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Digital Quantum Simulation of Quantum Many-Body Systems
Get PDFQuantum computing has emerged as a promising technology, heralding a new era of computational capabilities, with the simulation of quantum many-body systems as one of its primary objectives. Although fault-tolerant quantum computers are still years away, noisy intermediate-scale quantum (NISQ) devices have been fabricated and leveraged to perform small-scale quantum simulations. In this thesis, we demonstrate simulations of quantum many-body systems on these near-term quantum computers. We specifically focus on physical quantities pertaining to the linear-response framework, which include two-point correlation functions and Green's functions, of small-scale spin and molecular models. Additionally, as quantum hardware increases in qubit count, simulation of these quantum algorithms on classical computers that closely resemble those planned for execution on quantum hardware becomes increasingly critical. The final part of this thesis examines such a simulation using tensor network algorithms on classical computers.
We first present the study of finite-temperature physics of spin models on quantum hardware. Employing the quantum imaginary time evolution (QITE) algorithm, we demonstrate the computation of diverse finite-temperature observables, including energy, static and dynamical correlation functions, and excitation spectra of the Heisenberg model and the transverse-field Ising model of up to four sites on five-qubit IBM Quantum devices. Accurate determination of these finite-temperature properties on quantum computers is made possible by several algorithmic improvements, including a method to exploit symmetries that reduces the quantum resources required by QITE, circuit optimization procedures to reduce circuit depth, and error-mitigation techniques to improve the quality of raw hardware data. This work demonstrates that the ansatz-independent QITE algorithm is capable of computing diverse finite-temperature observables on near-term quantum devices.
The second work implements an algorithm for frequency-domain response properties of diatomic molecules using a novel high-fidelity three-qubit iToffoli gate. Although it is natural to compute response properties in the time domain due to the natural ability of quantum computers to apply unitary time evolutions, obtaining the frequency-domain properties from the time-domain properties typically requires a time duration that results in quantum circuits exceeding the circuit depth limitations of near-term quantum computers. In this work, we carry out computations of the response properties directly in the frequency domain using the linear combination of unitaries (LCU) algorithm. Execution of the LCU-based protocol on quantum hardware is enabled by the iToffoli gate, which enables a ~50\% reduction in circuit depth and ~40\% reduction in circuit execution time in the LCU circuits compared to the traditional gate set. We show that the molecular properties obtained with the iToffoli gate exhibit comparable or better agreement with analytical results than those obtained when CZ gates are the only multi-qubit gates. This work is among the first demonstrations of the practical usage of a native multi-qubit gate in quantum simulation, with diverse potential applications to near-term quantum computation.
Finally, this thesis conducts a tensor network simulation of measurement-induced state preparation on classical computers. Specifically, we simulate the phase transition in random-bond Ising models (RBIM) by performing measurements on the cluster states. The simulation is carried out on NVIDIA H100 graphical processing units (GPUs) using the cuQuantum library. We present simulation of correlation functions in one dimension (1D) and ferromagnetic susceptibilities in two dimensions (2D), observing a phase transition from the ferromagnetic phase to spin-glass phase in the 2D model. The tensor network simulation incorporates up to 176 qubits on the 2D lattice. This work paves the way for future explorations of tensor network simulations of measurement-induced quantum computation protocols with GPU-accelerated tensor network libraries.</p
Ultrafast Optical Studies of Pressure-Tuned Spin-Orbit Materials
Get PDFThe advent of quantum materials has provided researchers with a remarkable opportunity to delve into the intricate interplay among various degrees of freedom, encompassing charge, orbital, spin, and lattice dynamics. Transition metal compounds, possessing distinct characteristics, exemplify the captivating competition between interactions arising from different degrees of freedom, each with comparable strength. These interactions encompass the on-site Coulomb interaction, kinetic hopping, spin-orbit coupling (SOC), crystal electric field splitting, and Hunds exchange coupling. In correlated electron systems of this nature, the intricate interplay of these complex interactions gives rise to a plethora of exotic phenomena, rendering the understanding of each variable a daunting task. Hence, it becomes imperative to explore their responses to external stimuli, and in this regard, hydrostatic pressure emerges as a versatile tool capable of tuning the strength of competing interactions and shifting the delicate balance between coexisting and competing ground states. This engenders a rich diversity of quantum phases and holds the potential to decouple these intertwined variables in phase transitions, thus unveiling the distinctive roles played by each constituent.
