Physics and Astronomy

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This is the collection for the University of Waterloo's Department of Physics and Astronomy.

Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).

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Quantum Monte Carlo Simulations of Rydberg Atom Arrays
(University of Waterloo, 2025-07-07) Merali, Ejaaz
Rydberg atom arrays form a promising platform for quantum computation. Through their strong, long-range interaction, they are able to encode various difficult combinatorial problems, as well as hosting a plethora of intriguing physical phenomena. In this thesis, we develop and apply a Stochastic Series Expansion Quantum Monte Carlo method to simulate Rydberg systems at zero-temperature and above. We then apply this simulation method alongside variational models to verify correctness of both methods. The data produced from the simulations is also used to train Neural Network wavefunctions, which we find are effectively able to grasp some of the physics of the Rydberg atom array on a square lattice.
A Machine Learning Model for Trapped-ion State Classification
(University of Waterloo, 2025-05-14) Balaniuk, Severyn
Academia and industry have been working to build a quantum computer that is able to perform certain tasks significantly better than classical computers. This thesis focuses on improving a trapped-ion-based approach to quantum computing. This platform has advanced significantly over the last 10 years, but there are numerous issues we need to resolve to make this architecture scalable. We consider experiments that use a high-sensitivity photon detection module as the readout tool. This setup lets us see qubit measurement outcomes as a fluorescent signal on a digital camera. This thesis addresses the problem of classifying fluorescence states for experimental systems of up to four ions, representing them as binary sequences. Our model hopefully will be able to classify systems with 8, 16, and 32 ions, allowing for further application of this methodology as quantum computers grow in scale. Our datasets are mainly unlabelled, which is the biggest challenge for training an accurate machine learning (ML) model. Nevertheless, we showed a significant improvement in classification accuracy with reduced bias over legacy models on unlabelled data containing mixed states of a four-ion system. We tested different machine learning architectures like feed-forward neural network (FFNN), convolutional neural networks (CNN), and semi-supervised learning to evaluate their efficiency for our specific dataset and tested their performance. In addition, we also developed and improved our own FFNN architecture with custom loss functions.
Towards Optical Simulation of Topological Phenomena with Ring Resonators
(University of Waterloo, 2025-04-30) Kuchhal, Bharat
In recent years, there has been a growing interest in synthetic dimensions. Unlike physical dimensions where one is restricted with three possible dimensions, one can tailor a lattice system with several higher order dimensions even with a lower-order physical system. In this thesis, we will explore, both theoretically and experimentally, how equidistant frequency modes in a resonator—specifically a ring resonator—can be used as a synthetic dimension. In this respect, we will first explore basics of resonators by reviewing a Fabry Perot resonator and developing a coupled-mode theory to understand its transmission and reflection spectrum. We will then expand and develop a coupled-mode theory for the case of a ring resonator, and explore experimental results for a basic fiber-beam splitter based ring resonator. Next, we will modify the ring resonator with a few off the shelf fiber optic components like a Dense Division Wavelength Multiplexing filter, a fiber electro-optic modulator, and an optical amplifier, and see how they transform the transmission characteristics. Lastly, we will modulate the ring resonator at the same frequency as the free-spectral range of the resonator to couple the modes to observe a band structure in the reciprocal space, much like atoms in a periodic solid-state crystal coupled via Coulomb interactions lead to energy bands in the conjugate momentum space. For this purpose, we will develop a coupled-mode theory for a ring resonator modulated by a phase modulator, look at some theoretical results for symmetric and asymmetric band structures, and observe some experimental results for the symmetric case. Thus, we highlight the potential of fiber ring resonators as versatile platforms for optical simulation of topological systems. Further, the ability to replicate higher-dimensional phenomena using frequency modes opens new pathways for investigating exotic physical behaviors, such as non-Hermitian systems and synthetic magnetic fields, in compact and experimentally accessible setups.
