are scalable to the required rotation frequency for Advance LIGO, firmly establishing the viability of this technique for application in current and future gravitational-wave detectors. We conclude with a discussion of the implications of these results for squeezing enhancement in Advanced LIGO and beyond.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2016.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 219-229).
A precision measurement of the e⁺p/e⁻p elastic scattering cross section ratio at the OLYMPUS experiment
Henderson, Brian Scott
Measurements of the ratio of the proton elastic form factors ([mu]pGe/Gm) using Rosenbluth separation and those using polarization-based techniques show a strong discrepancy, which has persisted both in modern experimental results and in re-analyses of previous data. The most widely accepted hypothesis to explain this discrepancy is the treatment of the contributions from hard two-photon exchange (TPE) to elastic electron-proton scattering in the radiative corrections applied to the Rosenbluth separation measurements. Calculations of the hard TPE contribution are highly model dependent, but the effect may be measured experimentally with a precise determination of the ratio of the positron-proton and electron-proton elastic scattering cross sections. The OLYMPUS experiment collected approximately 4 fb-1 of e+p and e-p scattering data at the DORIS storage ring at DESY in 2012, with the goal of measuring the elastic [sigma]e+p/[sigma]e-p ratio over the kinematic range (0.4
Threshold electrodisintegration of the deuteron at high momentum transfer
Schmitt, William Michael, 1965-
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1993.; Includes bibliographical references (p. 201-206).
Fluid dynamics in action
In this thesis we formulate an effective field theory for nonlinear dissipative fluid dynamics. The formalism incorporates an action principle for the classical equations of motion as well as a systematic approach to thermal and quantum fluctuations around the classical motion of fluids. The dynamical degrees of freedom are Stuckelberg-like fields associated with diffeomorphisms and gauge transformations, and are related to the conservation of the stress tensor and a U(1) current if the fluid possesses a charge. This inherently geometric construction gives rise to an emergent "fluid space-time", similar to the Lagrangian description of fluids. We develop the variational formulation based on symmetry principles defined on such fluid space-time. Through a prescribed correspondence, the dynamical fields are mapped to the standard fluid variables, such as temperature, chemical potential and velocity. This allows to recover the standard equations of fluid dynamics in the limit where fluctuations are negligible. Demanding the action to be invariant under a discrete transformation, which we call local KMS, guarantees that the correlators of the stress tensor and the current satisfy the fluctuation-dissipation theorem. Local KMS invariance also automatically ensures that the constitutive relations of the conserved quantities satisfy the standard constraints implied e.g. by the second law of thermodynamics, and leads to a new set of constraints which we call generalized Onsager relations. Requiring the above properties to hold beyond tree-level leads to introducing fermionic partners of the original degrees of freedom, and to an emergent supersymmetry. We also outline a procedure for obtaining the effective field theory for fluid dynamics by applying the holographic Wilsonian renormalization group to systems with a gravity dual.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2016.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 207-213).
Quantum gas microscopy of strongly correlated fermions
Cheuk, Lawrence W
This thesis describes experiments on ultracold fermionic atoms, and can be divided into two areas. The first concerns spin-orbit coupling; the second concerns quantum gas microscopy. With the use of Raman transitions, ID spin-orbit coupling of ultracold 6Li was realized. Using a novel type of spectroscopy, spin-injection spectroscopy, where the spin, energy, and momentum are all resolved, we directly observed the spinful dispersions of the spin-orbit bands. In addition, we demonstrated selective adiabatic loading of the spin-orbit bands, which can be used to create a spinless Fermi gas with effective p-wave interactions. Spin-injection spectroscopy was further applied to a novel spinful lattice system created using Raman and radio-frequency coupling, which allowed for state tomography of spinful bands. The second part of this thesis describes quantum gas microscopy of ultracold fermions. This enables one to simulate the Fermi-Hubbard model, a prototypical strongly correlated model, with site-resolved detectioi and control capablities. A new apparatus that can detect fermionic 40K in a square lattice with single-site resolution was constructed. High-fidelity site-resolved imaging was achieved using Raman imaging, which allowed for the direct observation of the band-insulating, the metallic, and the Mott-insulating states of the Hubbard model. The interactiondriven Mott insulator, where doubly occupied sites are highly suppressed, illustrates the strongly correlated nature of the Hubbard model. Harnessing the capability to measure the occupations of individual lattice sites with the microscope, we explored spatial correlations of both spin and charge in the Hubbard model as a function of doping. For the spin correlations, we observed weakening of antiferromagnetic correlations away from half-filling. However, in the charge correlations between local magnetic moments, non-monotonic behavior was observed. This can be understood as arising from competition between Pauli-blocking, dominant at low fillings, and doublon-holon bunching, which arises from superexchange and is strongest at half-filling. The anti-bunching correlations at low filling can be interpreted as the first direct real-space observation of the interaction-enhanced Pauli hole.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 239-251).
