Physics Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/2800
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Item LOCAL MOLECULAR FIELD THEORY FOR NON-EQUILIBRIUM SYSTEMS(2019) Baker III, Edward Bigelow; Weeks, John D; Chemical Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Local Molecular Field (LMF) theory is a framework for modeling the long range forces of a statistical system using a mimic system with a modified Hamiltonian that includes a self consistent molecular potential. This theory was formulated in the equilibrium context, being an extension of the Weeks Chandler Andersen (WCA) theory to inhomogeneous systems. This thesis extends the framework further into the nonequilibrium regime. It is first shown that the equilibrium derivation can be generalized readily by using a nonequilibrium ensemble average and its relevant equations of motion. Specifically, the equations of interest are fluid dynamics equations which can be generated as moments of the BBGKY hierarchy. Although this approach works well, for the application to simulations it is desirable to approximate the LMF potential dynamically during a single simulation, instead of a nonequilibrium ensemble. This goal was pursued with a variety of techniques, the most promising of which is a nonequilibrium force balance approach to dynamically approximate the relevant ensemble averages. This method views a quantity such as the particle density as a field, and uses the statistical equations of motion to propagate the field, with the forces in the equations computed from simulation. These results should help LMF theory become more useful in practice, in addition to furthering the theoretical understanding of near equilibrium molecular fluids.Item Quantum Compiling Methods for Fault-Tolerant Gate Sets of Dimension Greater than Two(2019) Glaudell, Andrew Noble; Taylor, Jacob M; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Fault-tolerant gate sets whose generators belong to the Clifford hierarchy form the basis of many protocols for scalable quantum computing architectures. At the beginning of the decade, number-theoretic techniques were employed to analyze circuits over these gate sets on single qubits, providing the basis for a number of state-of-the-art quantum compiling algorithms. In this dissertation, I further this program by employing number-theoretic techniques for higher-dimensional gate sets on both qudit and multi-qubit circuits. First, I introduce canonical forms for single qutrit Clifford+T circuits and prove that every single-qutrit Clifford+T operator admits a unique such canonical form. I show that these canonical forms are T-optimal and describe an algorithm which takes as input a Clifford+T circuit and outputs the canonical form for that operator. The algorithm runs in time linear in the number of gates of the circuit. Our results provide a higher-dimensional generalization of prior work by Matsumoto and Amano who introduced similar canonical forms for single-qubit Clifford+T circuits. Finally, we show that a similar extension of these normal forms to higher dimensions exists, but do not establish uniqueness. Moving to multi-qubit circuits, I provide number-theoretic characterizations for certain restricted Clifford+T circuits by considering unitary matrices over subrings of Z[1/√2, i]. We focus on the subrings Z[1/2], Z[1/√2], Z[1/√−2], and Z[1/2, i], and we prove that unitary matrices with entries in these rings correspond to circuits over well-known universal gate sets. In each case, the desired gate set is obtained by extending the set of classical reversible gates {X, CX, CCX} with an analogue of the Hadamard gate and an optional phase gate. I then establish the existence and uniqueness of a normal form for one of these gate sets, the two-qubit gate set of Clifford+Controlled Phase gate CS. This normal form is optimal in the number of CS gates, making it the first normal form that is non-Clifford optimal for a fault tolerant universal multi-qubit gate set. We provide a synthesis algorithm that runs in a time linear in the gate count and outputs the equivalent normal form. In proving the existence and uniqueness of the normal form, we likewise establish the generators and relations for the two-qubit Clifford+CS group. Finally, we demonstrate that a lower bound of 5 log2 (1/ε) + O(1) CS gates are required to ε-approximate any 4 × 4 unitary matrix. Lastly, using the characterization of circuits over the Clifford+CS gate set and the existence of an optimal normal form, I provide an ancilla-free inexact synthesis algorithm for two-qubit unitaries using the Clifford+SC gate set for Pauli-rotations. These operators require 6 log2 (1/ε) + O(1) CS gates to synthesize in the typical case and 8 log2 (1/ε) + O(1) in the worst case.Item STUDIES IN NONEQUILIBRIUM QUANTUM THERMODYNAMICS(2019) Smith, Andrew Maven; Jarzynski, Christopher; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The first part of this thesis focuses on verifying the quantum nonequilibrium work relation in the presence of decoherence. The nonequilibrium work relation is a generalization of the second law of thermodynamics that links nonequilibrium work measurements to