Theory and Algorithms Commons^™

Applying Hallgren’S Algorithm For Solving Pell’S Equation To Finding The Irrational Slope Of The Launch Of A Billiard Ball, Sangheon Choi

Mathematical Sciences Technical Reports (MSTR)

This thesis is an exploration of Quantum Computing applied to Pell’s equation in an attempt to find solutions to the Billiard Ball Problem. Pell’s equation is a Diophantine equation in the form of x² − ny² = 1, where n is a given positive nonsquare integer, and integer solutions are sought for x and y. We will be applying Hallgren’s algorithm for finding irrational periods in functions, in the context of billiard balls and their movement on a friction-less unit square billiard table. Our central research question has been the following: Given the cutting sequence of the billiard …

Establishing The Legal Framework To Regulate Quantum Computing Technology, Kaya Derose

Catholic University Journal of Law and Technology

No abstract provided.

Patch-Wise Training With Convolutional Neural Networks To Synthetically Upscale Cfd Simulations, John P. Romano, Alec C. Brodeur, Oktay Baysal

Mechanical & Aerospace Engineering Faculty Publications

This paper expands the authors’ prior work[1], which focuses on developing a convolutional neural network (CNN) model capable of mapping time-averaged, unsteady Reynold’s-averaged Navier-Stokes (URANS) simulations to higher resolution results informed by time-averaged detached eddy simulations (DES). The authors present improvements over the prior CNN autoencoder model that result from hyperparameter optimization, increased data set augmentation through the adoption of a patch-wise training approach, and the predictions of primitive variables rather than vorticity magnitude. The training of the CNN model developed in this study uses the same URANS and DES simulations of a transonic flow around several NACA 4-digit airfoils …

Machine Learning-Based Jet And Event Classification At The Electron-Ion Collider With Applications To Hadron Structure And Spin Physics, Kyle Lee, James Mulligan, Mateusz Płoskoń, Felix Ringer, Feng Yuan

Physics Faculty Publications

We explore machine learning-based jet and event identification at the future Electron-Ion Collider (EIC). We study the effectiveness of machine learning-based classifiers at relatively low EIC energies, focusing on (i) identifying the flavor of the jet and (ii) identifying the underlying hard process of the event. We propose applications of our machine learning-based jet identification in the key research areas at the future EIC and current Relativistic Heavy Ion Collider program, including enhancing constraints on (transverse momentum dependent) parton distribution functions, improving experimental access to transverse spin asymmetries, studying photon structure, and quantifying the modification of hadrons and jets in …

The Effect Of The Width Of The Incident Pulse To The Dielectric Transition Layer In The Scattering Of An Electromagnetic Pulse — A Qubit Lattice Algorithm Simulation, George Vahala, Linda Vahala, Abhay K. Ram, Min Soe

Electrical & Computer Engineering Faculty Publications

The effect of the thickness of the dielectric boundary layer that connects a material of refractive index n₁ to another of index n₂is considered for the propagation of an electromagnetic pulse. A qubit lattice algorithm (QLA), which consists of a specially chosen non-commuting sequence of collision and streaming operators acting on a basis set of qubits, is theoretically determined that recovers the Maxwell equations to second-order in a small parameter ϵ. For very thin boundary layer the scattering properties of the pulse mimics that found from the Fresnel jump conditions for a plane wave - except that …

Machine-Assisted Discovery Of Integrable Symplectic Mappings, T. Zolkin, Y. Kharkov, S. Nagaitsev

Physics Faculty Publications

We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e., integrals of motion. The core idea of the algorithm is based on the knowledge that the evolution of an integrable system in the phase space is restricted to a lower-dimensional submanifold. Limiting ourselves to polygon invariants of motion, we analyze the shape of individual trajectories thus successfully distinguishing integrable motion from chaotic cases. For example, our method rediscovers some of the famous McMillan-Suris integrable mappings and ultradiscrete Painlevé equations. In total, …

Hhl Algorithm On The Honeywell H1 Quantum Computer, Adrik B. Herbert, Eric A. F. Reinhardt

Discovery Undergraduate Interdisciplinary Research Internship

The quantum algorithm for linear systems of equations (HHL algorithm) provides an efficient tool for finding solutions to systems of functions with a large number of variables and low sensitivity to changes in inputs (i.e. low error rates). For complex problems, such as matrix inversion, HHL requires exponentially less computational time as compared with classical computation methods. HHL can be adapted to current quantum computing systems with limited numbers of qubits (quantum computation bits) but a high reusability rate such as the Honeywell H1 quantum computer. Some methods for improving HHL have been proposed through the combination of quantum and …