A Multi-Phase Analysis of Gas Dynamics and Perturbations in the Galaxy Cluster Cores
(University of Waterloo, 2025-02-14) Li, Muzi; McNamara, Brian
This thesis provides a detailed analysis of gas kinematics and their interactions across various phases within galaxy cluster cores. It examines the processes that generate gas perturbations and the factors that contribute to the thermal stability of the intracluster medium (ICM). A focus is placed on exploring the origins of multi-phase gas and the mechanisms—particularly AGN feedback—that either couple or decouple their motions. Radio-mechanical AGN feedback is identified as one of the most promising heating mechanisms that prevent the cooling of gas. However, the debate on the details of the heating transport processes has remained open. The atmospheres of 5 cool-core clusters, Abell 2029, Abell 2107, Abell 2151, RBS0533 and RBS0540, have short central cooling times but little evidence of cold gas, and jet-inflated bubbles. The amplitudes of gas density fluctuations were measured using a new statistical analysis of X-ray surface brightness fluctuations within the cool cores of these ‘spoil’ clusters in Chapter 2. The derived velocities of gas motions, typically around 100 - 200 km/s, are comparable to those in atmospheres around central galaxies experiencing energetic feedback, such as in the Perseus Cluster, and align well with the turbulent velocities expected in the ICM. Regardless of the mechanisms driving these perturbations, turbulent heating appears sufficient to counteract radiative losses in four of the five spoiler cluster cores. We thus suggest that other mechanisms, such as gas sloshing, may be responsible for generating turbulence, offering a plausible solution to suppress cooling in these structureless atmospheres. Multiphase filaments, key byproducts of AGN feedback, are frequently observed near central galaxies, with their morphologies and kinematics closely linked to bubbles. In Chapter 3, we analyzed the velocity structure functions (VSFs) of warm ionized gas and cold molecular gas, identified through [OII] emission and CO emissions observed by the Keck Cosmic Web Imager (KCWI) and the Atacama Large Millimeter/submillimeter Array (ALMA), respectively, in four clusters: Abell 1835, PKS 0745-191, Abell 262, and RXJ0820.9+0752. Excluding Abell 262, where gas forms a circumnuclear disk, the remaining clusters exhibit VSFs steeper than the Kolmogorov slope. The VSFs of CO and [OII] in RXJ0820 and Abell 262 show close alignment, whereas in PKS 0745 and Abell 1835, were differentiated across most scales, likely due to the churning caused by the radio-AGN. The large-scale consistency in Abell 1835 and RXJ0820, together with scale-dependent velocity amplitudes of the hot atmospheres obtained from Chandra X-ray data, may support the idea of cold gas condensation from the hot atmospheres. X-ray observations have previously been constrained by low energy resolution, which has impeded direct measurements of velocity fields in galaxy clusters. However, the recent release of initial data from the X-ray Imaging and Spectroscopy Mission (XRISM) provides a non-dispersive energy resolution of about 5 eV, facilitating the measurement of line broadening and shifts. In Chapter 4 of this thesis, I detail my contributions to calibrating the optical blocking filters for XRISM using synchrotron beamlines at the Canadian Light Source (CLS) and Advanced Light Source (ALS) prior to its launch, and I discuss the model-based estimation of the parameters of the calibrated filters. This capability for direct measurement of plasma velocities is expected to greatly improve our understanding of the ICM dynamics with high accuracy.
Investigating Abundances in Galaxy Clusters and Gas Motions in M87 using XRISM
(University of Waterloo, 2025-01-24) Dizdar, Neo; McNamara, Brian
Galaxy clusters are the forefront of extragalactic diffuse X-ray astrophysics, yet there are still many questions about their formation and evolution. The creation of XRISM, a new X-ray imaging and spectroscopy mission, will study the metal abundance history of clusters and the conversion of jet energy into atmospheric kinetic energy. XRISM’s payload contains an instrument with the highest spectral resolution (5 eV) in the field of X-ray astronomy so far. With this resolution, we observed metal abundances and the broadening of metal lines through turbulent motions in the intracluster medium. In this thesis I present the conversion of data from the Chandra X-ray Observatory to XRISM’s high-resolution format. This includes the preparation and selection of clusters in Chandra, simulating selected clusters for XRISM and applying for proposals. Finally, we extracted abundance and velocity information from the Virgo cluster’s early XRISM data.
