Theory and Algorithms Commons^™

Computational Insights Into Nucleosome Dynamics In Epigenetics Using Molecular Dynamics Simulations, Rutika Patel

Dissertations, Theses, and Capstone Projects

Nucleosome core particles (NCP) are the building blocks that form a highly organized and compact chromatin structure. Nucleosomes package DNA in the nucleus of eukaryotic cells. The NCP consists of about 147 base pairs of DNA wrapped around the histone octamer, with 1.65 superhelical turns in a left-handed manner. The histone octamer is composed of two copies of H3, H4, H2A, and H2B. Together with histone H1 and linker DNA, they further assemble into a higher-order chromatin structure. The nucleosome complex is stabilized by electrostatic interactions between positively charged histone residues and the negatively charged DNA backbone. To effectively access …

Search For Slow-Moving Magnetic Monopoles With An Improved High-Energy Event Removal Algorithm, Reeshi N. Gihosal

Honors Theses

Fermilab’s NOvA (NuMI Off-axis 𝑣𝑒 Appearance) experiment focuses on understanding the behavior of neutrinos and how they affect the cosmos. A sub-focus of the NOvA experiment is the search for magnetic monopoles. These elusive particles have not yet been observed in nature, leaving their behavior to be mysterious. The Far Detector, located in Ash River, MN, is integral in the search for these particles. This project is on simulated magnetic monopoles with speeds thousandths the speed of light, with focus on the role of slicing algorithms in event reconstruction using the NOvA experiment’s reconstruction algorithm. Using sample data, analysis occurred …

Towards Physics-Informed Neural Networks For Simulating Multiphase Geothermal Convection​*, Daniel C. Patton, Andrew Harrison Eno

Campus Research Month

Water and steam flow through porous rock, transferring heat via conduction and buoyancy-driven convection caused by density differences. Traditional numerical methods (finite-volume/finite-element) model this well but can become memory-intensive and unstable for long, high-detail simulations. This work demonstrates a Physics-Informed Neural Network (PINN) using a finite-difference approach within the NVIDIA PhysicsNeMo framework to simulate magma chambers in 2D. Tested on the Rio Pisco pluton in Peru, results are compared with the USGS HYDROTHERM model. PINNs learn from physical laws, offering accurate, flexible solutions with less data and development effort.

Explainable Physics-Based Constraints On Reinforcement Learning For Accelerator Optimization, Jonathan Colen, Malachi Schram, Kishansingh Rajput, Armen Kasparian

Data Science Faculty Publications

We present a reinforcement learning (RL) framework for optimizing particle accelerator experiments that builds explainable physics-based constraints on agent behavior. The goal is to increase transparency and trust by letting users verify that the agent’s decision-making process incorporates suitable physics. Our algorithm uses a learnable surrogate function for physical observables, such as energy, and uses them to fine-tune how actions are chosen. This surrogate can be represented by a neural network or by an interpretable sparse dictionary model. We test our algorithm on a range of particle accelerator optimization environments designed to emulate the Continuous Electron Beam Accelerator Facility at …

Variational Autoencoder Inverse Mapper For Extraction Of Compton Form Factors: Benchmarks And Conditional Learning, Douglas Adams, Md Fayaz Bin Hossen, Joshua Bautista, Gia-Wei Chern, Simonetta Liuti, Marie Boër, Marija Čuić, Michael Engelhardt, Gary R. Goldstein, Huey-Wen Lin, Yaohang Li

Computer Science Faculty Publications

Deeply virtual exclusive scattering processes (DVES) serve as precise probes of nucleon quark and gluon distributions in coordinate space. These distributions are derived from generalized parton distributions (GPDs) via Fourier transform relative to proton momentum transfer. QCD factorization theorems enable DVES to be parameterized by Compton form factors (CFFs), which are convolutions of GPDs with perturbatively calculable kernels. Accurate extraction of CFFs from DVCS, benefiting from interference with the Bethe–Heitler (BH) process and a simpler final state structure, is essential for inferring GPDs. This paper focuses on extracting CFFs from DVCS data using a variational autoencoder inverse mapper (VAIM) and …