equilibrium free energies via an equality. Despite being well established for classical systems, a quantum work relation is conceptually difficult to construct for systems that interact with their environment. We argue that for a quantum system which undergoes decoherence but not dissipation, these conceptual difficulties do not arise and the work relation can be proven similarly to the case of an isolated system. This result is accompanied by an experimental demonstration using trapped ions. The second part of this thesis examines the relationship between quantum work and coherence by constructing analogous quantities in classical physics. It has recently been shown that quantum coherence can function as a resource for work extraction. Furthermore, it has been suggested that this property could be a truly quantum aspect of thermodynamics with no classical analog. We examine this assertion within the framework of classical Hamiltonian mechanics and canonical quantization. For classical states we define a so called non-uniformity measure and show that it is a resource for work extraction similar to quantum coherence. Additionally, we show that work extracted from non-uniformity and coherence agree in the classical limit. This calls into question the idea that coherence qualitatively separates classical and quantum thermodynamics. The final part of this thesis explores the connection between decoherence and adiabatic (quasistatic) driving. This topic is inspired by an experiment where it was seen that strong dephasing suppressed energy level transitions. Using a perturbative method we investigate this mechanism in the regime of small to moderate decoherence rate and ask if decoherence can help suppress energy transitions when compared with an adiabatic process without decoherence. We find that strategies that include decoherence are inferior to those where decoherence is absent.Item Topological dispersion relations in spin-orbit coupled Bose gases(2019) Valdes Curiel, Ana; Spielman, Ian; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum degenerate gases have proven to be an ideal platform for the simulation of complex quantum systems. Due to their high level of control it is possible to readily design and implement systems with effective Hamiltonians in the laboratory. This thesis presents new tools for the characterization and control of engineered quantum systems and describes their application in the realization of a topological system with Rashba-type spin-orbit coupling. The underlying properties of these engineered systems depend on their underlying energies. I describe a Fourier transform spectroscopy technique for characterizing the single particle spectrum of a quantum system. We tested Fourier spectroscopy by measuring the dispersion relation of a spin-1 spin-orbit coupled Bose-Einstein condensate (BEC) and found good agreement with our predictions. Decoherence due to uncontrolled fluctuations of the environment presents fundamental obstacles in quantum science. I describe an implementation of continuous dynamical decoupling (CDD) in a spin-1 BEC. We applied a strong radio-frequency (RF) magnetic field to the ground state hyperfine manifold of Rubidium-87 atoms, generating a dynamically protected dressed system that was first-order insensitive to changes in magnetic field. The CDD states constitute effective clock states and we observed a reduction in sensitivity to magnetic field of up to four orders of magnitude. We additionally show that the CDD states can be coupled in a fully connected geometry and thus enable the implementation of new models not possible using the bare atomic states. Finally, I describe a new realization of Rashba-type SOC using Raman coupled CDD states. Our system had non-trivial topology but no underlying crystalline structure that yields integer valued Chern numbers in conventional materials. We validated our procedure using Fourier transform spectroscopy to measure the full dispersion relation containing only a single Dirac point. We measured the quantum geometry underlying the dispersion relation and obtained the topological index using matter-wave interferometry. In contrast to crystalline materials, where topological indices take on integer values, our continuum system reveals an unconventional half-integer Chern number.Item QUANTUM ALGORITHMS FOR DIFFERENTIAL EQUATIONS(2019) Ostrander, Aaron Jacob; Childs, Andrew; Monroe, Chris; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis describes quantum algorithms for Hamiltonian simulation, ordinary differential equations (ODEs), and partial differential equations (PDEs). Product formulas are used to simulate Hamiltonians which can be expressed as a sum of terms which can each be simulated individually. By simulating each of these terms in sequence, the net effect approximately simulates the total Hamiltonian. We find that the error of product formulas can be improved by randomizing over the order in which the Hamiltonian terms are simulated. We prove that this approach is asymptotically better than ordinary product formulas and present numerical comparisons for small numbers of qubits. The ODE algorithm applies to the initial value problem for