UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.
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Item EXCURSION IN THE QUANTUM LOSS LANDSCAPE: LEARNING, GENERATING AND SIMULATING IN THE QUANTUM WORLD(2024) Rad, Ali; Hafezi, Mohammad; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Statistical learning is emerging as a new paradigm in science. This has ignited interestwithin our inherently quantum world in exploring quantum machines for their advantages in learning, generating, and predicting various aspects of our universe by processing both quantum and classical data. In parallel, the pursuit of scalable science through physical simulations using both digital and analog quantum computers is rising on the horizon. In the first part, we investigate how physics can help classical Artificial Intelligence (AI) by studying hybrid classical-quantum algorithms. We focus on quantum generative models and address challenges like barren plateaus during the training of quantum machines. We further examine the generalization capabilities of quantum machine learning models, phase transitions in the over-parameterized regime using random matrix theory, and their effective behavior approximated by Gaussian processes. In the second part, we explore how AI can benefit physics. We demonstrate how classical Machine Learning (ML) models can assist in state recognition in qubit systems within solid-state devices. Additionally, we show how ML-inspired optimization methods can enhance the efficiency of digital quantum simulations with ion-trap setups Finally, in the third part, we focus on how physics can help physics by using quantum systems to simulate other quantum systems. We propose native fermionic analog quantum systems with fermion-spin systems in silicon to explore non-perturbative phenomena in quantum field theory, offering early applications for lattice gauge theory models.Item EXPLORING QUANTUM MANY-BODY SYSTEMS IN PROGRAMMABLE TRAPPED ION QUANTUM SIMULATORS(2024) De, Arinjoy; Monroe, Christopher R; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum simulation is perhaps the most natural application of a quantum computer, where a precisely controllable quantum system is designed to emulate a more complex or less accessible quantum system. Significant research efforts over the last decade have advanced quantum technology to the point where it is foreseeable to achieve `quantum advantage' over classical computers, to enable the exploration of complex phenomena in condensed-matter physics, high-energy physics, atomic physics, quantum chemistry, and cosmology. While the realization of a universal fault-tolerant quantum computer remains a future goal, analog quantum simulators -- featuring continuous unitary evolution of many-body Hamiltonians -- have been developed across several experimental platforms. A key challenge in this field is balancing the control of these systems with the need to scale them up to address more complex problems. Trapped-ion platforms, with exceptionally high levels of control enabled by laser-cooled and electromagnetically confined ions, and all-to-all entangling capabilities through precise control over their collective motional modes, have emerged as a strong candidate for quantum simulation and provide a promising avenue for scaling up the systems. In this dissertation, I present my research work, emphasizing both the scalability and controllability aspects of \ion based trapped-ion platforms, with an underlying theme of analog quantum simulation. The initial part of my research involves utilizing a trapped ion apparatus operating within a cryogenic vacuum environment, suitable for scaling up to hundreds of ions. We address various challenges associated with this approach, particularly the impact of mechanical vibrations originating from the cryostat, which can induce phase errors during coherent operations. Subsequently, we detail the implementation of a scheme to generate phase-stable spin-spin interactions that are robust to vibration noise. In the second part, we use a trapped-ion quantum simulator operating at room temperature, to investigate the non-equilibrium dynamics of critical fluctuations following a quantum quench to the critical point. Employing systems with up to 50 spins, we show that the amplitude and timescale of post-quench fluctuations scale with system size, exhibiting distinct universal critical exponents. While a generic quench can lead to thermal critical behavior, a second quench from one critical state to another (i.e., double quench) results in unique critical behavior not seen in equilibrium. Our results highlight the potential of quantum simulators to explore universal scaling beyond the equilibrium paradigm. In the final part of the thesis, we investigate an analog of the paradigmatic string-breaking phenomena using a quantum spin simulator. We employ an integrated trapped-ion apparatus with $13$ spins that utilizes the individual controllability of laser beams to program a uniform spin-spin interaction profile across the chain, alongside 3-dimensional control of the local magnetic fields. We introduce two static probe charges, realized through local longitudinal magnetic fields, that create string tension. By implementing quantum quenches across the string-breaking point, we monitor non-equilibrium charge evolution with spatio-temporal resolution that elucidates the dynamical string