On the Initial Boundary Value Problem in Numerical Relativity
(University of Waterloo, 2025-01-23) Dailey, Conner; Afshordi, Niayesh; Schnetter, Erik
The principal goal of this thesis is to properly understand, characterize, and numerically implement initial boundary value problems in numerical relativity. Throughout the history of solving Einstein's field equations on computers, boundaries have been mostly dealt with in an approximate way. For example, boundaries might be placed far away from strongly gravitating sources, where approximations like linearized gravity are valid. It has become necessary however to place boundaries in the strong gravity regime of a dynamical spacetime to model complicated and interesting physics, which necessitates a complete understanding of the initial boundary value problem of Einstein's field equations. One motivation for this comes from a need to simulate black hole echoes. In classical general relativity, black holes are perfectly absorbing objects, where the mass of radially incoming wavepackets of matter or gravitational waves is absorbed by the black hole. Thus conclusive evidence of modifications to general relativity, such as quantum gravity, could include partial reflections of radially incoming wavepackets, called black hole echoes. To properly understand the modifications this would bring to detectable gravitational wave signals, we require simulations where reflecting boundary conditions are imposed close to the horizon of a black hole. Another motivation comes from recent advances in Cauchy characteristic matching, which combines state of the art numerical techniques to obtain physically accurate gravitational waveforms from simulations. This can allow numerical relativists to dramatically save on the computational cost of black hole merger simulations, but only if boundaries can be placed in the strong gravity regime. This thesis presents advances in simulating initial boundary value problems in numerical relativity. Starting with spherical symmetry, a framework for reflecting a scalar field in a fully dynamical spacetime is developed and implemented numerically using the Einstein-Christoffel formulation. The evolution of a wave packet and its numerical convergence, including when the location of a reflecting boundary is very close to the horizon of a black hole, is studied. Next, this approach is generalized to spacetimes with no symmetries and implemented numerically using the generalized harmonic formulation. The evolution equations are cast into a summation by parts scheme, which seats the numerical method closer to a class of provably numerically stable systems. State of the art numerical methods are demonstrated, including an embedded boundary numerical method that allows for arbitrarily shaped domains on a rectangular grid and even boundaries that evolve and move across the grid. As a demonstration of these frameworks, the evolution of gravitational wave scattering off of a boundary either inside or just outside the horizon of a black hole, is studied. Finally, a boundary condition framework designed to control quasi-local energy flux is proposed motivated by examples from electromagnetism.
Studies on the 1/f noise in Shunted Josephson Junctions and Effective Masses in 2DHG GaAs Hall Bars
(University of Waterloo, 2025-01-22) Coschizza, Andree; Kycia, Jan
Two projects are presented with the motivation of improving materials and devices for superconducting and semiconducting qubit applications. The first project focuses on quantifying the 1/f noise in SIS Josephson junctions using a dc SQUID. The current-voltage characteristics of two junctions are measured and the degree of thermal rounding is analyzed as a function of temperature. The current-voltage characteristics are then used to compute the voltage bias dependence of both the 1/f and white noise of the junction. Finally, the temperature dependence of the 1/f noise is investigated and found to exhibit a linear relationship within the region of 100mK-4.5K. This is then compared to similar systems in literature. The second project explores a GaAs/AlGaAs 2DHG system using quantum Hall effect measurements. The mobility and charge carrier density dependence is calculated, and an experiment is conducted to investigate their dependence on highly negative top gates. It is discovered that the mobility-density curve increases as the top gate is pushed to more negative values. Furthermore, the spin-orbit interaction is parameterized and compared to previously measured samples. Finally, the band structure of GaAs/AlGaAs holes is discussed in reference to the observed Shubnikov-de Haas oscillations. The effective mass corresponding to the light heavy hole subband is measured using the Ando, Fowler, and Stern equation at low magnetic field oscillations.
Time-resolved and equilibrium resonant X-ray studies of nematicity in cuprate superconductors
(University of Waterloo, 2025-01-16) Gupta, Naman Kumar; Hawthorn, David
Attracting four decades of experimental and theoretical investigations since the discovery of high-temperature superconductivity, cuprates have become an essential benchmark for the exploration of intertwined electronic symmetry-breaking phases such as superconductivity, magnetism, nematicity, charge or spin density wave order in strongly correlated systems. Understanding how these phases are intertwined is of general and fundamental interest to a wide range of quantum materials. This doctoral work employs the element- and orbital-specific sensitivity of time-resolved and equilibrium resonant X-ray scattering to investigate electronic nematicity and charge density wave (CDW) order in cuprates. By probing their responses to photoexcitation using ultrafast laser pump-probe setups, varying hole doping levels, and applying compressive uniaxial stress, this thesis attempts to disentangle, understand, and manipulate intertwined phases in stripe-ordered cuprates.