Probing local group galactic substructure with cosmological simulations
Dooley, Gregory (Gregory Alan)
The Lambda cold dark matter (ACDM) model is enormously successful at predicting large scale structure in the Universe. However, some tensions still remain on small scales, specifically regarding observed satellites of the Milky Way (MW) and Andromeda. Foremost among the problems have been the missing satellite, too big to fail, and cusp/core problems, which concern the expected abundance of satellites and their inner structure. This Ph.D. thesis consists of a series of studies using dark matter only cosmological N-body simulations of MW-mass galaxies to address topics related to these issues. In light of the recent Planck mission, I investigate how changes to cosmological parameters affect dark matter halo substructure. I find that the process of continuous sub-halo accretion and destruction leads to a steady state description of most subhalo properties in a given host, unchanged by small fluctuations in cosmological parameters. Subhalo concentration, maximum circular velocity, and formation times, however, are somewhat affected. One way to reduce the central density of satellites, as needed to solve the cusp/core and too big to fail problems, is through self-interacting dark matter (SIDM). I search for new implications of SIDM and find that stars in satellites spread out to larger radii and are tidally stripped at a higher rate in SIDM than CDM, even though the mass loss rate of dark matter is unchanged. These signatures should be particularly prominent in ultrafaint dwarf galaxies for the class of otherwise difficult to constrain velocity-dependent SIDM models. I also helped carry out the Caterpillar project, a suite of 36 high mass resolution (~ 10' Mo/particle) simulations of MW-like galaxies used to study diversity in halo substructure. To these, I apply abundance matching and reionization models to make novel predictions about the abundance of satellites in isolated dwarf galaxies out to 8 Mpc to help guide future searches. Applying the same techniques to predict satellites within 50 kpc of the LMC, I discover large discrepancies with the observed stellar mass function, which may lead to new constraints on the galaxy stellar mass-halo mass relationship, and the ability of reionization to leave dark matter halos entirely dark.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 315-358).
Characterization of jets in heavy ion collisions using photons at the LHC with the CMS detector
Barbieri, Richard Alexander
Using the CMS detector at the LHC, a quantitative study of jet energy loss and angular deflection inside the high energy-density medium formed in PbPb collisions is made. Photons are used to measure the initial state of a color-charged probe while jet reconstruction is used to measure the final state. Significant loss of energy to the medium as a function of initial parton momentum is observed, while no significant angular deflection is found.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 135-138).
Electroweak physics and evidence for a Higgs boson decaying to a pair of tau leptons with the CMS detector
.Studies of the electroweak interactions using final states with leptons in proton-proton collisions at the Large Hadron Collider at [square root of] s = 7 TeV, [square root of] s = 8 TeV, and [square root of] s = 13 TeV center-of-mass energies are described. Measurements of total inclusive and fiducial W and Z boson production cross sections and their ratios are performed. The W and Z bosons are observed via their decays to electrons and muons. An indirect determination of the total width of the W boson and the B(W --> lv) from the measured cross section ratios is described. The discovery of a new boson with a mass of 125 GeV at the Large Hadron Collider in 2012 sheds a new light on understanding the nature of electroweak symmetry breaking. A question of great significance is whether the new field couples to fermions through a Yukawa coupling interaction predicted in the standard model of particles. Evidence of the 125 GeV Higgs boson decay to a pair of tau leptons with an observed significance of 3.1 standard deviations is established. The nature of the Higgs sector is probed through searches for neutral resonances decaying to a pair of tau leptons in gluon-fusion and b-quark associated production modes with no observation of a significant excess. In addition, the feasibility of measuring the standard model Higgs boson self-coupling with an expected data sample corresponding to an integrated luminosity of 3000 fb-1 is studied.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 157-170).