breaking. Furthermore, by initializing the charges away from the string boundary, we generate isolated charges and observe localization effects that arise from the interplay between confinement and lattice effects.Item Quantum Advantage in Sensing and Simulation(2024) Ehrenberg, Adam; Gorshkov, Alexey V; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Since the discovery of Shor's factoring algorithm, there has been a sustained interest in finding more such examples of quantum advantage, that is, tasks where a quantum device can outperform its classical counterpart. While the universal, programmable quantum computers that can run Shor's algorithm represent one direction in which to search for quantum advantage, they are certainly not the only one. In this dissertation, we study the theory of quantum advantage along two alternative avenues: sensing and simulation. Sensing refers to the task of measuring some unknown quantity with the smallest possible error. In many cases, when the sensing apparatus is a quantum device, this ultimate achievable precision, as well as specific protocols producing estimators with this precision, are unknown. In this dissertation, we help close this gap for both qubit-based and photonic quantum sensors for the specific task of measuring a linear function of unknown parameters. We use quantum Fisher information and the quantum Cramér-Rao bound to derive limits on their ultimate precision. We further develop an algebraic framework that allows us to derive protocols saturating these bounds and better understand the quantum resources, such as entanglement, that are necessary to implement these protocols. In doing so, we help clarify how quantum resources like entanglement lead to more precise sensing. We also study a specific form of simulation called Gaussian Boson Sampling, which is a member of the broad framework of random sampling tasks that have become a popular method for demonstrating quantum advantage. While many of the theoretical underpinnings of these random sampling tasks, including Gaussian Boson Sampling, are well understood, many questions remain. Anticoncentration, which is strongly related to the moments of the output distribution, is a particularly relevant property when it comes to formally proving the existence of quantum advantage. We develop a graph-theoretic framework to calculate these moments, and we show that there is a transition in the strength of anticoncentration as a function of how many of the photonic modes are initially squeezed. We therefore demonstrate a transition in the evidence for the so-called approximate average-case hardness of Gaussian Boson Sampling, hence clarifying in what regimes we have the strongest evidence for quantum advantage. Finally, we also discuss the simulation complexity of Many-Body Localized systems. Many-Body Localization is a widely studied phase of matter that is often characterized by the appearance of a large number of quasilocal integrals of motion (operators that commute with the Hamiltonian) that interact via exponentially decaying interactions. In this dissertation, we study a phenomenological form of Many-Body Localization and show three main results. First, we demonstrate that, for polynomially long evolution times under a Hamiltonian in the Many-Body Localized phase, there is a quasipolynomial-time classical algorithm that can perform strong simulation of the output state. On the flip side, our second result is that, when the evolution time is exponentially long, weak simulation of the output state becomes formally classically hard. Finally, as a consequence of our classical results, we show the approximate quantum circuit complexity of these Hamiltonians grows sublinearly in the evolution time (in contrast with the proposed linear growth for chaotic Hamiltonians). Thus, this work helps clarify whether and how we might find quantum advantage via simulating certain types of condensed matter systems.Item Topology from Quantum Dynamics of Ultracold Atoms(2023) Reid, Graham Hair; Rolston, Steven L; Spielman, Ian B; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Ultracold atoms are a versatile platform for studying quantum physics in the lab. Usingcarefully chosen external fields, these systems can be engineered to obey a wide range of effective Hamiltonians, making them an ideal system for quantum simulation experiments studying exotic forms of matter. In this work, we describe experiments using 87Rb Bose–Einstein condensates (BECs) to study exotic topological matter based on out-of-equilibrium effects. The topological states are prepared through the quantum dynamics of the ultracold atom system subjected to a highly tunable lattice potential described by the bipartite Rice–Mele (RM) model, created by combining dressing from a radiofrequency (RF) magnetic field and laser fields driving Raman transitions. We describe a form of crystal momentum-resolved quantum state tomography, which functions by diabatically changing the lattice parameters, used to reconstruct the full pseudospin quantum state. This allows us to calculate topological invariants characterizing the system. We apply these techniques to study out-of-equilibrium states of our lattice system, described by various combinations of sublattice, time-reversal and particle-hole symmetry. Afterquenching between lattice configurations, we observe the resulting time-evolution and follow the Zak phase