Physical Sciences and Mathematics Commons^™

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 …

Development Of A Collaborative Research Platform For Efficient Data Management And Visualization Of Qubit Control, Devanshu Brahmbhatt

Computer Science and Engineering Theses

This thesis introduces QubiCSV, a pioneering open-source platform for quantum computing field. With an emphasis on collaborative research, QubiCSV addresses the critical need for specialized data management and visualization tools in qubit control. The platform is crafted to overcome the challenges posed by the high costs and complexities associated with quantum experimental setups. It emphasizes efficient utilization of resources through shared ideas, data, and implementation strategies. One of the primary obstacles in quantum computing research has been the ineffective management of extensive calibration data and the inability to visualize complex quantum experiment outcomes effectively. QubiCSV fills this gap by offering …

Point Modules And Line Modules Of Certain Quadratic Quantum Projective Spaces, Jose E. Lozano

Mathematics Dissertations

During the past 36 years, some research in noncommutative algebra has been driven by attempts to classify AS-regular algebras of global dimension four. Such algebras are often considered to be noncommutative analogues of polynomial rings. In the 1980s, Artin, Tate, and Van den Bergh introduced a projective scheme that parametrizes the point modules over a graded algebra generated by elements of degree one. In 2002, Shelton and Vancliff introduced the concept of line scheme, which is a projective scheme that parametrizes line modules.

This dissertation is in two parts. In the first part, we consider a 1-parameter family of quadratic …

Contributions Of Tunneling In 8Π-6Π Electrocyclic Cascade Reactions Of Bicyclo[4.2.0]Octa-2,4-Diene Moieties, Ishika Jain, Claire Castro, William L. Karney

Featured Student Work

Six-electron electrocyclic reactions usually require relatively high temperatures; however recent research has shown that such reactions can occur at significantly lower temperatures in biosynthetic and biomimetic pathways. Pathways resulting in bicyclo[4.2.0]octa-2,4-diene moieties arise from thermally allowed 8π-6π electrocyclization cascade reactions of 1,3,5,7-octatetraenes, as in the biosynthesis of endiandric acids, elysiapyrones, and numerous other natural products. We report multidimensional tunneling calculations to explore the possible contribution of heavy-atom tunneling (e.g. by carbon) to biosynthetic pathways and biomimetic syntheses, and thus to provide a more complete picture of biochemical kinetics. M06-2X/cc-pVDZ calculations on the 8π-6π cascade cyclizations of methylated octatetraene model systems …

Design And Fabrication Of A Trapped Ion Quantum Computing Testbed, Christopher A. Caron

Masters Theses

Here we present the design, assembly and successful ion trapping of a room-temperature ion trap system with a custom designed and fabricated surface electrode ion trap, which allows for rapid prototyping of novel trap designs such that new chips can be installed and reach UHV in under 2 days. The system has demonstrated success at trapping and maintaining both single ions and cold crystals of ions. We achieve this by fabricating our own custom surface Paul traps in the UMass Amherst cleanroom facilities, which are then argon ion milled, diced, mounted and wire bonded to an interposer which is placed …

Modified Geometries, Clifford Algebras And Graphs: Their Impact On Discreteness, Locality And Symmetr, Roma Sverdlov

Mathematics & Statistics ETDs

In this dissertation I will explore the question whether various entities commonly used in quantum field theory can be “constructed". In particular, can spacetime be “constructed" out of building blocks, and can Berezin integral be “constructed" in terms of Riemann integrals.

As far as “constructing" spacetime out of building blocks, it has been attempted by multiple scientific communities and various models were proposed. But the common downfall is they break the principles of relativity. I will explore the ways of doing so in such a way that principles of relativity are respected. One of my approaches is to replace points …

The Mceliece Cryptosystem As A Solution To The Post-Quantum Cryptographic Problem, Isaac Hanna

Senior Honors Theses

The ability to communicate securely across the internet is owing to the security of the RSA cryptosystem, among others. This cryptosystem relies on the difficulty of integer factorization to provide secure communication. Peter Shor’s quantum integer factorization algorithm threatens to upend this. A special case of the hidden subgroup problem, the algorithm provides an exponential speedup in the integer factorization problem, destroying RSA’s security. Robert McEliece’s cryptosystem has been proposed as an alternative. Based upon binary Goppa codes instead of integer factorization, his cryptosystem uses code scrambling and error introduction to hinder decrypting a message without the private key. This …

The Future Between Quantum Computing And Cybersecurity, Daniel Dorazio

Williams Honors College, Honors Research Projects

Quantum computing, a novel branch of technology based on quantum theory, processes information in ways beyond the capabilities of classical computers. Traditional computers use binary digits [bits], but quantum computers use quantum binary digits [qubits] that can exist in multiple states simultaneously. Since developing the first two-qubit quantum computer in 1998, the quantum computing field has experienced rapid growth.

