Physical Sciences and Mathematics Commons^™

Quantics Tensor Trains: The Study Of A Continuous Lattice Model And Beyond, Aleix Bou Comas

Dissertations, Theses, and Capstone Projects

This four-chapter dissertation studies the efficient discretization of continuous variable functions with tensor train representation. The first chapter describes all the methodology used to discretize functions and store them efficiently. In this section, the algorithm tensor renormalization group is explained for self-containment purposes. The second chapter centers around the XY model. Quantics tensor trains are used to describe the transfer matrix of the model and compute one and two-dimensional quantities. The one dimensional magnitudes are compared to analytical results with an agreement close to machine precision. As for two dimensions, the analytical results cannot be computed. However, the critical temperature …

Improving The Scalability Of Neural Network Surface Code Decoders, Kevin Wu

Undergraduate Honors Theses

Quantum computers have recently gained significant recognition due to their ability to solve problems intractable to classical computers. However, due to difficulties in building actual quantum computers, they have large error rates. Thus, advancements in quantum error correction are urgently needed to improve both their reliability and scalability. Here, we first present a type of topological quantum error correction code called the surface code, and we discuss recent developments and challenges of creating neural network decoders for surface codes. In particular, the amount of training data needed to reach the performance of algorithmic decoders grows exponentially with the size of …

The Black-To-White Hole Transition, Farshid Soltani

Electronic Thesis and Dissertation Repository

Classically, an isolated black hole is a stable gravitational object. If however semiclassical effects are taken into account, an isolated black hole can be shown to slowly radiate its mass away in a process called evaporation. At the end of the evaporation process, when the size of the horizon becomes Planckian, the quantum nature of the gravitational field can no longer be neglected and the dynamics of the horizon is governed by quantum gravity. The main objective of this thesis is the systematic investigation of a tentative scenario for the “end of the life” of a black hole: the black-to-white …

Quantum Chaos, Integrability, And Hydrodynamics In Nonequilibrium Quantum Matter, Javier Lopez Piqueres

Doctoral Dissertations

It is well-known that the Hilbert space of a quantum many-body system grows exponentially with the number of particles in the system. Drive the system out of equilibrium so that the degrees of freedom are now dynamic and the result is an extremely complicated problem. With that comes a vast landscape of new physics, which we are just recently starting to explore. In this proposal, we study the dynam- ics of two paradigmatic classes of quantum many-body systems: quantum chaotic and integrable systems. We leverage certain tools commonly employed in equilibrium many-body physics, as well as others tailored to the …

Toward Local Madelung Mechanics In Spacetime, Mordecai Waegell

Mathematics, Physics, and Computer Science Faculty Articles and Research

It has recently been shown that relativistic quantum theory leads to a local interpretation of quantum mechanics wherein the universal wavefunction in configuration space is entirely replaced with an ensemble of local fluid equations in spacetime. For want of a fully relativistic quantum fluid treatment, we develop a model using the nonrelativistic Madelung equations, and obtain conditions for them to be local in spacetime. Every particle in the Madelung fluid is equally real, and has a definite position, momentum, kinetic energy, and potential energy. These are obtained by defining quantum momentum and kinetic energy densities for the fluid and separating …

Mechanistic Investigation Of C—C Bond Activation Of Phosphaalkynes With Pt(0) Complexes, Roberto M. Escobar, Abdurrahman C. Ateşin, Christian Müller, William D. Jones, Tülay Ateşin

Research Symposium

Carbon–carbon (C–C) bond activation has gained increased attention as a direct method for the synthesis of pharmaceuticals. Due to the thermodynamic stability and kinetic inaccessibility of the C–C bonds, however, activation of C–C bonds by homogeneous transition-metal catalysts under mild homogeneous conditions is still a challenge. Most of the systems in which the activation occurs either have aromatization or relief of ring strain as the primary driving force. The activation of unstrained C–C bonds of phosphaalkynes does not have this advantage. This study employs Density Functional Theory (DFT) calculations to elucidate Pt(0)-mediated C–CP bond activation mechanisms in phosphaalkynes. Investigating the …

Instability And Quantization In Quantum Hydrodynamics, Yakir Aharonov, Tomer Shushi

Mathematics, Physics, and Computer Science Faculty Articles and Research

We show how the quantum hydrodynamical formulation of quantum mechanics converts the nonlocality in the standard wave-like description of quantum systems by an instability of the quantum system, which opens the door to a new way for studying quantum systems based on known methodologies for studying the stability of fluids. As a second result, we show how the Madelung equations describe quantized energies without any external quantization conditions.