Photonics for technology : circuits, chip-scale LIDAR, and optical neural networks
Skirlo, Scott Alexander
This thesis focuses on a wide range of contemporary topics in modern electromagnetics and technology including topologically protected one-way modes, integrated photonic LIDAR, and optical neural networks. First, we numerically investigate large Chern numbers in photonic crystals and explore their origin from simultaneously gapping multiple band degeneracies. Following this, we perform microwave transmission measurements in the bulk and at the edge of ferrimagnetic photonic crystals. Bandgaps with large Chern numbers of 2, 3, and 4 are present in the experimental results 'which show excellent agreement with theory. We measure the mode profiles and Fourier transform them to produce dispersion relations of the edge modes, whose number and direction match our Chern number calculations. We use these waveguides to realize reflectionless power splitters and outline their application to general one-way circuits. Next we create a new chip-scale LIDAR architecture in analogy to planar RF lenses. Instead of relying upon many continuously tuned thermal phase shifters to implement nonmechanical beam steering, we use aplanatic lenses excited in their focal plane feeding ID gratings to generate discrete beams. We design devices which support up to 128 resolvable points in-plane and 80 resolvable points out-of-plane, which are currently being fabricated and tested. These devices have many advantages over conventional optical phased arrays including greatly increased optical output power and decreased electrical power for in-plane beamforming. Finally we explore a new approach for implementing convolutional neural networks through an integrated photonics circuit consisting of Mach-Zehnder Interferometers, optical delay lines, and optical nonlinearity units. This new platform, should be able to perform the order of a thousand inferences per second, at [mu]J power levels per inference, with the nearest state of the art ASIC and GPU competitors operating 30 times slower and requiring three orders of magnitude more power.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 163-175).
Observations of several discrete radio sources at 3.64 and 1.94 centimeters
Allen, Ronald J
Massachusetts Institute of Technology. Dept. of Physics. Thesis. 1967. Ph.D.; Bibliography: leaves 156-160.
Pion production in pion-nucleon collisions in the Chew-Low-Wick formalism
Rodberg, Leonard Sidney
Thesis (Ph.D.) Massachusetts Institute of Technology. Dept. of Physics, 1956.; Vita.; Bibliography: leaves 105-107.
Forced oscillations of electromagnetic cavity resonators
Clogston, Albert McCavour
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1941.; Vita.
Study of the electron component of the solar wind and magnetospheric plasma
Sittler, Edward Charles
Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Physics.; MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE.; Vita.; Includes bibliographical references.
A spatially resolved study of the KATRIN main spectrometer using a novel fast multipole method
Barrett, John Patrick, Ph. D. Massachusetts Institute of Technology
The Karlsruhe Tritium Neutrino (KATRIN) experiment is intended to make a sensitive (~ 200 meV) model-independent measurement of the neutrino mass through high precision electrostatic spectroscopy of the tritium /-decay spectrum. One of the principle components in this experiment is the main spectrometer which serves as an integrating MAC-E filter with 0(1) eV resolution. Thorough understanding of the transmission properties of the main spectrometer system is an inextricable challenge associated with this effort, and requires a very accurate and fast method for calculating the electrostatic fields created within its volume. To this end, the work described in this thesis documents the development of a novel variation on the Fast Multipole Method (FNM), which is a hybrid of the canonical algorithm and the Fast Fourier Transform on Multipoles (FFTM) method. This hybrid technique has been implemented to take advantage of scalable parallel computing resources and has been used to solve the Laplace boundary value problem using the Boundary Element Method with millions of degrees of freedom. Detailed measurements taken during the KATRIN main spectrometer commissioning phase are used to validate the fully three-dimensional electrostatic field calculation and the hybrid fast multipole method. Then, the hybrid method is used to greatly accelerate charged particle tracking in a high-statistics Monte Carlo simulation. The data from this simulation is then used to develop a spatially resolved model of the main spectrometer transmission function. This full transmission function model is then used to evaluate the performance of several of approximate transmission function models, the results of which show that a purely axially symmetric treatment of the main spectrometer is not sufficient. We conclude by addressing the appropriate level of measurement detail needed in order to reconstruct a realistic, non-axially symmetric transmission function model.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 333-350).