Cryptographic algorithms such as RSA and ECC, essential for internet security, rely on the difficulty of complex math problems that classical computers can’t solve. However, the advancement of quantum technology threatens these encryption systems. Algorithms, such as Shor’s, leverage the power …

Liouvillian Dynamics Of The Open Schwinger Model: String Breaking And Kinetic Dissipation In A Thermal Medium, Kyle Lee, James Mulligan, Felix Ringer, Xiaojun Yao

Physics Faculty Publications

Understanding the dynamics of bound state formation is one of the fundamental questions in confining quantum field theories such as Quantum Chromodynamics (QCD). One hadronization mechanism that has garnered significant attention is the breaking of a string initially connecting a fermion and an antifermion. Deepening our understanding of real-time string-breaking dynamics with simpler, lower dimensional models like the Schwinger model can improve our understanding of the hadronization process in QCD and other confining systems found in condensed matter and statistical systems. In this paper, we consider the string-breaking dynamics within the Schwinger model and investigate its modification inside a thermal …

Overcoming Atmospheric Effects In Quantum Cryptography, Brian Joseph Rollick

Doctoral Dissertations

Quantum Computers will have the potential to greatly assist us in problems such as searching, optimization and even drug discovery. Unfortunately, among these newfound capabilities is one which allows one to break RSA encryption in orders of magnitude less time. One promising countermeasure to secure our communication today and in the future is the one time pad, although it is very difficult to generate and distribute. Quantum Key Distribution offers a practical method for two authenticated parties to generate a key. Whereby the parties, Alice and Bob, share quantum states and use physical laws to place an upper bound on …

Contrasting Sea-Ice Algae Blooms In A Changing Arctic Documented By Autonomous Drifting Buoys, Victoria Hill, Bonnie Light, Michael Steele, Andrew Lowy Sybrandy

OES Faculty Publications

Novel observations of the seasonal evolution of an ice algal bloom on the Chukchi shelf were collected by two autonomous buoys deployed 180 km apart in first-year drifting sea ice. High attenuation of blue light in the bottom of the ice indicated considerable accumulation of ice algae biomass with derived Chlorophyll-a concentrations (Chl a) up to 184 mg m⁻². Differences in the magnitude and persistence of ice algae biomass under each buoy appear to have been driven by differences in snow thickness, as ice thickness was similar between the sites. Minimal snow cover (0.02 m) around …

Circulation Transfer Between Adjacent Target Bose-Einstein Condensates, Charles B. Henry

Honors College Theses

We propose an atomtronic rotation sensor design that consists of an array of Bose-Einstein Condensates (BECs) that are confined in a double-target-array potential. The rotation sensor's purpose is to measure the speed of the rotating frame, with respect to the “fixed stars", the sensor rests in. The atomtronic system is an ultracold gas of sodium atoms that have been compressed by laser light into a thin quasi-2D horizontal plane and further confined in the horizontal plane by a double-target-array potential. A target BEC is a combination of disk BEC that is surrounded by a ring BEC. A double-target BEC is …

Automation Of The Transition Identification Procedure For Trapping Rubidium Atoms In A Magneto-Optical Trap, Michael P. Fletcher

Physics

The words “quantum computer” often conjure images of science fiction and unrealistic technology from an impossible future. Some may even believe that they aren’t real or are only theoretical. The truth is that quantum computers are real, tangible systems with real life uses and rooted in credible scientific research. Today, many groups of scientists collaborate on research into better ways of implementing and improving quantum computing techniques. This paper will be addressing the systems required and phenomena used to achieve neutral atom trapping for quantum computation. This thesis will outline the physical phenomena involved with the frequency tuning process for …

New Aspects Of Optical Coherence And Their Potential For Quantum Technologies, Nathaniel Robert Miller

LSU Doctoral Dissertations

Currently, optical technology impacts most of our lives, from light used in scientific measurement to the fiber optic cables that makeup the backbone of the internet. However, as our current optical infrastructure grows, we discover that these technologies are not limitless. Astronomers find themselves unable resolve stars that are too close to one another. Meanwhile, the internet is always under threat as our computer technology improves and more complex ways to break encryption emerge, threatening our personal information and infrastructure. However, our current optical technology functions on classical principles, and can be easily improved by incorporating our knowledge of quantum …

Magnetic Microscopy And Search For Exotic Interaction Detection With Color Centers In Diamond, Nathaniel Ristoff