Trigonometric Continuous-Variable Gates And Hybrid Quantum Simulations Of The Sine-Gordon Model, Tommaso Rainaldi, Victor Ale, Matt Grau, Dmitri Kharzeev, Enrique Rico, Felix Ringer, Pubasha Shome, George Siopsis

Physics Faculty Publications

Hybrid qubit-qumode quantum computing platforms provide a natural setting for simulating interacting bosonic quantum field theories. However, existing continuous-variable gate constructions rely predominantly on polynomial functions of canonical quadratures. In this work, we introduce a complementary universality paradigm based on trigonometric continuous-variable gates, which enable a Fourier-like representation of bosonic operators and are particularly well suited for periodic and non-perturbative interactions. We present an ancilla-based framework for implementing trigonometric gates with arguments given by arbitrary Hermitian functions of qumode quadratures. The protocol yields unitary gates deterministically, and non-unitary gates through probabilistic post-selection. As a concrete application, we develop a hybrid …

Establishing Convergence Thresholds For Pre-Trajectory Sampling With Batched Execution Across Random Quantum Circuits, Taylor L. Eskew, Jerome F. Gonthier, Taylor L. Patti, Andrew N. Jordan

Student Scholar Symposium Abstracts and Posters

A crucial aspect of validating quantum protocols is understanding the noise produced by quantum computing devices. Using simulations that can replicate this noise allows for a lower-cost alternative to hardware experiments. Stochastic, so-called "trajectory" methods are often used as a quadratically reduced approximation to density matrix simulations, but traditional implementations have limited sampling capacity and provide no error-based metadata. The Pre-Trajectory Sampling with Batched Execution (PTSBE) [Patti et al., 2025] algorithm provides a solution by combining fine-tuned, well-documented noise sampling with computational intermediate caching.

While the original work is effective on quantum error correction circuits, its performance on general circuits …

Coupled Machine Learning Models: Combining Observations And Numerical Analysis In A Physics-Regularized Approach, Austin B. Schmidt

LSU New Orleans Theses and Dissertations

This dissertation investigates surrogate modeling for fixed-location environmental forecasting using novel data-combination techniques. The work surveys the landscape of observational measurements and numerically generated data, identifying similar research and gaps in current methodologies. The ratio-coupled training framework is introduced to combine two data sources per predicted feature through a tunable parameter that weights training signal strength. An optimization scheme is developed to simultaneously tune surrogate weights and the coupled signal ratio, allowing relative influence between signals to act as an explicit regularizer. Three case studies demonstrate the methodology and approach in a variety of contexts. The first study is based …

Advancing Real-World Implementation Of The Well Optimized Linear Finder (Wolf) High-Speed Atmospheric Turbulence Compensation Method, Timothy Evan Coon

Theses and Dissertations

This dissertation advances the real-world implementation of the Well Optimized Linear Finder (WOLF) method for high-speed Atmospheric Turbulence Compensation (ATC). Atmospheric turbulence introduces phase aberrations into optical wavefronts and degrades image quality in terrestrial imaging systems. Traditional phase diversity methods are computationally intensive and poorly suited to real-time operation. The WOLF method addresses these limitations through a novel, point-wise formulation of the optical transfer function (OTF) as a structured autocorrelation of the generalized pupil function (GPF). This formulation enables the estimation of phase aberrations at individual spatial coordinates with distributed computational complexity.

The research begins by developing a MATLAB-based simulation …

Algebraic Multigrid Methods For Nonsymmetric And Indefinite Problems: Theory And Applications, Ahsan Ali

Mathematics & Statistics ETDs

Algebraic multigrid (AMG) is a well-established and highly efficient solver for symmetric positive definite (SPD) systems arising from elliptic and parabolic PDEs, while nonsymmetric systems from hyperbolic PDEs remain a significant challenge. This dissertation develops AMG methods and theory for nonsymmetric problems. First, we develop a novel approach combining mode constraints from energy-minimization AMG with local approximations of ideal restriction in $\ell$AIR, resulting in constrained $\ell$AIR (C$\ell$AIR), which demonstrates scalable convergence across advective and diffusive problems. Second, we extend optimal AMG theory by deriving spectral radius estimates for the two-grid error transfer operator using matrix-induced orthogonality, enabling convergence predictions for …

Data Encoding, Compilation, And Algorithms For Quantum Machine Learning, Aviraj Sinha