and winding number. Depending on the symmetry configuration, the Zak phase may evolve continuously. In contrast, the winding number may jump between integer values when sublattice symmetry is transiently present in the time-evolving state. We observe a scenario where the winding number changes by ±2, yielding values that are not present in the native RM Hamiltonian. Finally, we describe a modulation protocol in which the configuration of the bipartite latticeis periodically switched, resulting in the Floquet eigenstates of the system having pseudospin-momentum locked linear dispersion, analogous to massless particles described by the Dirac equation. We modulate our lattice configuration to experimentally realize the Floquet system and quantify the drift velocity associated with the bands at zero crystal momentum. The linear dispersion of Floquet bands derives from nontrivial topology defined over the micromotion of the system, which we measure using our pseudospin quantum state tomography, in very good agreement with theory.Item Non-Integrable Dynamics in a Trapped-Ion Quantum Simulator(2021) Becker, Patrick Michael; Monroe, Christopher; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)From the first demonstration of a quantum logic gate in 1995 to the actualizationof a “quantum advantage” over classical technology a few years ago, the field of quantum information has made remarkable progress during my lifetime. Multiple quantum technology platforms have developed to the point that companies and governments are investing heavily in the industry. A primary focus is the development of fault-tolerant error correction, a technology expected to be necessary for large-scale digital quantum computers. Meanwhile analog quantum simulators, a subclass of quantum computers that apply unitary evolutions instead of digitized gates, are at the forefront of controllable quantum system sizes. In place of algorithms, analog quantum simulators are naturally suited to study many-body physics and model certain materials and transport phenomena. In this thesis I discuss an analog quantum simulator based on trapped +Yb171 ions and its use for studying dynamics and thermalizing properties of the non-integrable long-range Ising model with system sizes near the limit of classical tractability. In addition to the technical properties of the simulator, I present three select experiments that I worked on during my PhD. The first is an observation of a phenomenon in nonequilibrium physics, a dynamical phase transition (DPT). While equilibrium phase transitions follow robust universal principles, DPTs are challenging to describe with conventional thermodynamics. We present an experimental observation and characterization of a DPT with up to 53 qubits. We also explore the system’s ability to simulate physics beyond its own by implementing a quasiparticle confinement Hamiltonian. Here we see that the natural long-range interactions present in the simulator induce an effective confining potential on pairs of domain-wall quasiparticles, which behave similarly to quarks bound into mesons. We measure post-quench dynamics to identify how confinement introduces low-energy bound states and inhibits thermalization. Lastly, we use the individual-addressing capabilities of our simulator to implement Stark many-body localization (MBL) with a linear potential gradient. Stark MBL provides a novel, disorder-free method for localizing a quantum system that would otherwise thermalize under evolution. We explore how the localized phase depends on the gradient strength and uncover the presence of correlations using interferrometric double electron-electron resonance (DEER) measurements. These experiments show the capability of our experiment to study complex quantum dynamics in systems near 50 qubits and above.Item INITIAL STATE PREPARATION FOR SIMULATION OF QUANTUM FIELD THEORIES ON A QUANTUM COMPUTER(2020) Hamed Moosavian, Ali; Childs, Andrew; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this thesis, we begin by reviewing some of the most important Hamiltonian simulation algorithms that are applied in simulation of quantum field theories. Then we focus on state preparation which has been the slowest subroutine in previously known algorithms. We present two distinct methods that improve upon prior results. The first method utilizes classical computational tools such as Density Matrix Renormalization Group to produce an efficient quantum algorithm for simulating fermionic quantum field theories in 1+1 dimensions. The second method presented is a heuristic algorithm that can prepare the vacuum of fermionic systems in more general cases and more efficiently than previous methods. With our last method, state preparation is no longer the bottleneck, as its runtime has the same asymptotic scaling with the desired precision as the remainder of the simulation algorithm. We then numerically demonstrate the effectiveness of this last method for the 1+1 dimensional Gross-Neveu model.Item Algorithms for quantum simulation: design, analysis, implementation, and application(2020) Su, Yuan; Childs, Andrew M; Computer Science; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Simulating the Hamiltonian dynamics of quantum systems is one of the most promising applications of digital quantum computers. In this dissertation, we develop an understanding of quantum simulation algorithms concerning their