A Super Fast Algorithm For Estimating Sample Entropy, Weifeng Liu, Ying Jiang, Yuesheng Xu

Mathematics & Statistics Faculty Publications

: Sample entropy, an approximation of the Kolmogorov entropy, was proposed to characterize complexity of a time series, which is essentially defined as − log(B/A), where B denotes the number of matched template pairs with length m and A denotes the number of matched template pairs with m + 1, for a predetermined positive integer m. It has been widely used to analyze physiological signals. As computing sample entropy is time consuming, the box-assisted, bucket-assisted, x-sort, assisted sliding box, and kd-tree-based algorithms were proposed to accelerate its computation. These algorithms require O(N²) or …

Numerical Treatment For Special Type Of Mixed Linear Delay Volterra Integro-Differential Equations, Atheer J. Kadhim

Emirates Journal for Engineering Research

The idea of research is a representation of the nonlinear pseudo-random generators using state-space equations that is not based on the usual description as shift register synthesis but in terms of matrices. Different types of nonlinear pseudo-random generators with their algorithms have been applied in order to investigate the output pseudo-random sequences. Moreover, two examples are given for conciliated the results of this representation.

Computer Program Simulation Of A Quantum Turing Machine With Circuit Model, Shixin Wu

Mathematical Sciences Technical Reports (MSTR)

Molina and Watrous present a variation of the method to simulate a quantum Turing machine employed in Yao’s 1995 publication “Quantum Circuit Complexity”. We use a computer program to implement their method with linear algebra and an additional unitary operator defined to complete the details. Their method is verified to be correct on a quantum Turing machine.

Computational Studies Of Carbon Nanocluster Solidification, Chathuri C. Silva

Dissertations

A subset of micron-size meteoritic carbon particles formed in red giant atmospheres show a core-rim structure, likely condensed from a vapor phase into super-cooled carbon droplets that nucleated graphene sheets (~40Å) on randomly oriented 5-atom loops during solidification, followed by coating with a graphite rim. Similar particles form during slow cooling of carbon vapor in the lab.

Here we investigate the nucleation and growth of carbon rings and graphene sheets using density functional theory (DFT). Our objectives: (1). explore different computational techniques in DFT-VASP for various carbon structures and compare the results with literature, (2). investigate the nucleation and growth …

Rotating Scatter Mask For Directional Radiation Detection And Imaging, Darren Holland, Robert Olesen, Larry Burggraf, Buckley O'Day, James E. Bevins

AFIT Patents

A radiation imaging system images a distributed source of radiation from an unknown direction by rotating a scatter mask around a central axis. The scatter mask has a pixelated outer surface of tangentially oriented, flat geometric surfaces that are spherically varying in radial dimension that corresponds to a discrete amount of attenuation. Rotation position of the scatter mask is tracked as a function of time. Radiation counts from gamma and/or neutron radiation are received from at least one radiation detector that is positioned at or near the central axis. A rotation-angle dependent detector response curve (DRC) is generated based on …

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 …

Data-Driven Approaches To Complex Materials: Applications To Amorphous Solids, Dil Kumar Limbu

Dissertations

While conventional approaches to materials modeling made significant contributions and advanced our understanding of materials properties in the past decades, these approaches often cannot be applied to disordered materials (e.g., glasses) for which accurate total-energy functionals or forces are either not available or it is infeasible to employ due to computational complexities associated with modeling disordered solids in the absence of translational symmetry. In this dissertation, a number of information-driven probabilistic methods were developed for the structural determination of a range of materials including disordered solids to transition metal clusters. The ground-state structures of transition-metal clusters of iron, nickel, and …

Implications Of The Quantum Dna Model For Information Sciences, F. Matthew Mihelic

Faculty Publications

The DNA molecule can be modeled as a quantum logic processor, and this model has been supported by pilot research that experimentally demonstrated non-local communication between cells in separated cell cultures. This modeling and pilot research have important implications for information sciences, providing a potential architecture for quantum computing that operates at room temperature and is scalable to millions of qubits, and including the potential for an entanglement communication system based upon the quantum DNA architecture. Such a system could be used to provide non-local quantum key distribution that could not be blocked by any shielding or water depth, would …