Computer Science and Engineering Theses and Dissertations

Quantum computing enables new approaches to data processing, especially in quantum machine learning. Unlike classical systems, quantum data must be synthesized through operations and can exist in superposition. Encoding choices affect efficiency, noise resilience, and trainability—key factors in quantum machine learning models. This dissertation enhances quantum data encodings by extending quantum read-only memory (QROM) beyond binary representations, improving efficiency and parallelism. It introduces new compilation methods for quantum random number generators (QRNGs), supporting non-parametric distributions for post-quantum cryptography. Additionally, it explores Cayley graph-based encodings to extract spectral features for quantum machine learning.

Noise-Embedded Image Processing Based On Quantum Data Encodings, Yayu Mo

Multidisciplinary Studies Theses and Dissertations

Advancements in quantum information have significantly impacted the field of image processing, although challenges remain. Especially in the edge detection and image encoding area, distorted feature and noises would affect the further classification or super resolution tasks. In our work, we conduct researches on two stages to both evaluate the potential of Quantum-based Convolutional Structure in extracting distorted feature and further explore the effects of quantum noise channels on quantum image encodings.

In the first stage, we propose a method to extract distorted edge features by applying shallow layers in quantum convolutional neural networks (QCNN). By combining the advantages of …

32 - Nested Two Level Decomposition For Quantum Computing, Andrew Maciejunes, John Stenger, Dan Gunlycke, Nikos Chrisochoides

Undergraduate Research Symposium

Abstract—We present a two-level decomposition strategy for solving the Vehicle Routing Problem (VRP) using the Quantum Approximate Optimization Algorithm (QAOA). A Problem-Level Decomposition (PLD) partitions a 9-node (72-qubit) VRP into smaller Traveling Salesman Problem (TSP) instances. Each TSP is then further simplified via Circuit-Level Decomposition (CLD), enabling execution on near-term quantum devices. Our approach achieves up to 90% reductions in circuit depth and qubit count. These results demonstrate the feasibility of solving VRPs previously too complex for quantum simulators and provide early evidence of potential quantum utility.

Robust Spacecraft Autonomy For Deep Space Exploration In Special Euclidean Group Se(3), Matthew Wittal

Doctoral Dissertations and Master's Theses

Over the past half-century, humanity has gained extensive experience conducting manned spaceflight near Earth. Arguably, "near Earth" could even include the Moon — the most distant destination humans have reached. However, "near" in this work primarily refers low Earth orbit (LEO). One could argue that we have not truly left Earth since the Apollo, as spacecraft in some LEOs remain subject to atmospheric drag thus emphasizing their continued connection to Earth's immediate environment. Reflecting on this, it becomes clear that humanity has largely remained bound to Earth’s immediate vicinity since the Apollo missions reached the Moon. However, that is set …

Ai For Nuclear Physics: The Exclaim Project, S. Liuti, D. Adams, M. Boër, G. W. Chern, M. Cuic, M. Engelhardt, G. R. Goldstein, B. Kriesten, Y. Li, H. W. Lin, M. Sievert, D. Sivers

Computer Science Faculty Publications

An overview of the recent activity of the newly funded EXCLusives with AI and Machine learning (EXCLAIM) collaboration is presented. The main goal of the collaboration is to develop a framework to implement AI and machine learning techniques in problems emerging from the phenomenology of high energy exclusive scattering processes from nucleons and nuclei, maximizing the information that can be extracted from various sets of experimental data, while implementing theoretical constraints from lattice QCD. A specific perspective embraced by EXCLAIM is to use the methods of theoretical physics to understand the working of ML, beyond its standardized applications to physics …

High Antarctic Coastal Productivity In Polynyas Revealed By Considering Remote Sensing Ice-Adjacency Effects, Hilde Oliver, Jessica S. Turner, Alexandre Castagna, Henry Houskeeper, Heidi Dierssen

OES Faculty Publications

Ocean color-based estimates of Antarctic net primary productivity (NPP) have indicated low nearshore productivity in ice-adjacent waters, contrasting with coupled physical–biogeochemical models. To understand this discrepancy, we assessed satellite records of polynya NPP by comparing field data with two satellite imagery datasets derived using different processing schemes. Our results indicate historical underestimation of chlorophyll a for imagery obtained using default atmospheric correction processing within approximately 100 km of ice-covered coastlines due to adjacency effects. Using radiative transfer modeling, we find that biases in ocean color polynya observations due to adjacency effects correspond to the high albedo of ice and snow. …