Neurovascular Coupling in healthy human retina evaluated with Optical Coherence Tomography
(University of Waterloo, 2024-12-21) Dhaliwal, Khushmeet; Bizheva, Kostadinka
Retinal neurodegenerative diseases such as glaucoma, age-related macular degeneration (AMD), diabetic retinopathy, and retinitis pigmentosa affect millions of people worldwide and pose a significant burden on public health and the economy. Glaucoma, impacting approximately 80 million people globally, is a leading cause of irreversible blindness. In 2019, an estimated 19.8 million Americans (12.6%) were living with AMD, of which about 1.49 million people faced vision-threatening conditions. An estimated 9.6 million people were living with diabetic retinopathy in 2021, with about 1.84 million of them experiencing vision-threatening stages. In the United States alone, vision impairments- including those resulting from these retinal diseases- cost an estimated $139 billion annually. Retinal neurodegenerative diseases not only cause progressive damage to the retinal morphology and vascular network, but also cause acute and transient metabolic, physiological, and blood flow changes at the early stages of the disease development which become permanent and chronic at the advanced stages of the disease. Neurovascular Coupling (NVC) refers to the transient vasodilation and increased retinal blood flow resulting from the increased metabolic activity of retinal neurons in response to visual stimulation. Over the past few decades, a range of imaging techniques from clinical ophthalmoscope and confocal microscopy to adaptive optics scanning laser ophthalmoscope and optical coherence tomography (OCT) have been used ex vivo and in vivo to study components of the neurovascular coupling and its underlying mechanisms. Techniques such as Laser Doppler Velocimetry, Optical Coherence Tomography Angiography (OCTA), and Doppler Optical Coherence Tomography (D-OCT) have been used to observe the vascular responses of the retina caused by visual stimulation. Additionally, Electroretinography (ERG) has been widely used in clinical settings to evaluate the electrical activity of the neuronal retina. More recently, an optical equivalent to ERG, Optoretinography (ORG) was developed and OCT technology, imaging protocols, and image processing algorithms were designed to conduct OCT-based ORG studies in the human and animal retina. However, most of the Doppler OCT, OCTA, and ORG studies have examined components of the neurovascular coupling separately, potentially overlooking the dynamic interactions and comprehensive responses inherent in neurovascular coupling. OCT, which acquires simultaneously both intensity and phase information, is particularly well-suited for investigating neurovascular coupling in the retina, as it enables a completely non-invasive approach for simultaneous monitoring of retinal blood flow dynamics and neuronal responses. The integration of a commercial ERG system with a research-grade OCT modality adds further value by offering easy control of the visual stimulus, use of clinically established ERG protocols designed to elicit responses from specific types of retinal neuronal cells, and using the ERG recordings to validate the visually-evoked neuronal responses. The main objectives of this PhD thesis were: 1. To develop a combined OCT+ERG imaging system to conduct in vivo and simultaneously morphological and functional imaging that can be utilized for investigating neurovascular coupling in the human retina. 2. To evaluate the performance and capabilities of the OCT+ERG system, imaging protocols, and image processing algorithms by conducting a pilot study on healthy human subjects. 3. To utilize the OCT+ERG technology to explore the neurovascular coupling mechanisms in the healthy human retina by extracting vascular and neuronal responses from different retinal layers simultaneously. 4. To examine the effects of different wavelengths and flicker frequencies on the dynamic retinal blood flow changes evoked by visual stimulation, providing deeper insights into the mechanisms of neurovascular coupling. Results from this PhD research have been summarized in three manuscripts that are either under review or under preparation for submission. Therefore, this PhD thesis was prepared in such a way that individual manuscripts represent separate thesis chapters.
The Evolution of Halo Properties Through Binary Major Mergers
(University of Waterloo, 2024-10-17) Marchioni, Justin; Taylor, James
Galaxy clusters are massive, gravitationally bound objects composed of a large population of galaxies. Each of these galaxies occupies a dark matter halo and collectively the cluster has its own extended halo. Cluster halos can be described by many structural properties including their mass, concentration, shape, spin, and asymmetry. These properties, among others, can be used as proxies to constrain cosmology. The issue with galaxy clusters is that they are still assembling at the present-day. These clusters primarily grow through mergers, where smaller systems coalesce to form larger ones. If the mass ratio between the two merging components is sufficiently large (i.e. 3:1 or below), this is known as a major merger. The effect of major mergers is to significantly redistribute the matter distribution in the host system. This leads to pronounced fluctuations in the cluster's structural properties during the merger, making measurements of these properties hard to interpret. Therefore, accurately predicting how cluster properties vary during mergers is important in order to use them as a cosmological tool. In this thesis, we use simulations to study how the structure of remnant systems evolves during mergers. These simulations consider the merger of two isolated components, each represented by truncated Navarro-Frenk-White (NFW) profiles. We find that mergers produce oscillations in structural parameters for both the overall remnant and the host system. For example, the host halo's concentration experiences one of two types of responses to the satellite's motion depending primarily on the pericentric passage distance of the orbit. Given the simulation results, we present a semi-analytic model for the evolution of structure in remnant systems due to isolated, binary mergers. The model consists of two components, a treatment for the orbital evolution of the satellite and a prescription for changes in the host halo's potential. This second component is often neglected when modeling satellite orbits in minor mergers. Interestingly, we find that adding a host halo response model has little impact on the orbital evolution of the satellite and its mass loss. In contrast, this model must be incorporated in order to accurately predict how the remnant's structure changes after the satellite first passes pericentre. While our model generally works well at replicating the median concentration for the first two orbits, it is unable to recreate any of the remnant's anisotropy properties (i.e. shape, spin, and asymmetry). Overall, our results provide a framework for analyzing the response of cluster halo properties to mergers in more realistic scenarios.