In Chapter I, a comprehensive discussion on pressure-induced phase transitions will ensue, encompassing phenomena such as insulator-metal transitions, spin-crossover transitions, structural transformations, and the fervent search for elusive quantum spin liquid and topological superconductive states. Chapter II shall delve into the experimental techniques that have been extensively employed throughout my research endeavors. This will encompass a synergistic combination of a high-pressure environment and cutting-edge ultrafast optical probing techniques, including optical second harmonic generation (SHG), harnessed by the high peak power of femtosecond lasers, as well as time-resolved reflectivity, capitalizing on the exceedingly short time duration of laser pulses. Moreover, a wide-field microscopy approach based on the magneto-optical Kerr effect shall be expounded upon, enabling direct observations of intricate domain structures. In subsequent chapters, three projects shall be elucidated, encompassing Weyl semimetals, with a specific focus on TaAs in Chapter III, Co3Sn2S2 in Chapter V, and an investigation into the spin-orbit-coupled Mott insulator Sr2IrO4 in Chapter IV.
The transition metal monopnictide family of Weyl semimetals recently has been shown to exhibit anomalously strong second-order optical nonlinearity, which is theoretically attributed to a highly asymmetric polarization distribution induced by their polar structure. We experimentally test this hypothesis by measuring optical SHG from TaAs across a pressure-tuned polar to non-polar structural phase transition. Despite the high-pressure structure remaining non-centrosymmetric, the SHG yield is reduced by more than 60% by 20 GPa as compared to the ambient pressure value. By examining the pressure dependence of distinct groups of SHG susceptibility tensor elements, we find that the yield is primarily controlled by a single element that governs the response along the polar axis. Our results confirm a connection between the polar axis and the giant optical nonlinearity of Weyl semimetals and demonstrate pressure as a means to tune this effect in situ.
Sr2IrO4 stands as an archetypal SOC-mediated Mott insulator, where the electronic and magnetic structures are highly sensitive to the intricacies of the crystallographic structure, particularly the rotation and tilting of the IrO6 cages. External pressure serves as a direct means to manipulate these characteristics. Under high pressure, fascinating phenomena have emerged, including the persistence of the insulating state up to an extreme pressure of 185 GPa, a sequence of magnetic transitions culminating in a quantum paramagnetic phase around 20 GPa. However, a dearth of information exists concerning the low-energy electronic band structure. To address this gap, we conducted time-resolved reflectivity measurements under pressures up to 14 GPa. Within the low-pressure range below 10 GPa, anomalies in the temperature-dependent reflectivity transients exhibit a trend akin to the Neel temperature. Yet, as pressure increases further, the temperature associated with these anomalies rises and deviates from the monotonically decreasing magnetic ordering temperature, thereby unveiling a mysterious underlying mechanism governing the relaxation dynamics.
In addition to the breaking of inversion symmetry, Weyl topology can also arise from the breaking of time reversal symmetry in magnetic systems, offering a fertile ground for investigating the intricate relationship between magnetism and topological order. Endeavors have been undertaken to manipulate magnetism as a means to tune the topological electronic band structure. Notably, the well-established ferromagnetic Weyl semimetal, Co3Sn2S2, has garnered significant attention due to its intriguing magnetic anomalies persisting below the Curie temperature. Further investigations have revealed that the distribution of magnetic domains and domain walls plays a pivotal role in elucidating these anomalies. Herein, we report the observation of domain structures using a wide-field Kerr microscope and the manipulation of said structures employing a mid-infrared laser and magnetic field. This study not only sheds light on domain-related properties but also holds promise for uncovering exotic topological phenomena exhibited at domain boundaries.</p
Bost–Connes–Marcolli System for the Siegel Modular Variety
Get PDFBost–Connes–Marcolli systems are an important type of quantum statistical mechanical systems which provide connections between the ergodic theory of dynamical systems, class field theory and von Neumann algebras. In this thesis, we generalize the GL₂-system to the case of the Siegel modular variety of degree two and study its various properties. We show that this dynamical system undergoes a spontaneous symmetry breaking phase transition and classify its equilibrium extremal states at different inverse temperatures. We next study its symmetry group and derive an intertwining equality between the action by symmetries and a subgroup of the Galois group of the Siegel modular field. Finally, we study the von Neumann algebras associated to the equilibrium states and classify their types
Guaranteed Policy Performance in Reinforcement Learning
Get PDFDecision-making is ubiquitous in everyday life. Increasingly, researchers are seeking answers on how to optimally solve sequential decision-making tasks. Thanks to recent availability of computation, advances in deep learning, and released open-sourced code, it has become easy to train a computational agent to make decisions in many domains. Nevertheless, in realistic scenarios where the consequences of failure are high, running a trained computational agent in the wild poses substantial risk.
The goal of this thesis is to develop and advance techniques that guarantee a learned agent does what we expect it to do. The thesis tackles two central questions:
1) Given an agent, how can we predict if it will perform desirably?
