Quantum Physics Commons^™

Symmetric Informationally Complete Positive Operator Valued Measures Minimize P-Norm Difference Between Quantum And Classical Probability Rules, Austin Monaghan

Graduate Masters Theses

Experimental violations of Bell's inequality demonstrate quantum theory's incompatibility with a local hidden-variable formulation. Simply put, either 1) measurements performed at one point in space may instantaneously influence far away systems ("spooky action at a distance") or 2) measurement outcomes are not the result of pre-existing properties. The act of measurement takes part in the very creation of the outcomes. If we reject condition 1 as a valid assumption, how can we interpret the significance of condition 2 i.e. no local parameters?  In QBism, condition 2 arises from something deeper: that the Born rule expresses a nonclassical condition for connecting …

Redesigning Quantum Theory, Matthew Weiss

Graduate Doctoral Dissertations

QBism understands quantum mechanics to be probability theory supplemented by additional nonclassical coherence conditions. In this dissertation, we develop these nonclassical coherence conditions from first principles, emphasizing the role of a well chosen reference measurement. After treating standard probability on subjective Bayesian lines, we demonstrate an equivalence between the QBist approach and the existing framework of generalized probabilistic theories. We show that the fundamental nonclassical coherence relation may almost always be taken to be a gentle modification of the law of total probability, and give a coherentist account of when an experimental scenario has a classical explanation. Finally, we show …

A Quantum Phase Space Description Of Local Noise In Atomic Ensembles, Andrew Kolmer Forbes

Physics & Astronomy ETDs

Nonclassicality in quantum sensors can improve sensitivity, but often increases susceptibility to noise. Thus, modeling physically relevant noise sources and analyzing their effect on quantum metrology are both of importance to the field of quantum sensing. In this dissertation, I demonstrate that local noise sources, which are present in almost all many-spin systems, can be tractably modeled when assuming permutation symmetry of the noise, and we show that many common local noise sources can be mapped to a Fokker-Planck equation on quantum phase space. We apply this description of noise to study quantum sensing using noisy probe states and establish …

Multiple-Valued Quantum Automata For Robotics, Yuchen Huang

Dissertations and Theses

This dissertation introduces a new type of quantum automata, their encoding and circuit realization. I concentrate on possible applications in robotics. Several methods and application of quantum automata and quantum circuit-based controllers for elementary robotic systems, with a focus on humanoid robot motion, emotion, and behavior generation are illustrated in detail. The research introduces several novel methodologies that bridge quantum computing principles with robotic control, aiming to overcome the limitations of classical deterministic and probabilistic approaches.

The dissertation first presents a quantum-circuit-based framework for generating non-repetitive and expressive (e)motions in a humanoid robot actor, using superposition and entanglement to produce …

Quantum Mechanics As A Framework For Data Assimilation And Its Application To Atmospheric Parameterization, David Freeman

Dartmouth College Ph.D Dissertations

Quantum mechanics, as a mathematical system, can be understood as a generalization of classical probability theory. Quantum Mechanical Data Assimilation (QMDA) is a method in which classical dynamical systems are embedded into a quantum mechanical setting, with an associated data assimilation scheme leveraging the operator algebraic setting. In this dissertation, the algebraic structure underlying the operator theoretic formulation of QMDA is discussed. A procedure for closure of dynamical systems based on QMDA, known as Quantum Mechanical Closure (QMCl), is then constructed, and the procedures for constructing the quantum embeddings and implementing QMCl in practice are laid out and implemented for …

Optimizing Fisher Information In Quantum Technology, Bran Purvis

LSU Doctoral Dissertations

Fisher information is a statistical metric whose inverse represents a lower bound on the variance of an unbiased estimator. Naturally, in order to make the best estimates of a given unknown parameter, one would desire to find ways to minimize the value of this lower bound. Thus, the Fisher information can also be used to compare the quality of different estimators for a given parameter: whichever estimator has a lower value for its Fisher information must also provide better estimates. The same holds true in the framework of quantum information theory, where an analog to the Fisher information, dubbed quantum …