Characterization and First Results of an Inverse Photoemission Spectrometer
(University of Waterloo, 2024-09-26) Bouliane, Michael; Hawthorn, David
This thesis discusses our efforts to characterize our home built inverse photoemission spectrometer. We review the relevant theoretical and practical considerations for the technique of inverse photoemssion spectroscopy. We then detail our efforts to characterize our low energy electron gun, presenting a method for determining the total current delivered by the beam using just a Faraday cup. Measurements of the beam’s profile are presented and are used to calculate the parallel momentum resolution of the beam. Equally important is the characterization of our photon detectors, which we show are operating in the proportional region with a minimal dark count rate. We ascertained a spectrometer energy resolution of 415(55) meV by performing inverse photoemission measurements on polycrystalline gold foil, single crystal Cu (111), and pyrolytic graphite. As a final demonstration of our spectrometer’s capabilities we provide a full unoccupied band mapping for pyrolytic graphite showing its ability to resolve dispersive electronic features in reciprocal space.
Towards Large Scale Quantum Simulations with Trapped Ions: Programmable XY model, Precise Light Sensing, and Extreme High Vacuum
(University of Waterloo, 2024-09-24) Kotibhaskar, Nikhil; Islam, Rajibul
We are currently witnessing a revolution in quantum technologies. Today's controllable quantum devices have reached a complexity that makes it practically intractable to fully simulate their dynamics using current classical supercomputers. Decades of fundamental research and development have led us to this point. In the coming years, billions of dollars in investments from governments and private entities are expected worldwide. Although general-purpose fault-tolerant quantum computers are expected to impact computing profoundly, today's quantum devices are best suited for their analog quantum operation, where a well-controlled quantum simulator mimics the dynamics of the other quantum system being studied. This affords an advantage over classical simulators at the cost of a restricted set of physical phenomena that can be studied. Today's quantum devices are already providing insights into large-scale entanglement, the underlying physics of high-temperature superconductivity, disordered quantum systems, and much more. Enhancing the capabilities of today's analog quantum simulators requires adding more classes of interactions, reducing errors due to calibration and noise, and increasing the system size to allow larger-scale simulations. The work described in this thesis directly addresses these core points for a system of trapped ions, which are ideal quantum simulators of the coupled dynamics of a large number of magnetic spins. First, the theory and experiment pertaining to the simulation of the anisotropic XY model on trapped ions has been presented. The theoretical proposal does not require added technical improvements over what has existed in the field for over a decade. The experimental validation is performed on a system with two 171Yb+ ions. This directly enhances the repertoire of trapped ions simulators and opens avenues to the exploration of high-temperature superconductivity, superfluidity, and spin liquids. The second result is the demonstration of the highest resolution readout of optical intensity and polarization using a single 171Yb+ ion as the field probe. The technique utilized the intensity- and polarization-dependent optical pumping of the ions as a signature to detect light parameters. This will be useful for the characterization of the optical addressing fields in trapped ion quantum simulators and hence for the calibration of large-scale quantum devices. Finally, the design and construction of a large-scale ion trapping apparatus for quantum simulation are described. The ion trap allows for the trapping of more than 50 ions, and the vacuum chamber used to house the trap with pressure below 1.5E-12 mbar (measurement limited by pressure gauge saturation) likely sets a record for the lowest pressure achieved on a room-temperature trapped ions system. This increases the useful simulation time of large-scale trapped-ion devices and paves the way for further enhancement of the scale of the simulations performed. Together, these results are another step in advancing the capabilities of today's quantum devices to explore physical phenomena far beyond the capability of classical supercomputers.