2) Can we structure the learning process to guarantee desirable post-learning performance?
On the former question, this thesis proposes multiple algorithms to evaluate such agents, finds factors that have high influence on the success of agent evaluation, and open-sources benchmarks for further development in the space.
On the latter question, this thesis formulates desirable agent behavior as a constrained optimization with varying types of constraints depending on the structure afforded to the practitioner. Constraining the search space over the learning process ensures post-learning behaviors will, by definition, perform as desired.</p
Bidirectional Interactions Between the Gut Microbiome and Nervous System
Get PDFThere is roughly one microbe for every human cell in your body. Though some are inconsequential hitchhikers, and some are potentially harmful, many perform beneficial roles. This thesis focuses on the function and interaction of resident microbes within laboratory mice, with the hope that it may translate to us as humans. Chapter (1) highlights recent findings of microbiome involvement in neurologic disorders. Each subsequent chapter presents a different interaction between the mammalian nervous system and gut microbiome. (2) Excitatory signaling in the brain is partially regulated by a genetic factor (Shank3), which is further modulated by environmental interactions through presence or absence of the gut microbiome. This genetic factor implicated in brain and behavior also affects gastrointestinal function and inflammation susceptibility. (3) Applying powerful genetic tools developed for the brain to the enteric nervous system reveals the impact of different enteric neuron populations on gut motility and fluid secretion as well as the immune system, pancreatic activity, and microbial populations. (4) Common opinion has shifted from the belief that microbes are primarily pathogens to viewing them as symbiotic organisms. With this paradigm shift, the artificially clean laboratory mouse microbiome has been found to stunt the immune system, and is being reevaluated. Male mice with natural “wild” microbiomes have altered behavioral and neurological profiles, which may reflect a more physiological state
Quantum Measurements with Superconducting Nanowire Single Photon Detectors
Get PDFSuperconducting Nanowire Single-Photon Detectors (SNSPDs) are high-performance photon counting detectors, typically operated just a few degrees above absolute zero. Comprising a current-biased nanowire transitioning between superconducting and resistive states upon photon absorption, SNSPDs generate voltage pulses for precise photon arrival time measurement. Initially demonstrated in the 1990s, SNSPDs are now mature devices widely employed in various fields, including space communication, biological imaging, and quantum technology. This thesis explores techniques to enhance usable count rate, dark count rate, timing resolution, and photon number resolution for both emerging and established SNSPD designs. We introduce a free space optical filtering method to minimize SNSPD dark count rates which is competitive with the state-of-the-art for fiber coupled SNSPDs, and especially impactful for space communication applications. We go on to study dynamics that limit SNSPD maximum count rates, presenting a calibration and in-situ correction procedure to significantly reduce jitter at high rates without additional hardware or offline processing. With an eye towards space communication applications beyond NASA's Deep Space Optical Communication (DSOC) project, we present a high-rate Pulse Position Modulation communication demo with SNSPDs. In the process we uncover a rich photon-number dependent response in these detectors and devise methods to properly leverage and manage it. Finally, we employ low-jitter SNSPDs in a high-rate entanglement distribution system, achieving high entanglement visibilities, and distillable entanglement rates. As this work focuses on optimizing SNSPD usage and analysis rather than device physics or fabrication, it is broadly applicable to any users of this single photon detection technology.</p
Learning, Verifying, and Erasing Errors on a Chaotic and Highly Entangled Programmable Quantum Simulator
Get PDFControlled quantum systems have the potential to make major advancements in tasks ranging from computing to metrology. In recent years, quantum devices have experienced tremendous progress, reaching meaningful, intermediate-scale sizes and demonstrating advantage over their classical counterparts. Still, sensing, learning, verifying, and hopefully mitigating errors in these systems is an outstanding and ubiquitous challenge facing all modern quantum platforms.
Here we review and expound upon one such platform: arrays of Rydberg atoms trapped in optical tweezers. We demonstrate several key advancements, including the first experimental realization of erasure conversion to prepare two-qubit Bell states with a fidelity in excess of 0.999, and to cool atoms to their motional ground state. We further showcase the tools of universal quantum processing via arbitrary single-qubit gates, fixed two-qubit gates, and mid-circuit measurement, and discuss applications of these techniques for metrology and computing.