Detectability of dynamical tidal effects and the detection of gravitational-wave transients with LIGO
Essick, Reed Clasey
Dynamical tidal effects impact the orbital motion of extended bodies, imprinting themselves in several measurable ways. This thesis explores the saturation of weakly nonlinear dynamical tidal interactions within two very different systems: hot Jupiters orbiting main-sequence hosts with radiative cores and compact stellar remnants inspiraling due to gravitational radiation. In addition, it discusses general aspects of detecting Gravitational Waves with ground-based laser interferometers. Data quality and noise reduction along with source parameter estimation, with particular emphasis on localization, are discussed in great detail. Conclusions drawn from statistical ensembles of simulated signals are applied to the first three confirmed detections of Gravitational Waves, all from the coalescence of binary black hole systems.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 186-201).
Quantum signal processing by single-qubit dynamics
Low, Guang Hao
Quantum computation is the most powerful realizable model of computation, and is uniquely positioned to solve specialized problems intractable to classical computers. This quantum advantage arises from directly exploiting the strangeness of quantum mechanics that is fundamental to reality. As such, one expects our understanding of quantum processes in physical systems to be indispensable to the design and execution of quantum algorithms. We present quantum signal processing, which exploits the dynamics of simple quantum systems to perform non-trivial computations. Such systems applied as computational modules in larger quantum algorithms, offer a natural physical alternative to standard tasks such as the calculation of elementary functions with integer arithmetic. The quantum advantage of this approach, based on simple physics, is of significant practical relevance. In cases, arbitrary bits of precision may be emulated using only constant space. Moreover, the simplicity and performance of quantum signal processing is such that it is the final missing ingredient for realizing a number of optimal quantum algorithms, particularly in Hamiltonian simulation. Quantum signal processing realizes a useful fusion of analog and digital models of quantum computation. At the physical level, we focus on how even a simple two-level system - the qubit, computes through optimal discrete-time quantum control. Whereas quantum control is typically used to synthesize unitary quantum gates, we solve the synthesis problem of unitary quantum functions with a fully characterization of achievable functions, and efficient techniques for their implementation. This furnishes a surprisingly rich framework in the analog model of quantum computation for computing functions. The generality of this model is realized by many applications, often with no modification, to quantum algorithms designed for digital quantum computers, in particular for matrix manipulation. In this manner, we solve a number of open problem related to optimal amplitude amplification algorithms, optimally computing on matrices with a quantum computer, and the simulation of physical systems.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 117-125).
Top mass determination using Effective Field Theories
Pathak, Aditya, Ph. D. Massachusetts Institute of Technology
The top quark mass is one of the most important Standard Model parameters and its mass has been measured at sub-percent precision by the Tevatron and LHC using Monte Carlo (MC) based methods. The resulting MC top mass parameter suffers from 0(1 GeV) uncertainty due to lack of specification of a precise field theoretic definition. Here a kinematic extraction method for obtaining a precisely defined short distance top mass at the LHC is proposed. A formula for factorized top jet mass cross section in the peak region is derived using methods of Effective Field Theory (EFT). It can then be used for direct comparison with data or for calibrating Monte Carlo simulations. Result for hard matching coefficient at two loops at the top mass scale is presented that enables N3LL logarithmic resumamtion of the cross section for top-jets in e+e- collisions. An effective theory setup for top mass extraction with soft drop grooming is derived, and is used to derive a factorization formula for the groomed jet mass distribution. Constraints from power counting in EFT limit the strength of groomers to "light grooming region". Studies with PYTHIA demonstrate that application of soft drop, even when restricted to light grooming, shows remarkable improvements in resilience to contamination from the underlying event (UE), has vastly reduced dependence the jet radius, and makes the top jet mass spectrum from pp collisions look like that of e+e- collisions as predicted. Modifications to the peaked spectrum from hadronization and UE for groomed top jets are suppressed and can be handled reliably. Using our factorization theorem results, a preliminary calibration study of Pythia top mass parameter is performed that yields results consistent with earlier calibrations for e+e- colliders.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 231-239).