Comment On “Photons Can Tell ‘Contradictory’ Answer About Where They Have Been”, Gregory Reznick, Carlotta Versmold, Jan Dziewior, Florian Huber, Harald Weinfurter, Justin Dressel, Lev Vaidman

Mathematics, Physics, and Computer Science Faculty Articles and Research

Yuan and Feng (Eur. Phys. J. Plus 138:70, 2023) recently proposed a modification of the nested Mach–Zehnder interferometer experiment performed by Danan et al. (Phys. Rev. Lett. 111:240402, 2013) and argued that photons give “contradictory” answers about where they have been, when traces are locally imprinted on them in different ways. They concluded that their results are comprehensible from what they call the “three-path interference viewpoint,” but difficult to explain from the “discontinuous trajectory” viewpoint advocated by Danan et al. We argue that the weak trace approach (the basis of the “discontinuous trajectory” viewpoint) provides a consistent explanation of the …

Improving The Proof Of The Born Rule Using A Physical Requirement On The Dynamics Of Quantum Particles, Yakir Aharonov, Tomer Shushi

Mathematics, Physics, and Computer Science Faculty Articles and Research

We propose a complete proof of the Born rule using an additional postulate stating that for a short enough time Δt between two measurements, a property of a particle will keep its values fixed. This dynamical postulate allows us to produce the Born rule in its explicit form by improving the result given in [1]. While the proposed postulate is still not part of the quantum mechanics postulates, every experiment obeys it, and it cannot be deduced using the standard postulates of quantum mechanics.

Gaussian Rbf Kernels Via Fock Spaces: Quaternionic And Several Complex Variables Settings, Antonino De Martino, Kamal Diki

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper, we study two extensions of the complex-valued Gaussian radial basis function (RBF) kernel and discuss their connections with Fock spaces in two different settings. First, we introduce the quaternionic Gaussian RBF kernel constructed using the theory of slice hyperholomorphic functions. Then, we consider the case of Gaussian RBF kernels in several complex variables.

Stabilizing Two-Qubit Entanglement With Dynamically Decoupled Active Feedback, Sacha Greenfield, Leigh Martin, Felix Motzoi, K. Birgitta Whaley, Justin Dressel, Eli M. Levenson-Falk

Mathematics, Physics, and Computer Science Faculty Articles and Research

We propose and analyze a protocol for stabilizing a maximally entangled state of two noninteracting qubits using active state-dependent feedback from a continuous two-qubit half-parity measurement in coordination with a concurrent, noncommuting dynamical decoupling drive. We demonstrate that such a drive can be simultaneous with the measurement and feedback, while also playing a key part in the feedback protocol itself. We show that robust stabilization with near-unit fidelity can be achieved even in the presence of realistic nonidealities, such as time delay in the feedback loop, imperfect state-tracking, inefficient measurements, dephasing from 1/f-distributed qubit-frequency noise, and relaxation. We …

Probing Central Spin Decoherence Dynamics Of Electronic Point Defects In Diamond And Silicon, Ethan Que Williams

Dartmouth College Ph.D Dissertations

Electron spins of point defects in diamond and silicon can exhibit long coherence times, making them attractive platforms for the physical implementation of qubits for quantum sensing and quantum computing. To realize these technologies, it is essential to understand the mechanisms that limit their coherence. Decoherence of these systems is well described by the central spin model, wherein the central electron spin weakly interacts with numerous electron and nuclear spins in its environment. The dynamics of the resultant dephasing can be probed with pulse electron paramagnetic resonance (pEPR) experiments.