time-independent first order linear ODEs. We approximate the propagator of the ODE by a truncated Taylor series, and we encode the initial value problem in a large linear system. We solve this linear system with a quantum linear system algorithm (QLSA) whose output we perform a post-selective measurement on. The resulting state encodes the solution to the initial value problem. We prove that our algorithm is asymptotically optimal with respect to several system parameters. The PDE algorithms apply the finite difference method (FDM) to Poisson's equation, the wave equation, and the Klein-Gordon equation. We use high order FDM approximations of the Laplacian operator to develop linear systems for Poisson's equation in cubic volumes under periodic, Neumann, and Dirichlet boundary conditions. Using QLSAs, we output states encoding solutions to Poisson's equation. We prove that our algorithm is exponentially faster with respect to the spatial dimension than analogous classical algorithms. We also consider how high order Laplacian approximations can be used for simulating the wave and Klein-Gordon equations. We consider under what conditions it suffices to use Hamiltonian simulation for time evolution, and we propose an algorithm for these cases that uses QLSAs for state preparation and post-processing.Item Machine Learning Approaches for Data-Driven Analysis and Forecasting of High-Dimensional Chaotic Dynamical Systems(2019) Pathak, Jaideep; Ott, Edward; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We consider problems in the forecasting of large, complex, spatiotemporal chaotic systems and the possibility that machine learning might be a useful tool for significant improvement of such forecasts. Focusing on weather forecasting as perhaps the most important example of such systems, we note that physics-based weather models have substantial error due to various factors including imperfect modeling of subgrid-scale dynamics and incomplete knowledge of physical processes. In this thesis, we ask if machine learning can potentially correct for such knowledge deficits. First, we demonstrate the effectiveness of using machine learning for model- free prediction of spatiotemporally chaotic systems of arbitrarily large spatial extent and attractor dimension purely from observations of the system’s past evolution. We present a parallel scheme with an example implementation based on the reservoir computing paradigm and demonstrate the scalability of our scheme using the Kuramoto-Sivashinsky equation as an example of a spatiotemporally chaotic system. We then demonstrate the use of machine learning for inferring fundamental properties of dynamical systems, namely the Lyapunov exponents, purely from observed data. We obtain results of unprecedented fidelity with our novel technique, making it possible to find the Lyapunov exponents of large systems where previously known techniques have failed. Next, we propose a general method that combines a physics-informed knowledge-based model and a machine learning technique to build a hybrid forecasting scheme. We further extend our hybrid forecasting approach to the difficult case where only partial measurements of the state of the dynamical system are available. For this purpose, we propose a novel technique that combines machine learning with a data assimilation method called an Ensemble Transform Kalman Filter (ETKF).Item Electronic and Magnetic Properties of MnP-Type Binary Compounds(2019) Campbell, Daniel James; Paglione, Johnpierre; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The interactions between electrons, and the resulting impact on physical properties, are at the heart of present-day materials science. This thesis looks at this idea through the lens of several compounds from a single family: the MnP-type transition metal pnictides. FeAs and FeP show long range magnetic order with some similarities to the high temperature, unconventional iron-based superconductors. CoAs lies on the border of magnetism, with strong fluctuations but no stable ordered state. CoP, in contrast, shows no strong magnetic fluctuations but serves as a useful baseline in determining the origin (from composition, structure, or magnetic order) of behavior in the other materials. For this work, single crystals were grown with two different techniques: solvent flux and chemical vapor transport. In the case of FeAs the flux method resulted in the highest quality crystals yet produced. Extensive work was then performed on these samples at the University of Maryland and the National High Magnetic Field Laboratory. Quantum oscillations observed in high magnetic fields, in combination with density functional theory calculations, give insight into the Fermi surfaces of these materials. Large magnetoresistance in the phosphides, but not the arsenides, demonstrates differences in the choice of pnictogen atom that cannot be simply a product of electron count. Angle-dependent linear magnetoresistance in FeP is a sign of a possible Dirac dispersion and topological physics, as has been hinted at in other MnP-type materials. Ultimately, it is possible to examine results for all four compounds and draw conclusions on the role of