Harnessing The Power Of Gradient-Based Simulations For Multi-Objective Optimization In Particle Accelerators, Kishansingh Rajput, Malachi Schram, Auralee Edelen, Jonathan Colen, Armen Kasparian, Ryan Roussel, Adam Carpenter, He Zhang, Jay Benesch

Data Science Faculty Publications

Particle accelerator operation requires simultaneous optimization of multiple objectives. Multi-objective optimization (MOO) is particularly challenging due to trade-offs between the objectives. Evolutionary algorithms, such as genetic algorithms (GAs), have been leveraged for many optimization problems, however, they do not apply to complex control problems by design. This paper demonstrates the power of differentiability for solving MOO problems in particle accelerators using a deep differentiable reinforcement learning (DDRL) algorithm. We compare the DDRL algorithm with model-free reinforcement learning (MFRL), GA, and Bayesian optimization (BO) for simultaneous optimization of heat load and trip rates in the continuous electron beam accelerator facility. The …

Time-Marching Quantum Algorithm For Simulation Of Nonlinear Lorenz Dynamics, Efstratios Koukoutsis, George Vahala, Min Soe, Kyriakos Hizanidis, Linda Vahala, Abhay K. Ram

Electrical & Computer Engineering Faculty Publications

Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by developing an explicit quantum algorithm that implements the time evolution of a second-order time-discretized version of the Lorenz model. The Lorenz model is a celebrated system of nonlinear ordinary differential equations that has been extensively studied in the contexts of climate science, fluid dynamics, and chaos theory. Our algorithm possesses a recursive structure and requires only a linear number of copies of the initial state …

Further Results On Learning Quantum Measurement Classes: Quantum Pac Model For Povm Hypothesis Classes, Arka Prabha Das

Electronic Theses & Dissertations (2024 - present)

This thesis investigates the problem of learning from quantum systems, where each example consists of a quantum state paired with a classical outcome. The task centers on choosing an effective measurement rule from a fixed set to enable accurate prediction of the classical outcome from the quantum state. A central focus lies in understanding whether joint measurement strategies that cannot be separated into local operations offer a real benefit in terms of the number of examples needed for successful learning. We examine conditions under which a non-separable measurement within a given hypothesis class achieves strictly better sample complexity bounds compared …

Improving 2–5 Qubit Quantum Phase Estimation Circuits Using Machine Learning, Charles Woodrum, Torrey J. Wagner, David E. Weeks

Faculty Publications

Quantum computing has the potential to solve problems that are currently intractable to classical computers with algorithms like Quantum Phase Estimation (QPE); however, noise significantly hinders the performance of today’s quantum computers. Machine learning has the potential to improve the performance of QPE algorithms, especially in the presence of noise. In this work, QPE circuits were simulated with varying levels of depolarizing noise to generate datasets of QPE output. In each case, the phase being estimated was generated with a phase gate, and each circuit modeled was defined by a randomly selected phase. The model accuracy, prediction speed, overfitting level …

Learning, Optimizing, And Simulating Fermions With Quantum Computers, Andrew Zhao

Physics & Astronomy ETDs

Fermions are fundamental particles which obey seemingly bizarre quantum-mechanical principles, yet constitute all the ordinary matter that we inhabit. As such, their study is heavily motivated from both fundamental and practical incentives. In this dissertation, we will explore how the tools of quantum information and computation can assist us on both of these fronts. We primarily do so through the task of partial state learning: tomographic protocols for acquiring a reduced, but sufficient, classical description of a quantum system. Developing fast methods for partial tomography addresses a critical bottleneck in quantum simulation algorithms, which is a particularly pressing issue for …

Predicting Biomolecular Properties And Interactions Using Numerical, Statistical And Machine Learning Methods, Elyssa Sliheet

Mathematics Theses and Dissertations

We investigate machine learning and electrostatic methods to predict biophysical properties of proteins, such as solvation energy and protein ligand binding affinity, for the purpose of drug discovery/development. We focus on the Poisson-Boltzmann model and various high performance computing considerations such as parallelization schemes.