Using a 2.5 GHz pEPR spectrometer built in-house, we performed multi-pulse …

Exciton Dynamics, Interaction, And Transport In Monolayers Of Transition Metal Dichalcogenides, Saroj Chand

Dissertations, Theses, and Capstone Projects

Monolayers Transition metal dichalcogenides (TMDs) have attracted much attention in recent years due to their promising optical and electronic properties for applications in optoelectronic devices. The rich multivalley band structure and sizable spin-orbit coupling in monolayer TMDs result in several optically bright and dark excitonic states with different spin and valley configurations. In the proposed works, we have developed experimental techniques and theoretical models to study the dynamics, interactions, and transport of both dark and bright excitons.

In W-based monolayers of TMDs, the momentum dark exciton cannot typically recombine optically, but they represent the lowest excitonic state of the system …

Programmable Heisenberg Interactions Between Floquet Qubits, Long B. Nguyen, Yosep Kim, Akel Hashim, Noah Goss, Brian Marinelli, Bibek Bhandari, Debmalya Das, Ravi K. Naik, John Mark Kreikebaum, Andrew N. Jordan, David I. Santiago, Irfan Siddiqi

Mathematics, Physics, and Computer Science Faculty Articles and Research

The trade-off between robustness and tunability is a central challenge in the pursuit of quantum simulation and fault-tolerant quantum computation. In particular, quantum architectures are often designed to achieve high coherence at the expense of tunability. Many current qubit designs have fixed energy levels and consequently limited types of controllable interactions. Here by adiabatically transforming fixed-frequency superconducting circuits into modifiable Floquet qubits, we demonstrate an XXZ Heisenberg interaction with fully adjustable anisotropy. This interaction model can act as the primitive for an expressive set of quantum operations, but is also the basis for quantum simulations of spin systems. To illustrate …

What Does ‘(Non)-Absoluteness Of Observed Events’ Mean?, Emily Adlam

Mathematics, Physics, and Computer Science Faculty Articles and Research

Recently there have emerged an assortment of theorems relating to the ‘absoluteness of emerged events,’ and these results have sometimes been used to argue that quantum mechanics may involve some kind of metaphysically radical non-absoluteness, such as relationalism or perspectivalism. However, in our view a close examination of these theorems fails to convincingly support such possibilities. In this paper we argue that the Wigner’s friend paradox, the theorem of Bong et al and the theorem of Lawrence et al are all best understood as demonstrating that if quantum mechanics is universal, and if certain auxiliary assumptions hold, then the world …

Questioning Reality: The Progressive Development Of Modern Physics, Joshua Lancman

STEM for Success Showcase

Humanity has a tendency to divide time. The past is distinct from the present which is entirely separate from the future. In supposedly 20-20 vision history is neatly divided into different sections, distinct eras with sharp lines between them. What is present and in the future is always modern. What is past is something else with another name.

Yet time is not divided so neatly. We know this living through it: years and decades blend into one another in a non-uniform progression. To divide human history into separate eras is a necessary simplification, as it helps to ascribe order onto …

Existence Of Well-Defined Pointer Observable Selects Tensor Product Factorizations Of Quantum Systems, Brian Lee

CMC Senior Theses

In the decoherence account of quantum mechanics, a choice of particular tensor product structure (a particular partition of system into subsystems) is assumed. We explore whether it is possible to relax this arbitrary choice by requiring that a valid tensor product structure admits a quasi-classical description. Such tensor product structures are said to be quasi-classical or decoherence-selected tensor product structures. This project generalizes a 2-qubit quasi-classical tensor product structure selection algorithm to an n-qubit selection algorithm, which allows us to, for the first time, consider the relationship between decoherence-selected tensor product structures and locality-selected tensor product structures. To generalize the …

Economic Entanglement: The Quantum Race Between The United States And China, Isabella Willhite

Regis University Student Publications (comprehensive collection)

The United States and China are both currently home to the strongest economies and militaries in the world. Despite their interdependence, trade wars have escalated between the two countries in the past few years. While past trade wars have been focused on purely economic protectionism or ideological stances, the trade wars of today signify a shift towards protecting critical emerging technologies. The important emerging technology of today is quantum computing, which will forever change the way that computers encrypt, process, and decode information. The United States and China are on the eve of the “quantum race,” in which they will …

Single-Stage Few-Cycle Pulse Amplification, Sagnik Ghosh, Nathan G. Drouillard, Tj Hammond