Physics & Astronomy ETDs

Nitrogen vacancy (NV) centers have been used extensively for the measurement of magnetic fields in applications of geology, biology, medicine, and fundamental physics. In regard to fundamental physics, NV centers offer a unique opportunity to test potential velocity dependant spin-spin interactions as well as velocity-spin interactions at the micron scale. In regards to magnetic materials, NV centers offer a platform to investigate magnetic properties of nanoparticles in an individual, but highly parallelized measurement. In this work, an experiment is proposed to measure a potential fundamental interaction between spins, mediated by an integer spin boson. These velocity dependent interactions will couple …

Binary Classifiers For Noisy Datasets: A Comparative Study Of Existing Quantum Machine Learning Frameworks And Some New Approaches, Nikolaos Schetakis, Davit Aghamalyan, Paul Robert Griffin, Michael Boguslavsky

Research Collection School Of Computing and Information Systems

This technology offer is a quantum machine learning algorithm applied to binary classification models for noisy datasets which are prevalent in financial and other datasets. By combining hybrid-neural networks, quantum parametric circuits, and data re-uploading we have improved the classification of non-convex 2-dimensional figures by understanding learning stability as noise increases in the dataset. The metric we use for assessing the performance of our quantum classifiers is the area under the receiver operator curve (ROC AUC). We are interested to collaborate with partners with use cases for binary classification of noisy data. Also, as quantum technology is still insufficient for …

An Introduction To Generalized Entropy And Some Quantum Applications, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The concept of generalized entropy is introduced and some of its properties are studied. Irreversible time evolution can be generated by a non-Hermitian superoperator on the states of the system. The case when irreversibility comes about from embedding the system in a thermal reservoir is looked at. The time evolution is found compatible both with equilibrium thermodynamics and entropy production near the final state. Some examples are presented as well as a longer introduction as to how this might play a role in the black hole information loss paradox.

Solving Chromatic Number With Quantum Search And Quantum Counting, David Lutze

Master's Theses

This thesis presents a novel quantum algorithm that solves the Chromatic Number problem. Complexity analysis of this algorithm revealed a run time of O(2^n/2n²(log2n)²). This is an improvement over the best known algorithm, with a run time of 2ⁿn^O(1) [1]. This algorithm uses the Quantum Search algorithm (often called Grover's Algorithm), and the Quantum Counting algorithm. Chromatic Number is an example of an NP-Hard problem, which suggests that other NP-Hard problems can also benefit from a speed-up provided by quantum technology. This has wide implications as many real world problems can …

Optomechanical Quantum Entanglement, Kahlil Y. Dixon

LSU Doctoral Dissertations

As classical technology approaches its limits, exploration of quantum technologies is critical. Quantum optics will be the basis of various cutting-edge research and applications in quantum technology. In particular, quantum optics quite efficacious when applied to quantum networks and the quantum internet. Quantum Optomechanics, a subfield of quantum optics, contains some novel methods for entanglement generation. These entanglement production methods exploit the noise re-encoding process, which is most often associated with creating unwanted phase noise in optical circuits. Using the adapted two-photon formalism and experimental results, we simulate (in an experimentally viable parameter space) optomechanical entanglement generation experiments. These simulations …

Quantum Optics, Entanglement, And Bell's Theorem, Andrew D. Poverman

Senior Projects Spring 2021

The field of quantum optics provides a wonderful setting in which to study fundamental aspects of quantum mechanics such as entanglement, Bell's theorem, and non-locality. This thesis presents theoretical discussions of qubits, entanglement, and Bell's theorem in addition to experimental discussions on the nature of photons, creating entangled states using Spontaneous Parametric Down-Conversion (SPDC), and a Bell Test with polarization entangled photons. The experimental sections are written to be useful as instructions for one to conduct these experiments on their own. By doing these experiments, one will gain familiarity with quantum optics experiments as well as a firmer grasp on …

Classical And Quantum Integrability: A Formulation That Admits Quantum Chaos, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The concept of integrability of a quantum system is developed and studied. By formulating the concepts of quantum degree of freedom and quantum phase space, a realization of the dynamics is achieved. For a quantum system with a dynamical group G in one of its unitary irreducible representative carrier spaces, the quantum phase space is a finite topological space. It is isomorphic to a coset space G=R by means of the unitary exponential mapping, where R is the maximal stability subgroup of a fixed state in the carrier space. This approach has the distinct advantage of exhibiting consistency between classical …

Unclonable Secret Keys, Marios Georgiou

Dissertations, Theses, and Capstone Projects

We propose a novel concept of securing cryptographic keys which we call “Unclonable Secret Keys,” where any cryptographic object is modified so that its secret key is an unclonable quantum bit-string whereas all other parameters such as messages, public keys, ciphertexts, signatures, etc., remain classical. We study this model in the authentication and encryption setting giving a plethora of definitions and positive results as well as several applications that are impossible in a purely classical setting.