design, analysis, implementation, and application. We implement three leading simulation algorithms, employing diverse techniques to tighten their error analyses and optimize circuit implementations. We produce concrete resource estimates for simulating a Heisenberg spin system, a problem arising in condensed matter physics that is otherwise difficult to solve on a classical computer. The resulting circuits are orders of magnitude smaller than those for the simplest classically-infeasible instances of factoring and quantum chemistry, suggesting the simulation of spin systems as a promising candidate for an early demonstration of practical quantum computation. We design new simulation algorithms by using classical randomness. We show that by simply randomizing how the terms in the Hamiltonian are ordered, one can prove stronger bounds for product formulas and thereby give more efficient quantum simulations. We also develop a classical sampler for time-dependent Hamiltonians, using which we give a simulation algorithm that substantially improves over previous approaches when the Hamiltonian varies significantly with time. We propose a general theory to analyzing product formulas, an approach to quantum simulation widely used in experimental demonstrations but whose error scaling was poorly understood. Our approach directly exploits the commutativity of Hamiltonian, overcoming the limitations of prior error analyses. We prove new speedups of product formulas for simulating many quantum systems, including simulations of nearest-neighbor lattice systems, second-quantized plane-wave electronic structure, $k$-local Hamiltonians, rapidly decaying power-law interactions, and clustered Hamiltonians, nearly matching or even outperforming the best previous results in quantum simulation. We accompany our analysis with numerical calculation, which suggests that the bounds also have nearly tight constant prefactors. We identify applications of quantum simulation to designing other quantum algorithms and improving quantum Monte Carlo methods. We develop an algorithmic framework ``quantum singular value transformation'' using techniques from quantum simulation and apply it to implement principal component regression. We also apply our new analysis of product formulas and obtain improved quantum Monte Carlo simulations of the transverse field Ising model and quantum ferromagnets.Item Photon Thermalization in Driven Open Quantum Systems(2018) Wang, Chiao-Hsuan; Taylor, Jacob M; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Light is a paradigmatic quantum field, with individual excitations---photons---that are the most accessible massless particles known. However, their lack of mass and extremely weak interactions mean that typically the thermal description of light is that of blackbody radiation. As the temperature of the light decreases, the overall number of photons approaches zero. Therefore, efforts for quantum optics and optical physics have mostly focused on driving systems far from equilibrium to populate sufficient numbers of photons. While lasers provide a severe example of a nonequilibrium problem, recent interests in the near-equilibrium physics of so-called photon gases, such as in Bose condensation of light or in attempts to make photonic quantum simulators, suggest one re-examine near-equilibrium cases. In this thesis, we consider peculiar driven open quantum system scenarios where near-equilibrium dynamics can lead to equilibration of photons with a finite number, following a thermal description closer to that of an ideal gas than to blackbody radiation. Specifically, we show how laser cooling of a well-isolated mechanical mode or atomic motion can provide an effective bath which enables control of both the chemical potential and temperature of the resulting grand canonical ensemble of photon. We then theoretically demonstrate that Bose condensation of photons can be realized by cooling an ensemble of two-level atoms inside a cavity. Finally, we find that the engineered chemical potential for light not only admits future applications in many-body quantum simulations, facilitates preparation of near-equilibrium photonic states, but also enables an analogous voltage bias for photonic circuit elements.Item Nonlinear Optics Quantum Computation and Quantum Simulation with Circuit-QED(2014) Adhikari, Prabin; Taylor, Jacob M.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Superconducting quantum circuits are a promising approach for realizations of large scale quantum information processing and quantum simulations. The Josephson junction, which forms the basis of superconducting circuits, is the only known nonlinear non-dissipative circuit element, and its inherent nonlinearities have found many different applications. In this thesis I discuss specific implementations of these circuits. I show that strong two-photon nonlinearities can be induced by coupling photons in the microwave domain to Josephson nonlinearities. I then propose a method to simulate a parent Hamiltonian that can potentially be used to observe fractional quantum Hall states of light. I will also explore how superconducting circuits can be used to modify system-bath couplings to emulate a chemical potential for photons. Finally, I consider the limitations of devising a scheme to couple superconducting circuits to trapped ions, and consider the challenges for such hybrid approaches.