Physics Publications

Kerr instability can be exploited to amplify visible, near-infrared, and midinfrared ultrashort pulses. We use the results of Kerr instability amplification theory to inform our simulations amplifying few-cycle pulses. We show that the amplification angle dependence is simplified to the phase-matching condition of four-wave mixing when the intense pump is considered. Seeding with few-cycle pulses near the pump leads to broadband amplification without spatial chirp, while longer pulses undergo compression through amplification. Pumping in the midinfrared leads to multioctave spanning amplified pulses with single-cycle duration not previously predicted. We discuss limitations of the amplification process and optimizing pump and seed …

A Formalism For Extracting Track Functions From Jet Measurements, Kyle Lee, Ian Moult, Felix Ringer, Wouter J. Waalewijn

Physics Faculty Publications

The continued success of the jet substructure program will require widespread use of tracking information to enable increasingly precise measurements of a broader class of observables. The recent reformulation of jet substructure in terms of energy correlators has simplified the incorporation of universal non-perturbative matrix elements, so called “track functions”, in jet substructure calculations. These advances make it timely to understand how these universal non-perturbative functions can be extracted from hadron collider data, which is complicated by the use jet algorithms. In this paper we introduce a new class of jet functions, which we call (semi-inclusive) track jet functions, which …

Double Distributions And Pseudodistributions, A. V. Radyushkin

Physics Faculty Publications

We describe the approach to lattice extraction of generalized parton distributions (GPDs) that is based on the use of the double distribution (DD) formalism within the pseudodistribution framework. The advantage of using DDs is that GPDs obtained in this way have the mandatory polynomiality property, a nontrivial correlation between 𝓍 and ξ dependences of GPDs. Another advantage of using DDs is that the D-term appears as an independent entity in the DD formalism rather than a part of GPDs H and E. We relate the ξ dependence of GPDs to the width of the α profiles of the corresponding DDs …

Gluon Helicity From Global Analysis Of Experimental Data And Lattice Qcd Ioffe Time Distributions, J. Karpie, R. M. Whitehill, W. Melnitchouk, C. Monahan, K. Orginos, J.-W. Qui, D. G. Richards, N. Sato, S. Zafeiropoulos, Jefferson Lab Angular Momentum And Hadstruc Collaboration

Physics Faculty Publications

We perform a new global analysis of spin-dependent parton distribution functions with the inclusion of Ioffe time pseudodistributions computed in lattice QCD (LQCD), which are directly sensitive to the gluon helicity distribution, Δg. These lattice data have an analogous relationship to parton distributions as do experimental cross sections, and can be readily included in global analyses. We focus in particular on the constraining capability of current LQCD data on the sign of Δg at intermediate parton momentum fractions x, which was recently brought into question by analysis of data in the absence of parton positivity constraints. …

Quantum Logic Control And Precision Measurements Of Molecular Ions In A Ring Trap: An Approach For Testing Fundamental Symmetries, Yan Zhou, Joshua O. Island, Matt Grau

Physics Faculty Publications

This paper presents an experimental platform designed to facilitate quantum logic control of polar molecular ions in a segmented ring ion trap, paving the way for precision measurements. This approach focuses on achieving near-unity state preparation and detection, as well as long spin-precession coherence. A distinctive aspect lies in separating state preparation and detection conducted in a static frame from parity-selective spin precession in a rotating frame. Moreover, the method is designed to support spatially and temporally coincident measurements on multiple ions prepared in states with different sensitivity to the new physics of interest. This provides powerful techniques to probe …

Solutions To The Kaluza-Klein Field Equations, Abel Eshete

All Graduate Theses, Dissertations, and Other Capstone Projects

This Alternate Paper Plan explores Kaluza-Klein theory, a multidimensional framework designed to unify Einstein’s gravitational field theory and Maxwell’s electromagnetic field theory. The objectives of this research can be summarized in two key areas: The first objective is to present a comprehensive introduction to the compactified Kaluza-Klein theory. The second aim involves the application of differential geometry, specifically E ́lie Cartan’s tetrad formalism, to derive exact solutions in two distinct scenarios: a. A Levi-Civita spacetime, b. A general spherical system. Furthermore, Lagrangian and Hamiltonian formalism are utilized to define stability conditions and describe gravitational lensing and Precession of Perihelion within …