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 …

Continuous-Variable Quantum Computation Of The O(3) Model In 1+1 Dimensions, Raghav G. Jha, Felix Ringer, George Siopsis, Shane Thompson

Physics Faculty Publications

We formulate the O(3) nonlinear sigma model in 1+1 dimensions as a limit of a three-component scalar field theory restricted to the unit sphere in the large squeezing limit. This allows us to describe the model in terms of the continuous-variable (CV) approach to quantum computing. We construct the ground state and excited states using the coupled-cluster Ansatz and find excellent agreement with the exact diagonalization results for a small number of lattice sites. We then present the simulation protocol for the time evolution of the model using CV gates and obtain numerical results using a photonic quantum simulator. We …

Applications Of Independent And Identically Distributed (Iid) Random Processes In Polarimetry And Climatology, Dan Kestner

Dissertations, Master's Theses and Master's Reports

The unifying theme of this thesis is the characterization of “perfect randomness,” i.e., independent and identically distributed (IID) stochastic processes as these are applied in physical science. Two specific and mathematically distinct applications are chosen: (i) Radar and optical polarimetry; (ii) Analysis of time series in meteorology. In (i), IID process of a special kind, namely, with a distribution defined by symmetry, is used to link its multivariate Gaussian density to uniformity on the Poincaré sphere. This “statistical ellipsometry” approach is then used to relate polarimetric mismatches or imbalances to ellipsometric variables and suitably chosen cross-correlation measures. In (ii), recently …

Accelerating Markov Chain Monte Carlo Sampling With Diffusion Models, N. T. Hunt-Smith, W. Melnitchouk, F. Ringer, N. Sato, A. W. Thomas, M. J. White

Physics Faculty Publications

Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model that can draw global samples with the aim of approximating the posterior. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. We then present our adapted Metropolis-Hastings algorithm which combines local proposals with global proposals taken from a diffusion model that is regularly trained on the samples produced during the …

Proof Of Principle For A Self-Governing Prediction And Forecasting Reward Algorithm, Jose Osvaldo Gonzalez-Hernandez, Jonathan Marino, Ted Rogers, Brandon Velasco

Physics Faculty Publications

We use Monte Carlo techniques to simulate an organized prediction competition between a group of scientific experts acting under the influence of a "self-governing" prediction reward algorithm. Our aim is to illustrate the advantages of a specific type of reward distribution rule that is designed to address some of the limitations of traditional forecast scoring rules. The primary extension of this algorithm as compared with standard forecast scoring is that it incorporates measures of both group consensus and question relevance directly into the reward distribution algorithm. Our model of the prediction competition includes parameters that control both the level of …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Human And Technical Factors In The Adoption Of Quantum Cryptographic Algorithms, Alyssa Pinkston

Mathematical Sciences Technical Reports (MSTR)

The purpose of this research is to understand what factors would cause users to choose quantum key distribution (QKD) over other methods of cryptography. An Advanced Encryption Standard (AES) key can be exchanged through communication using the Rivest, Shamir, Adleman (RSA) cryptographic algorithm, QKD, or post-quantum cryptography (PQC). QKD relies on quantum physics where RSA and PQC use complex mathematics to encrypt data. The BB84 quantum cryptographic protocol involves communication over a quantum channel and a public channel. The quantum channel can be technically attacked by beamsplitting or intercept/resend. QKD, like other forms of cryptography, is vulnerable to social attacks …

Machine Learning-Based Data And Model Driven Bayesian Uncertanity Quantification Of Inverse Problems For Suspended Non-Structural System, Zhiyuan Qin

All Dissertations

Inverse problems involve extracting the internal structure of a physical system from noisy measurement data. In many fields, the Bayesian inference is used to address the ill-conditioned nature of the inverse problem by incorporating prior information through an initial distribution. In the nonparametric Bayesian framework, surrogate models such as Gaussian Processes or Deep Neural Networks are used as flexible and effective probabilistic modeling tools to overcome the high-dimensional curse and reduce computational costs. In practical systems and computer models, uncertainties can be addressed through parameter calibration, sensitivity analysis, and uncertainty quantification, leading to improved reliability and robustness of decision and …