Interactions And Applications Of Optical Angular Momentum In Magneto-Optical Material, Seth R. Nelson

Dissertations, Master's Theses and Master's Reports

This dissertation explores the interactions and applications of optical angular momentum within magneto-optical materials. Beginning with a theoretical and experimental analysis of multiple reflection and refraction phenomena within magneto-optical material. We derive and verify the dependence of refractive indices on optical spin angular momentum and magneto-optical magnetization, resulting in nonreciprocal elliptical and linear polarization beam splitting effects and wavevector discretization. We fabricate a magnetless slab waveguide isolator with minimal optical loss. Extending our study to optical orbital angular momentum, we introduce a perturbation to the electronic transition model in bismuth-substituted iron garnets. We demonstrate that this perturbation leads to nonreciprocal …

Issues And Challenges In Silicon Based Quantum Computing, Rafia Ayub

Electronic Theses & Dissertations (2024 - present)

Silicon-based quantum computing has emerged as a promising platform for scalable and fault-tolerant quantum information processing. This thesis investigates the use of silicon quantum dots as qubits, addressing a key limitation in their implementation—charge noise and decoherence. We explore the physical and electronic properties of silicon quantum dots, focusing on their coherence times, tunability, and compatibility with existing semiconductor fabrication technologies. Through theoretical analysis and numerical simulations, we examine the impact of material imperfections and propose strategies to mitigate decoherence effects, thereby enhancing qubit stability. Additionally, we discuss potential pathways for integrating silicon quantum dots into large-scale quantum architectures. Our …

Representation Theory And Its Applications In Physics, Max Varverakis

Master's Theses

Representation theory, which encodes the elements of a group as linear operators on a vector space, has far-reaching implications in physics. Fundamental results in quantum physics emerge directly from the representations describing physical symmetries. We first examine the connections between specific representations and the principles of quantum mechanics. Then, we shift our focus to the braid group, which describes the algebraic structure of braids. We apply representations of the braid group to physical systems in order to investigate quasiparticles known as anyons. Finally, we obtain governing equations of anyonic systems to highlight the differences between braiding statistics and conventional Bose-Einstein/Fermi-Dirac …

Studying Superconducting Thin Films For Quantum Computing Applications, Bernardo Jaime Langa Junior

All Theses

Superconducting qubits have emerged as a promising platform for realizing error-corrected quantum computing. Reaching the minimum threshold for error correction requires scaling the number of qubits well beyond the current numbers while improving their coherence and minimizing their crosstalk. Such daunting demands require groundbreaking innovations in the design of superconducting quantum circuits as well as in engineering the materials integrated into the devices. This thesis explores materials solutions for two different scalability problems: 1) crosstalk and 2) loss due to surface oxidation. The crosstalk is addressed by making voltage-tunable superconductor-semiconductor Josephson junctions (JJs). For the loss due to surface oxidation, …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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.

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 …

An Introduction To Supersymmetric Quantum Mechanics, Vincent R. Siggia

Theses and Dissertations

In this thesis, the general framework of supersymmetric quantum mechanics and the path integral approach will be presented (as well as the worked out example of the supersymmetric harmonic oscillator). Then the theory will be specialized to the case of supersymmetric quantum mechanics on Riemannian manifolds, which will start from a supersymmetric Lagrangian for the general case and the special case for S2. Afterwards, there will be a discussion on the superfield formalism. Concluding this thesis will be the Hamiltonian formalism followed by the inclusion of deforma- tions by potentials.