Quantum Simulation Of Schrödinger's Equation, Mohamed Eltohfa

Capstone and Graduation Projects

Quantum computing is one of the promising active areas in physics research. This is because of the potential of quantum algorithms to outperform their classical counterparts. Grover’s search algorithm has a quadratic speed-up compared to the classical linear search. The quantum simulation of Schrödinger’s equation has an exponential memory save-up compared to the classical simulation. In this thesis, the ideas and tools of quantum computing are reviewed. Grover’s algorithm is studied and simulated as an example. Using the Qiskit quantum computing library, a code to simulate Schrödinger’s equation for a particle in one dimension is developed, simulated locally, and run …

Understanding The Research And Applications Of Quantum Computing, Joshua Foss

Williams Honors College, Honors Research Projects

In-Depth research of current quantum computing understanding and practices. Presentation of possible new and creative applications of quantum computing.

An Update On The Computational Theory Of Hamiltonian Period Functions, Bradley Joseph Klee

Graduate Theses and Dissertations

Lately, state-of-the-art calculation in both physics and mathematics has expanded to include the field of symbolic computing. The technical content of this dissertation centers on a few Creative Telescoping algorithms of our own design (Mathematica implementations are given as a supplement). These algorithms automate analysis of integral period functions at a level of difficulty and detail far beyond what is possible using only pencil and paper (unless, perhaps, you happen to have savant-level mental acuity). We can then optimize analysis in classical physics by using the algorithms to calculate Hamiltonian period functions as solutions to ordinary differential equations. The simple …

Machine Learning Corrected Quantum Dynamics Calculations, A. Jasinski, J. Montaner, R. C. Forrey, B. H. Yang, P. C. Stancil, Naduvalath Balakrishnan, J. Dai, A. Vargas-Hernandez, R. V. Krems

Chemistry and Biochemistry Faculty Research

Quantum scattering calculations for all but low-dimensional systems at low energies must rely on approximations. All approximations introduce errors. The impact of these errors is often difficult to assess because they depend on the Hamiltonian parameters and the particular observable under study. Here, we illustrate a general, system- and approximation-independent, approach to improve the accuracy of quantum dynamics approximations. The method is based on a Bayesian machine learning (BML) algorithm that is trained by a small number of exact results and a large number of approximate calculations, resulting in ML models that can generalize exact quantum results to different dynamical …

Quantum Random Walk Search And Grover's Algorithm - An Introduction And Neutral-Atom Approach, Anna Maria Houk

Physics

In the sub-field of quantum algorithms, physicists and computer scientist take classical computing algorithms and principles and see if there is a more efficient or faster approach implementable on a quantum computer, i.e. a ”quantum advantage”. We take random walks, a widely applicable group of classical algorithms, and move them into the quantum computing paradigm. Additionally, an introduction to a popular quantum search algorithm called Grover’s search is included to guide the reader to the development of a quantum search algorithm using quantum random walks. To close the gap between algorithm and hardware, we will look at using neutral-atom (also …

Global Gradient-Based Phase Unwrapping Algorithm For Increased Performance In Wavefront Sensing, Bryan R. Bartelt

Theses and Dissertations

As the reliance on satellite data for military and commercial use increases, more effort must be exerted to protect our space-based assets. In order to help increase our space domain awareness (SDA), new approaches to ground-based space surveillance via wavefront sensing must be adopted. Improving phase-unwrapping algorithms in order to assist in phase retrieval methods is one way of increasing the performance in current adaptive optics (AO) systems. This thesis proposes a new phase-unwrapping algorithm that uses a global, gradient-based technique to more rapidly identify and correct for areas of phase wrapping during particular phase retrieval methods. This is beneficial …

Sparsity And Weak Supervision In Quantum Machine Learning, Seyran Saeedi

Theses and Dissertations

Quantum computing is an interdisciplinary field at the intersection of computer science, mathematics, and physics that studies information processing tasks on a quantum computer. A quantum computer is a device whose operations are governed by the laws of quantum mechanics. As building quantum computers is nearing the era of commercialization and quantum supremacy, it is essential to think of potential applications that we might benefit from. Among many applications of quantum computation, one of the emerging fields is quantum machine learning. We focus on predictive models for binary classification and variants of Support Vector Machines that we expect to be …

Quantum Algorithms With Applications To Simulating Physical Systems, Anirban Ch Narayan Chowdhury

Physics & Astronomy ETDs

The simulation of quantum physical systems is expected to be an important application for quantum computers. The work presented in this dissertation aims to improve the resource requirements of quantum computers for solving simulation problems, by providing both novel quantum algorithms and improved implementations of existing ones. I present three main results that cover diverse aspects of simulation including equilibrium physics, the preparation of useful quantum states, and simulations based on classical stochastic processes. The results rely on established quantum algorithms and other recent techniques which I review. My first original contribution is a new quantum algorithm to sample from …

Using Forensics To Introduce Ir Spectroscopy & Molecular Modeling, Joseph T. Golab

Faculty Publications & Research

A student activity is reported that analyzes “medical evidence” with experimental and computational methods. The lesson demonstrates benefits of solving practical problems with integrated tools.

