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Full-Text Articles in Physics
Human And Technical Factors In The Adoption Of Quantum Cryptographic Algorithms, Alyssa Pinkston
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 …
Applying Hallgren’S Algorithm For Solving Pell’S Equation To Finding The Irrational Slope Of The Launch Of A Billiard Ball, Sangheon Choi
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 …
Implementation Of A Least Squares Method To A Navier-Stokes Solver, Jada P. Lytch, Taylor Boatwright, Ja'nya Breeden
Implementation Of A Least Squares Method To A Navier-Stokes Solver, Jada P. Lytch, Taylor Boatwright, Ja'nya Breeden
Rose-Hulman Undergraduate Mathematics Journal
The Navier-Stokes equations are used to model fluid flow. Examples include fluid structure interactions in the heart, climate and weather modeling, and flow simulations in computer gaming and entertainment. The equations date back to the 1800s, but research and development of numerical approximation algorithms continues to be an active area. To numerically solve the Navier-Stokes equations we implement a least squares finite element algorithm based on work by Roland Glowinski and colleagues. We use the deal.II academic library , the C++ language, and the Linux operating system to implement the solver. We investigate convergence rates and apply the least squares …
Computer Program Simulation Of A Quantum Turing Machine With Circuit Model, Shixin Wu
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.
Spectrally-Resolved Imaging Of The Transverse Modes In Multimode Vcsels, Stephan A. Misak, Dan G. Dugmore, Kirsten A. Middleton, Evan R. Hale, Kelly R. Farner, Kent D. Choquette, Paul O. Leisher
Spectrally-Resolved Imaging Of The Transverse Modes In Multimode Vcsels, Stephan A. Misak, Dan G. Dugmore, Kirsten A. Middleton, Evan R. Hale, Kelly R. Farner, Kent D. Choquette, Paul O. Leisher
Rose-Hulman Undergraduate Research Publications
Vertical-cavity surface-emitting lasers (VCSELs) enable a range of applications such as data transmission, trace sensing, atomic clocks, and optical mice. For many of these applications, the output power and beam quality are both critical (i.e. high output power with good beam quality is desired). Multi-mode VCSELs offer much higher power than single-mode devices, but this comes at the expense of lower beam quality. Directly observing the resolved mode structure of multi-mode VCSELs would enable engineers to better understand the underlying physics and help them to develop multi-mode devices with improved beam quality. In this work, a low-cost, high-resolution (<3 >pm) …