In the authentication setting, we define the notion of one-shot signatures, a fundamental element in building unclonable keys, where the signing key not only …

Qwasi: The Quantum Walk Simulator, Warren V. Wilson

Theses and Dissertations

As quantum computing continues to evolve, the ability to design and analyze novel quantum algorithms becomes a necessary focus for research. In many instances, the virtues of quantum algorithms only become evident when compared to their classical counterparts, so a study of the former often begins with a consideration of the latter. This is very much the case with quantum walk algorithms, as the success of random walks and their many, varied applications have inspired much interest in quantum correlates. Unfortunately, finding purely algebraic solutions for quantum walks is an elusive endeavor. At best, and when solvable, they require simple …

Many Body Localization With Rydberg Atoms, Alicia Handian

Physics and Astronomy Summer Fellows

Systems are known to thermalize, or reach equilibrium, with the passing of time. However, when this does not occur, the quantum states of the system may be localized. Localized states carry information of the system’s initial state that is typically lost during the process of thermalization. We aim to study thermalization and localization in systems of rubidium Rydberg atoms, and to further understand these phenomena via simulation while we are developing a more refined experiment.

Simulating Quantum Systems Using The D-Wave Quantum Computer, Justin M. Copenhaver, Raunaq Kumaran, Birgit Kaufmann, Adam Wasserman

Discovery Undergraduate Interdisciplinary Research Internship

No abstract provided.

Quantum Computing And Quantum Algorithms, Daniel Serban

Senior Honors Theses

The field of quantum computing and quantum algorithms is studied from the ground up. Qubits and their quantum-mechanical properties are discussed, followed by how they are transformed by quantum gates. From there, quantum algorithms are explored as well as the use of high-level quantum programming languages to implement them. One quantum algorithm is selected to be implemented in the Qiskit quantum programming language. The validity and success of the resulting computation is proven with matrix multiplication of the qubits and quantum gates involved.

Entropy In Quantum Mechanics And Applications To Nonequilibrium Thermodynamics, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Classical formulations of the entropy concept and its interpretation are introduced. This is to motivate the definition of the quantum von Neumann entropy. Some general properties of quantum entropy are developed, such as the quantum entropy which always increases. The current state of the area that includes thermodynamics and quantum mechanics is reviewed. This interaction shall be critical for the development of nonequilibrium thermodynamics. The Jarzynski inequality is developed in two separate but related ways. The nature of irreversibility and its role in physics are considered as well. Finally, a specific quantum spin model is defined and is studied in …

On Characterizing Quantum Processes And Detectors, Kevin Valson Jacob

LSU Doctoral Dissertations

In 2009, physicists at the National Institute of Standards and Technology in Colorado, Boulder developed what could arguable be called the first rudimentary quantum computer [1]. The past decade has seen unprecedented improvements in quantum information science culminating in the demonstration of quantum supremacy --- that quantum computers can solve problems that are impractical to be solved on the best supercomputers [2]. This remarkable progress necessitates the development of techniques to characterize the quantum devices that are being developed. In my thesis, I will focus on such devices that manipulate and detect light.

In Chapter 1, I will introduce the …

Noise Resilience Of Variational Quantum Compiling, Kunal Sharma, Sumeet Khatri2, M. Cerezo, Patrick J. Coles

Faculty Publications

Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitary U is compiled into a short-depth gate sequence V. In this work, we report on a surprising form of noise resilience for these algorithms. Namely, we find one often learns the correct gate sequence V (i.e. the correct variational parameters) despite various sources of incoherent noise acting during the cost-evaluation circuit. Our main results are rigorous theorems stating that the optimal variational parameters …

Characterizing Complexity In A Semiconductor With Optical Feedback From Two Mirrors, Layla M. Abrams

2020 Symposium Posters

Lasers are stable devices with a broad spectrum of applications. They can be perturbed to induce complex dynamics in their output intensity. One interesting regime in semiconductor lasers is that the output intensity of the laser emits a sequence of non-regular optical spikes. This behavior resembles that of neurons. We use a semiconductor laser with optical feedback from two mirrors to characterize the behavior of the laser's power output. The data is then analyzed by transforming the intensity time series into a sequence of patterns or words. By doing this we want to explore how the laser changes its preferred …