Development of the CHORD Galaxy Search Strategy
(University of Waterloo, 2024-09-24) Hopkins, Hans; Lang, Dustin; Taylor, James
This thesis presents my contribution to the CHORD galaxies science case. I helped develop an algorithm that can automatically pick out galaxies from CHORD driftscan data. The method used is a matched filter, and it acts on spatial data and spectral data. On the spatial side, it searches for point sources. Because CHORD is a highly redundant interferometer, it suffers from spatial aliasing. I present a program that is able to predict the severity of spatial aliasing. It predicts that integrating over periods of time is required to break the alias degeneracy, and that "dithering" CHORD (rotating it by a couple degrees) further helps in reducing the alias issue. I offer a framework for estimating the probability of spatial alias confusion. On the frequency side, I present a method of running the matched filter quickly. CHORD frequency data undergoes a process called upchannelization, which would distort the shape of a galaxy profile. I show how this can be accounted for without incurring a large time-cost penalty. Lastly, I discuss how a full matched filter program would be put together, and implications that my research has on selecting search parameters for a future CHORD galaxy survey.
Studying Unmodeled Physics from Gravitational Wave Data
(University of Waterloo, 2024-09-24) Dideron, Guillaume; Lehner, Luis
This thesis explores the detection and analysis of unmodeled physics in Gravitational Wave (GW) data. To this end, we develop the SCoRe framework, which uses the Correlated Residual Power Spectrum (CRPS) between pairs of detectors to identify deviations from our Standard Model (SM) of GW. This model includes General Relativity (GR) as the theory describing gravity, binary Black Holes (BHs) and Neutron Star (NS) merging as the sources of GWs, our model of the noise in the detectors, and the template waveform models used for data analysis. The thesis starts with a theoretical overview of GW physics, including an overview of GR, and how it describes the way GWs are generated and how they propagate and interact with matter. We then discuss the practical aspects of GW detection: the modelling of the noise in the detectors and the data analysis techniques used to extract and interpret GW signals. Next, we describe the SCoRe framework in Chapter 2, which is designed to distinguish between noise and deviations from the SM, while also shedding light on the underlying physics of the deviation. We detail its three main components: cross-correlating residual power between detectors, projecting onto physically motivated or agnostic bases, and combining information from multiple events by assuming a dependence of the unmodeled physics on the source parameters. To illustrate the method, we apply the SCoRe framework to toy models in Chapter 3. We demonstrate how the method can recover unmodeled signals without prior assumptions about their form, how to choose the timescale of cross-correlation, and how the method can be used to perform a null test of the SM. In Chapter 4, we then forecast the precision with which the SCoRe method can recover a deviation from the SM from a population of Binary Black Hole (BBH) mergers observed by a network of third-generation GW detectors. As the method leverages the dependence of the deviation from the SM on the source parameters, we investigate the effect the distribution of these parameters has on the method. For a model where the deviation scales with the chirp mass as a decaying power law, we show that the precision of the constraints on the deviation decreases as the power law becomes steeper. This has implications for constraining higher-dimensional operators in Effective Field Theories (EFTs) of gravity: higher dimensional operators correspond to steeper power laws and are, therefore, harder to constrain with the method. Finally, in Chapter 5, we illustrate another approach to testing the SM of GWs, where the GW signal in an alternative theory of gravity is numerically computed. We give an overview of the mathematical challenges and describe a method, the “fixing the equations” method, which aims to reduce pathologies in evolving EFTs of gravity by controlling energy flow to high frequencies.
Path Integral Monte Carlo simulations of solid parahydrogen using many-body interaction potentials
(University of Waterloo, 2024-09-23) Ibrahim, Alexander; Roy, Pierre-Nicholas
We construct ab initio many-body potential energy surfaces (PES) and use them to perform high-accuracy path integral Monte Carlo (PIMC) simulations of solid parahydrogen. We first perform PIMC simulations of solid parahydrogen using the Faruk-Schmidt-Hinde (FSH) potential, an ab initio 1D two-body PES for parahydrogen constructed by the Roy group in 2015. The simulations are successful at reproducing experimental results for the equilibrium density and for the vibrational matrix shift for solid parahydrogen. However, we find that the two-body PES on its own is too energetically repulsive at higher densities, and greatly overestimates the pressure as a function of density. To improve the accuracy of our simulations, we must include higher-order many-body interactions, such as the three-body and four-body interactions. We then construct an isotropic ab initio three-body PES for parahydrogen. The energies are calculated using the coupled cluster method with singles, doubles, and perturbative triples excitations (CCSD(T)). The calculations are performed using an AVTZ atom-centred basis set, with additional (3s3p2d) midbond functions. We use a machine learning method called the reproducing kernel Hilbert space (RKHS) method to construct a PES from the ab initio energies. The three-body PES is attractive at short distances. We perform PIMC simulations of solid parahydrogen using both the two-body FSH potential and the new three-body PES. The inclusion of the three-body PES improves the agreement with experiment at lower densities. However, at higher densities, the attractive interaction of the three-body PES overcorrects for the repulsive wall of the two-body PES, resulting in a severe underestimation of the pressure-density curve. Next, we construct an isotropic ab initio four-body PES for parahydrogen. The energies are calculated using the CCSD(T) method, using an AVDZ atom-centred basis set with additional (3s3p2d) midbond functions. We use a multilayer perceptron (MLP) to construct a PES from the ab initio energies. We find that the four-body PES is repulsive at short distances. We anticipate that the inclusion of the four-body PES alongside the aforementioned two-body and three-body PESs will improve the agreement of the PIMC simulations of solid parahydrogen with experiment to higher densities than previously found.