A Theoretical Model Of Underground Dipole Antennas For Communications In Internet Of Underground Things, Abdul Salam, Mehmet C. Vuran, Xin Dong, Christos Argyropoulos, Suat Irmak

Faculty Publications

The realization of Internet of Underground Things (IOUT) relies on the establishment of reliable communication links, where the antenna becomes a major design component due to the significant impacts of soil. In this paper, a theoretical model is developed to capture the impacts of change of soil moisture on the return loss, resonant frequency, and bandwidth of a buried dipole antenna. Experiments are conducted in silty clay loam, sandy, and silt loam soil, to characterize the effects of soil, in an indoor testbed and field testbeds. It is shown that at subsurface burial depths (0.1-0.4m), change in soil moisture impacts …

@Yourlocation: A Spatial Analysis Of Geotagged Tweets In The Us, Ocean Mckinney

CMC Senior Theses

This project examines the spatial network properties observable from geo-located tweet data. Conventional exploration examines characteristics of a variety of network attributes, but few employ spatial edge correlations in their analysis. Recent studies have demonstrated the improvements that these correlations contribute to drawing conclusions about network structure. This thesis expands upon social network research utilizing spatial edge correlations and presents processing and formatting techniques for JSON (JavaScript Object Notation) data.

Genetic Algorithm Design Of Photonic Crystals For Energy-Efficient Ultrafast Laser Transmitters, Troy A. Hutchins-Delgado

Shared Knowledge Conference

Photonic crystals allow light to be controlled and manipulated such that novel photonic devices can be created. We are interested in using photonic crystals to increase the energy efficiency of our semiconductor whistle-geometry ring lasers. A photonic crystal will enable us to reduce the ring size, while maintaining confinement, thereby reducing its operating power. Photonic crystals can also exhibit slow light that will increase the interaction with the material. This will increase the gain, and therefore, lower the threshold for lasing to occur. Designing a photonic crystal for a particular application can be a challenge due to its number of …

Sampling Complexity Of Bosonic Random Walkers On A One-Dimensional Lattice, Gopikrishnan Muraleedharan, Akimasa Miyake, Ivan Deutsch

Shared Knowledge Conference

Computers based quantum logic are believed to solve problems faster and more efficiently than computers based on classical boolean logic. However, a large-scale universal quantum computer with error correction may not be realized in near future. But we can ask the question: can we devise a specific problem that a quantum device can solve faster than current state of the art super computers? One such problem is the so called "Boson Sampling" problem introduced by Aaronson and Arkhipov. The problem is to generate random numbers according to same distribution as the output number configurations of photons in linear optics. It …

Development Of A Slab-Based Monte Carlo Proton Dose Algorithm With A Robust Material-Dependent Nuclear Halo Model, John Wesley Chapman Jr

LSU Doctoral Dissertations

Pencil beam algorithms (PBAs) are often utilized for dose calculation in proton therapy treatment planning because they are fast and accurate under most conditions. However, as discussed in Chapman et al (2017), the accuracy of a PBA can be limited under certain conditions because of two major assumptions: (1) the central-axis semi-infinite slab approximation; and, (2) the lack of material dependence in the nuclear halo model. To address these limitations, we transported individual protons using a class II condensed history Monte Carlo and added a novel energy loss method that scaled the nuclear halo equation in water to arbitrary geometry. …

Efficient Phase Retrieval For Off-Axis Point Spread Functions, Salome Esteban Carrasco

Theses and Dissertations

A novel pairing of phase retrieval tools allows for efficient estimation of pupil phase in optical systems from images of point spread functions (PSFs). The phase retrieval algorithm uses correlation of modeled phase in the focal plane to decouple aberrations that are difficult to identify in complex PSFs. The use of a phase kernel that departs from the Fresnel approximation for off-axis PSFs is a more accurate representation of wavefront phase in finite conjugate imaging. The combination of the approximation and phase correlation algorithm can be more efficient and accurate than generic algorithms.