each of the two elements in the formula, which can be extended to other members of this family.Item Nonequilibrium Dynamics in Open Quantum Systems(2019) Young, Jeremy; Rolston, Steven L; Gorshkov, Alexey V; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Due to the variety of tools available to control atomic, molecular, and optical (AMO) systems, they provide a versatile platform for studying many-body physics, quantum simulation, and quantum computation. Although extensive efforts are employed to reduce coupling between the system and the environment, the effects of the environment can never fully be avoided, so it is important to develop a comprehensive understanding of open quantum systems. The system-environment coupling often leads to loss via dissipation, which can be countered by a coherent drive. Open quantum systems subject to dissipation and drive are known as driven-dissipative systems, and they provide an excellent platform for studying many-body nonequilibrium physics. The first part of this dissertation will focus on driven-dissipative phase transitions. Despite the nonequilibrium nature of these systems, the corresponding phase transitions tend to exhibit emergent equilibrium behavior. However, we will show that in the vicinity of a multicritical point where multiple phase transitions intersect, genuinely nonequilibrium criticality can emerge, even though the individual phase transitions on their own exhibit equilibrium criticality. These nonequilibrium multicritical points can exhibit a variety of exotic phenomena not possible for their equilibrium counterparts, including the emergence of complex critical exponents, which lead to discrete scale invariance and spiraling phase boundaries. Furthermore, the Liouvillian gap can take on complex values, and the fluctuation-dissipation theorem is violated, corresponding to an effective temperature which gets "hotter" and "hotter" at longer and longer wavelengths. The second part of this dissertation will focus on Rydberg atoms. In particular, we study how the spontaneous generation of contaminant Rydberg states drastically modifies the behavior of a driven-dissipative Rydberg system due to the resultant dipole-dipole interactions. These interactions lead to a complicated competition of both blockade and anti-blockade effects, leading to strongly enhanced Rydberg populations for far-detuned drive and reduced Rydberg populations for resonant drive.Item Topological Rare Earth Half-Heusler HoPtBi(2019) Roncaioli, Connor Andrew; Paglione, Johnpierre; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Magnetic HoPtBi is created and characterized as a new half-Heusler Weyl-candidate. By analogy with the well-studied GdPtBi system we undertake measurements intended to understand the normal state of this material, before extending our study to search for characteristics of Weyl behavior. We find a material with semiconducting properties as well as a low temperature antiferromagnetic transition below 1.25K and a Curie-Weiss paramagnetic system above. Analysis of the magnetoresistance in HoPtBi finds multiple Weyl-like characteristics, including potential chiral anomaly and anomalous Hall angle components. Finally we found significant anisotropic magnetoresistance in HoPtBi dependent on field alignment relative to the crystalline axes of the material, which is unexpected for a paramagnetic compound. We will show that these behaviors indicate a material with a Fermi surface readily tuned by application of magnetic field.Item Many-Body Dephasing in a Cryogenic Trapped Ion Quantum Simulator(2019) Kaplan, Harvey B.; Monroe, Christopher R; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)While realizing a fully functional quantum computer presents a long term technical goal, in the present, there are small to mid-sized quantum simulators (up to $\sim 100$ qubits), that are capable of approaching specialized problems. The quantum simulator discussed here uses trapped ions to act as qubits and is housed in a cryogenically cooled vacuum chamber in order to reduce the background pressure, thereby increasing ion chain length and life-time. The details of performance and characterization of this cryogenic apparatus are discussed, and this system is used to study many-body dephasing in a finite-sized quantum spin system. How a closed quantum many-body system relaxes and dephases as a function of time is important to understand when dealing with many-body spin systems. In this work, the first experimental observation of persistent temporal fluctuations after a quantum quench is presented with a tunable long-range interacting transverse-field Ising Hamiltonian. The fluctuations in the average magnetization of a finite-size system of spin-$1/2$ particles are measured presenting a direct measurement of relaxation dynamics in a non-integrable system. This experiment is in the regime where the properties of the system are closely related to the integrable Hamiltonian with global coupling. The system size is varied in order to investigate the dependence on finite-size scaling, and the system size scaling exponent extracted from the measured fluctuations is consistent with theoretical prediction.