Strongly interacting photons via Rydberg-Rydberg interactions
Liang, Qiyu, Ph. D. Massachusetts Institute of Technology
A quantum nonlinear optical medium, i.e. a medium where the light propagation depends on photon number, has been a long-standing goal due to its applications in quantum information, communication and metrology. When the medium is nonlinear at single photon level, it can be viewed as strong interactions between individual photons mediated by the medium. Here, we achieve such strong interactions by coupling the photons to highly polarizable Rydberg states with a phenomena called electromagnetically induced transparency (EIT). The strong van der Waals or dipole-dipole interactions between Rydberg excitations map to the photons under EIT conditions. The photons are incident on a cigar-shaped laser-cooled rubidium cloud in free space. After the photons emerge out of the cloud, we measure the photon correlations from time-resolved single photon detections, which reveal crucial information about the quantum states of strongly interacting two or three photons. In this thesis, I will present four experiments. The first two experiments demonstrate quantum nonlinearities with a propagating continuous wave (cw) light field via Rydberg-Rydberg interactions in the dissipative and dispersive regimes, respectively. In the dissipative regime, strong photon anti-bunching is observed. In the dispersive regime, we achieve a conditional phase shift ~ [pi]/4, together with photon-bunching driven by attractive force. Moreover, the photons acquire a finite mass and we see evidence for a diphoton molecule. In the third experiment, by measuring higher-order correlation functions, we observe a three-photon bound state evidenced by tighter binding in addition to a larger conditional phase shift than the two-photon states. By comparing with an effective field theory, our results suggest that there might be a three-photon force on top of the pairwise interactions owing to the saturation of the interaction. Namely, only one Rydberg excitation can be created within a characteristic length scale called blockade radius. Finally, we explore the exchange interaction instead of the widely studied blockade shifts. Under the exchange interactions, a propagating photon and a stored one experience coherent collisions protected by a symmetry of the Hamiltonian and pick up a robust [pi]/2 phase shift.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 181-188).
Practical fault-tolerant quantum computation
Yoder, Theodore J
For the past two and a half decades, a subset of the physics community has been focused on building a new type of computer, one that exploits the superposition, interference, and entanglement of quantum states to compute faster than a classical computer on select tasks. Manipulating quantum systems requires great care, however, as they are quite sensitive to many sources of noise. Surpassing the limits of hardware fabrication and control, quantum error-correcting codes can reduce error-rates to arbitrarily low levels, albeit with some overhead. This thesis takes another look at several aspects of stabilizer code quantum error-correction to discover solutions to the practical problems of choosing a code, using it to correct errors, and performing fault-tolerant operations. Our first result looks at limitations on the simplest implementation of fault-tolerant operations, transversality. By defining a new property of stabilizer codes, the disjointness, we find transversal operations on stabilizer codes are limited to the Clifford hierarchy and thus are not universal for computation. Next, we address these limitations by designing non-transversal fault-tolerant operations that can be used to universally compute on some codes. The key idea in our constructions is that error-correction is performed at various points partway through the non-transversal operation (even at points when the code is not-necessarily still a stabilizer code) to catch errors before they spread. Since the operation is thus divided into pieces, we dub this pieceable fault-tolerance. In applying pieceable fault tolerance to the Bacon-Shor family of codes, we find an interesting tradeoff between space and time, where a fault-tolerant controlled-controlled-Z operation takes less time as the code becomes more asymmetric, eventually becoming transversal. Further, with a novel error-correction procedure designed to preserve the coherence of errors, we design a reasonably practical implementation of the controlled-controlled-Z operation on the smallest Bacon-Shor code. Our last contribution is a new family of topological quantum codes, the triangle codes, which operate within the limits of a 2-dimensional plane. These codes can perform all encoded Clifford operations within the plane. Moreover, we describe how to do the same for the popular family of surface codes, by relation to the triangle codes.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2018.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 190-201).