Spectral, information-theoretic, and perturbative methods for quantum learning and error mitigation
(University of Waterloo, 2024-09-17) Peters, Evan; Kempf, Achim
We present spectral and information-theoretic characterizations of learning tasks involving quantum systems, and develop new perturbative error mitigation techniques for near-term devices. In the first part of this thesis, we explore connections between quantum information and learning theory. We demonstrate theoretically that kernel bandwidth enables quantum kernel methods associated with a high dimensional quantum feature space to generalize. We then characterize quantum machine learning models that generalize despite overfitting their training data, contradicting standard expectations from learning theory. In such learning tasks, the learner may fail due to noise in the input data. So we next consider a setting where the learner has access to correlated auxiliary noise, a resource that contains information about an otherwise unknown noise source corrupting input data. We use classical Shannon theory to relate the strength of these correlations to the classical capacity of a bit flip channel with correlated auxiliary noise, and we extend this analysis to derive the quantum capacity of a quantum bit flip channel given access to an auxiliary system entangled with the environmental source of the noise. Finally, we derive an information-theoretic guarantee for the learnability of data by an optimal learner and, extending this technique to a quantum setting, we introduce and characterize an entanglement manipulation task that generalizes the notion of classical learning. The second part of this thesis introduces techniques for error mitigation on near-term quantum processors and provides guarantees in the perturbative limit. We introduce a technique for mitigating measurement errors using truncated matrix operations. We then propose and characterize a technique that uses the time-reversibility of a quantum circuit to measure the quality of a subset of qubits, and we apply this technique to assign logical circuits to qubits on a physical device in a nearly optimal manner using a simulated annealing optimization algorithm.
Automated Tuning and Optimal Control of Spin Qubits in Quantum Dot Devices
(University of Waterloo, 2024-09-17) Paurevic, Andrija; Baugh, Jonathan
Silicon quantum dots present a promising foundation for realizing scalable quantum processors, leveraging the advantages of a mature semiconductor industry. Two significant challenges hinder their development: the laborious tuning of these devices and the coherent control of their spin qubits. This thesis presents contributions towards addressing these challenges by harnessing physics-informed machine learning. Tuning these devices involves navigating complex parameter spaces, plagued with variability and fabrication imperfections, to identify optimal operating conditions. This process demands extensive time and resources by a researcher to perform large amounts of data collection and analysis. My work takes steps towards on achieving fully autonomous tuning of these devices, with the automated formation of a single quantum dot. This work involves the application of data analysis and computer vision techniques to extract relevant features from data, guiding the tuning process in real-time. This tool allows single quantum dots to be formed autonomously, freeing researchers to focus on investigating the physics of the device. Progress in multi-dot systems was also made by developing a data segmentation model that successfully identifies and segments charge and dot configurations in charge stability diagram data. This enables rapid data analysis to determine optimal voltage settings for achieving the desired device state. Optimal control is crucial for guiding quantum systems through unitary operations while minimizing decoherence. Using a simulated open quantum system Hamiltonian for spin qubits, I developed a protocol to optimize experimental control signals, allowing for the implementation of unitary gate operations with arbitrary fidelity. The protocol designed experimental pulses for single-qubit rotations and entangling gates in a two-qubit system, achieving fidelities above the error correction threshold. Additionally, it utilizes modern machine learning frameworks, making it scalable to multi-qubit systems. The work presented in this thesis serves as an important foundation for future advancements in our research group.