Then, we turn to the many-body regime, generating highly entangled states with up to 60 atoms through analog quench dynamics. We reveal the emergence of random behavior from unitary quantum evolution, and uncover a universal form of quantum ergodicity linking quantum and statistical mechanics. We exploit these discoveries to verify the global many-body fidelity and then realize practical applications like parameter estimation and noise learning. Finally, we compare against both state-of-the-art quantum and classical processors: we introduce a new proxy for the experimental mixed state entanglement which is comparable amongst all quantum platforms, and that reflects the classical complexity of quantum simulation.</p
Acoustic Biosensors for Noninvasive Imaging of Molecular Processes
Get PDFUnderstanding biology in its native context has been a major scientific endeavor. Yet, it is challenging to visualize cellular dynamics at the molecular scale in the context of a living organism at the macroscopic scale. Ultrasound imaging represents a promising candidate to address this challenge, with its unique advantages of large imaging volume, deep penetration, and good spatiotemporal resolution. However, ultrasound was historically limited in retrieving molecular information that biology carries. Until very recently, the discovery of the first ultrasound-interacting biomolecules, gas vesicles (GVs), established a connection between connect cellular function and ultrasound signals, which later enabled ultrasound imaging of gene expression and thus the location of GV-expressing cells. Going beyond location tracking, this thesis describes the engineering of GV-based acoustic biosensors that made it possible to noninvasively image the dynamics of cellular signaling in living organisms.
GVs are genetically encoded intracellular air-filled “balloons” that are encapsulated by protein shells. The acoustic biosensor design leverages the GV surface protein GvpC, which controls GVs' ultrasound scattering by setting the stiffness of their protein shell. We developed the first acoustic biosensors by engineering GvpC to change its confirmation and thereby GVs’ ultrasound contrast in response to the activity or concentration of specific molecules. Specifically, we first built the biosensors for three different types of enzymes and demonstrated noninvasive imaging of enzyme activity inside probiotic cells in the mouse colon in vivo. Next, we engineered the acoustic biosensors for calcium, a ubiquitous signaling molecule that is essential in many cellular processes (e.g., neural activity). With the first generation of this calcium sensor for ultrasound, we demonstrated imaging of receptor-specific calcium signaling deep inside the mouse brain through the intact skull noninvasively, which opened up the possibility of whole-brain neuroimaging that can lead to many breakthroughs in neuroscience. Last, we established a high-throughput engineering platform to develop all these GV-based imaging agents in a much shorter time frame. Collectively, this thesis presents the first demonstration of noninvasively imaging dynamic cellular signaling with acoustic biosensors and the feasibility of efficiently improving them for potential real-world applications with our engineering pipeline, opening up a new route towards understanding biology across scales.</p
Discrete Constrained Willmore Surfaces
Get PDFThis thesis introduces discrete conformal variational problems as a versatile toolkit for the construction and manipulation of smooth surfaces in three-dimensions. Smooth curves and surfaces can be characterized as minimizers of squared curvature bending energies subject to constraints. In the univariate case with an isometry (length) constraint this leads to classic non-linear splines. For surfaces, isometry is too rigid a constraint, so we instead ask for minimizers of the Willmore (squared mean curvature) energy subject to a conformality constraint. Conformal transformations are desirable in applications because they preserve angles, and consequentially also mesh quality and the fidelity of geometric data. The conformal structure of a surface can be specified in terms of finitely many geometric parameters, and therefore provides a suitable interface for the free form design of surfaces. We term these surfaces conformal surface splines. Until now, however, there has been no systematic study of discrete conformal variational problems.
The main contribution of this thesis is analysis and numerical computation of discrete constrained Willmore surfaces. We present an efficient algorithm for computing discrete (conformally) constrained Willmore surfaces using triangle meshes of arbitrary topology. We also introduce free boundary conditions and point constraints for conformal immersions that increase the controllability of surfaces defined as minimizers of conformal variational problems. We demonstrate the applicability of our framework to geometric modeling and mathematical visualization.
To understand the Möbius invariant discretization of the Willmore energy underlying conformal surface splines, we describe a new quaternionic description of the conformal three-sphere, along with realizations of the spaces of circles, spheres, and point pairs in Euclidean three-space. We give an interpretation of the Willmore energy as the curvature of a quaternionic connection that has a clear geometric interpretation in terms of mean curvature spheres rolling over the surface. Building on this interpretation, we prove that the Möbius invariant discretization of the Willmore energy is equal to the curvature of a discrete connection defined by rolling the edge circumspheres. Conservation laws for discrete Willmore surfaces are also derived, finding applications in the prescription of tangent planes at point constraints.</p
Essays on Trustworthy Online Platforms
No full textThis thesis investigates strategies to enhance the trustworthiness of data-driven online platforms, focusing on combating misinformation, managing disruptive behavior, and fostering positive interactions. I explore multiple approaches, including the analysis of Twitter's misinformation mitigation efforts, the evaluation of moderation practices within a popular online game, and the development of innovative methods for analyzing text data on online platforms