The Entropic Dynamics Approach To The Paradigmatic Quantum Mechanical Phenomena, Susan Difranzo

Legacy Theses & Dissertations (2009 - 2024)

Standard Quantum Mechanics, although successful in terms of calculating and predicting

Key Encryption Through Quantum Optics, Madison Durrance, Zach Galberd, Abbey Savage, Tristan Cabrera, Josh Hoffman

Georgia College Student Research Events

Cryptography has been around since the dawn of human civilization to send private messages for commercial, military, and political purposes. Some of the most important ciphers are the Vigenère cipher, the enigma, and the more modern RSA. Because of the development of the internet, private encryption has also become increasingly more important. The weakest link of encryption is the key creation and key distribution. A key is needed to encrypt and decipher codes and is needed by both the user and sender. A solution to this problem is the generation of quantum key distributions. In our experiment, we are now …

Simulation Of Nuclear Fusion Using A One Dimensional Particle In Cell Method, Steven T. Margell

Cal Poly Humboldt theses and projects

In this thesis several novel techniques are developed to simulate fusion events in an isotropic, electrostatic three-dimensional Deuterium-Tritium plasma. These techniques allow us to accurately predict three-dimensional collision events with a one-dimensional model while simultaneously reducing compute time via a nearest neighbor algorithm. Furthermore, a fusion model based on first principles is developed that yields an average fusion reactivity which correlates well with empirical results.

Toward Analog Quantum Computing: Simulating Designer Atomic Systems, Jacob L. Bigelow, Veronica L. Sanford

Physics and Astronomy Summer Fellows

We use a magneto-optical trap to cool rubidium atoms to temperatures in the _µK range. On the _µs timescales of our experiment, the atoms are moving slowly enough that they appear stationary. We then excite them to a Rydberg state, where the outer electron is loosely bound. In these high energy states, the atoms can exchange energy with each other. Since the energy exchange depends on the separation and the relative orientation of the atoms, we can potentially control their interactions by controlling the spatial arrangements of the atoms. We model this system using simulations on a supercomputer …

Isotropic Oscillator Under A Magnetic And Spatially Varying Electric Field, David L. Frost Mr., Frank Hagelberg

Undergraduate Honors Theses

We investigate the energy levels of a particle confined in the isotropic oscillator potential with a magnetic and spatially varying electric field. Here we are able to exactly solve the Schrodinger equation, using matrix methods, for the first excited states. To this end we find that the spatial gradient of the electric field acts as a magnetic field in certain circumstances. Here we present the changes in the energy levels as functions of the electric field, and other parameters.

Controllability Of Open Quantum Optical Systems: Photon Fock States In A Cavity, Byron Henry Lowry

Doctoral Dissertations and Master's Theses

There has always been a significant interest in using optical systems to control quantum phenomena. A major barrier to controllability of quantum optical systems is the fact that the systems are usually innite dimensional open systems, two cases which have mostly negative controllability results. This thesis develops three new definitions of controllability and reformulates a previous controllability theorem in order to apply the theorem to the system of interest. Then, the controllability of a pumped dissipative quantum optical cavity with engineered decoherence is investigated using previously developed concepts in quantum control theory, as well as the ones developed in this …

Hilbert Space Theory And Applications In Basic Quantum Mechanics, Matthew Gagne

Mathematics

We explore the basic mathematical physics of quantum mechanics. Our primary focus will be on Hilbert space theory and applications as well as the theory of linear operators on Hilbert space. We show how Hermitian operators are used to represent quantum observables and investigate the spectrum of various linear operators. We discuss deviation and uncertainty and briefly suggest how symmetry and representations are involved in quantum theory.

The Fine-Tuning Of Nomic Behavior In Multiverse Scenarios, Max Lewis Edward Andrews

Masters Theses

The multiverse hypothesis (the view that there is not just one world or universe in existence, bur rather that there are many) is the leading alternative to the competing fine-tuning hypothesis (the laws of physics and constants are fine-tuned for the existence of life). The multiverse dispels many aspects of the fine-tuning argument by suggesting that there are different initial conditions in each universe, varying constants of physics, and the laws of nature lose their known arbitrary values; thus, making the previous single-universe argument from fine- tuning incredibly weak. The position that will be advocated will be that a form …