Practical design and demonstration of algorithms for quantum devices
(University of Waterloo, 2024-09-17) Ray, Annie; Laflamme, Raymond
The emergence of noisy intermediate-scale quantum (NISQ) devices represents a significant milestone in the journey towards the development of large-scale fault tolerant quantum computers. These devices have not only opened avenues for demonstrating a quantum advantage but have also advanced the practical development of quantum algorithms for solving challenging problems in physics, chemistry, and computer science. Most notably, this progress has necessitated a tailored approach to algorithm development that considers the specific architecture and hardware constraints of these quantum devices in order to effectively use them. However, the most useful instances of problems that we hope to solve with quantum computers require significant hardware improvements over the state-of-the-art, including at least a hundred fold increase in the number of qubits. The transition from intermediate-scale to large-scale quantum computers also presents other formidable challenges, particularly for engineering precise quantum control at scale. This thesis attempts to narrow the gap between intermediate and large-scale devices by proposing methods to mitigate noise effects on NISQ devices and by enhancing standard quantum algorithms to minimize resource overhead. One focus is on error correction strategies capable of managing noise on quantum devices. Specifically, we demonstrate the robustness of the sweep rule (a decoder for topological quantum codes) against measurement errors in quantum codes. Additionally, we experimentally demonstrate the improvement in performance of entangling non-Clifford operations when encoded in the [[8,3,2]] code, strengthening the case for error correction. Furthermore, we improve a well-known technique known as imaginary time evolution to reduce the associated qubit and entangling gate overhead, making it more amenable to implementation on NISQ devices. By exploring these avenues, we aim to strike a balance, leveraging NISQ devices to expand their computational capabilities in the short term while serving as a sandbox for the development of future large-scale fault-tolerant quantum computers.
Analytical and Computational Studies of Quasi-1D Spin Models
(University of Waterloo, 2024-09-16) Chen, Yushao; He, Yin-Chen; Melko, Roger
This thesis explores quasi one-dimensional (quasi-1D) quantum spin systems, specifically focusing on Kitaev ladders, Heisenberg ladders, and Motzkin chains. The research employs a combination of analytical and numerical tools to systematically study the phase diagrams of these low-dimensional spin lattices, developing a standardized pipeline for analyzing future models of interest within the field of quantum physics. At the core of this investigation is the deep interconnection between low-dimensional quantum systems and their corresponding tensor network structures. Utilizing Matrix Product States (MPS) and the Density Matrix Renormalization Group (DMRG) methodologies, the thesis provides detailed insights into the phase behaviors of these quasi-1D systems. This includes examining novel phenomena such as quantum spin liquids, various magnetic orderings, and symmetry-protected topological orders. These findings not only enhance our understanding of quantum physics but also highlight the effectiveness and adaptability of tensor network approaches in tackling complex theoretical problems.
Aspects of Quantum Gravity: From Black Hole Thermodynamics to Holography
(University of Waterloo, 2024-09-16) Yang, Jiayue; Mann, Robert; Afshordi, Niayesh
Understanding the nature of quantum gravity remains one of the cutting-edge challenges in modern theoretical physics. Despite widespread interest and extensive research, the formulation of a complete theory of quantum gravity remains an unsolved problem. This thesis aims to explore quantum gravity from two primary perspectives: black hole thermodynamics and holography. Black hole chemistry extends black hole thermodynamics by incorporating the cosmological constant, treating the black hole mass as enthalpy rather than energy, and interpreting the cosmological constant and its conjugate variable as pressure and volume, respectively. Holographic complexity investigates the duality between gravitational quantities in the bulk and quantum complexity on the boundary. This includes various proposals such as complexity=volume (CV), complexity=spacetime volume (CV2.0), complexity=action (CA), and complexity=anything proposals. In our exploration of black hole thermodynamics, we investigate phase transitions near quadruple points, where four distinct black hole phases coexist. Utilizing the free-energy landscape technique within the framework of four-dimensional Einstein gravity coupled with nonlinear electrodynamics (NLE), we undertake the first investigation into the dynamics of recently discovered multicriticality in black holes. By treating off-shell Gibbs free energy as a potential and solving the Smoluchowski equation numerically, we capture the evolution of the state probability distributions during black hole phase transitions. Our study reveals how off-shell Gibbs free energy, shaped by ensemble temperatures, influences these transitions and highlights intricate behaviours such as weak and strong oscillations. In our investigation of holography, we analyze the complexity of conformal field theories (CFTs) compactified on a circle with a Wilson line, corresponding to magnetized solitons in four-dimensional and five-dimensional Anti-de Sitter space (AdS). We explore three distinct proposals for holographic complexity. Our study reveals that these proposals exhibit a confinement-deconfinement phase transition driven by variations in the Wilson line, with the complexity of formation acting as the order parameter for this transition. We find that the proposed volume and action complexity functionals obey a scaling relation with the radius of the circle. We show that this scaling law is applicable to a broad family of potential complexity functionals and conjecture that the scaling law applies to the complexity of conformal field theories on a circle in more general circumstances.

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