Robert L. Singleton
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View article: Truncated Modular Exponentiation Operators: A Strategy for Quantum Factoring
Truncated Modular Exponentiation Operators: A Strategy for Quantum Factoring Open
Modular exponentiation (ME) operators are one of the fundamental components of Shor's algorithm, and the place where most of the quantum resources are deployed. These operators are often referred to as the bottleneck of the algorithm. I pr…
View article: Truncated Modular Exponentiation Operators: A Strategy for Quantum Factoring
Truncated Modular Exponentiation Operators: A Strategy for Quantum Factoring Open
Modular exponentiation (ME) operators are one of the fundamental components of Shor's algorithm, and the place where most of the quantum resources are deployed. I propose a method for constructing the ME operators that relies upon the simp…
View article: Simultaneous gamma-ray, charged-particle, and x-ray observations of capsule implosions for charged-particle stopping power measurements
Simultaneous gamma-ray, charged-particle, and x-ray observations of capsule implosions for charged-particle stopping power measurements Open
View article: Shor's Factoring Algorithm and Modular Exponentiation Operators
Shor's Factoring Algorithm and Modular Exponentiation Operators Open
We provide a pedagogical presentation of Shor's factoring algorithm, which is a quantum algorithm for factoring very large numbers (of order of hundreds to thousands of bits) in polynomial time. In contrast, all known classical algorithms …
View article: Shor's Factoring Algorithm and Modular Exponentiation Operators
Shor's Factoring Algorithm and Modular Exponentiation Operators Open
These are pedagogical notes on Shor's factoring algorithm, which is a quantum algorithm for factoring very large numbers (of order of hundreds to thousands of bits) in polynomial time. In contrast, all known classical algorithms for the fa…
View article: Measurements of ion-electron energy-transfer cross section in high-energy-density plasmas
Measurements of ion-electron energy-transfer cross section in high-energy-density plasmas Open
We report on measurements of the ion-electron energy-transfer cross section utilizing low-velocity ion stopping in high-energy-density plasmas at the OMEGA laser facility. These measurements utilize a technique that leverages the close rel…
View article: Grover's Algorithm with Diffusion and Amplitude Steering
Grover's Algorithm with Diffusion and Amplitude Steering Open
We review the basic theoretical underpinnings of the Grover algorithm, providing a rigorous and well motivated derivation. We then present a generalization of Grover's algorithm that searches an arbitrary subspace of the multi-dimensional …
View article: Assessment of Discretization Uncertainty Estimators Based on Grid Refinement Studies
Assessment of Discretization Uncertainty Estimators Based on Grid Refinement Studies Open
This paper presents the assessment of the performance of nine discretization uncertainty estimates based on grid refinement studies including methods that use grid triplets and others that use a largest number of data points, which in this…
View article: Floating-Point Calculations on a Quantum Annealer: Division and Matrix Inversion
Floating-Point Calculations on a Quantum Annealer: Division and Matrix Inversion Open
Systems of linear equations are employed almost universally across a wide range of disciplines, from physics and engineering to biology, chemistry and statistics. Traditional solution methods such as Gaussian elimination become very time c…
View article: Review of the first charged-particle transport coefficient comparison workshop
Review of the first charged-particle transport coefficient comparison workshop Open
View article: BPS Explained III: The Leading Order Behavior of the BBGKY Hierarchy in a Plasma
BPS Explained III: The Leading Order Behavior of the BBGKY Hierarchy in a Plasma Open
This is the third in a series of lectures on the technique of dimensional continuation, employed by Brown, Preston and Singleton (BPS), for calculating Coulomb energy exchange rates in a plasma. Two important examples of such processes are…
View article: Multimaterial Heat Flow Verification
Multimaterial Heat Flow Verification Open
Multimaterial heat diffusion can be a challenging numerical problem when the material boundaries are misaligned with the numerical grid. Even when the boundaries start out aligned, they typically become misaligned through hydrodynamic moti…
View article: Floating-Point Calculations on a Quantum Annealer: Division and Matrix\n Inversion
Floating-Point Calculations on a Quantum Annealer: Division and Matrix\n Inversion Open
Systems of linear equations are employed almost universally across a wide\nrange of disciplines, from physics and engineering to biology, chemistry and\nstatistics. Traditional solution methods such as Gaussian elimination become\nvery tim…
View article: Verification Studies for the Noh Problem Using Nonideal Equations of State and Finite Strength Shocks
Verification Studies for the Noh Problem Using Nonideal Equations of State and Finite Strength Shocks Open
The Noh verification test problem is extended beyond the commonly studied ideal gamma-law gas to more realistic equations of state (EOSs) including the stiff gas, the Noble-Abel gas, and the Carnahan–Starling EOS for hard-sphere fluids. Se…
View article: Extension of the planar Noh problem to aluminum, iron, copper, and tungsten
Extension of the planar Noh problem to aluminum, iron, copper, and tungsten Open
The classic Noh verification test problem is extended beyond the traditional ideal gas and applied to shock compression of condensed matter. Using the stiff-gas equation of state (EOS), which admits an exact analytical solution for the pla…
View article: Effects of alpha stopping power modelling on the ignition threshold in a directly-driven inertial confinement fusion capsule
Effects of alpha stopping power modelling on the ignition threshold in a directly-driven inertial confinement fusion capsule Open
View article: The Planar Sandwich and Other 1D Planar Heat Flow Test Problems in ExactPack
The Planar Sandwich and Other 1D Planar Heat Flow Test Problems in ExactPack Open
This report documents the implementation of several related 1D heat flow problems in the verification package ExactPack. In particular, the planar sandwich class defined by Dawes et al., as well as the classes PlanarSandwichHot, PlanarSand…
View article: Reaction-in-Flight neutrons as a test of stopping power in degenerate plasmas
Reaction-in-Flight neutrons as a test of stopping power in degenerate plasmas Open
Cryogenically cooled inertial confinement fusion capsule designs are suitable for studies of reaction-in-flight (RIF) neutrons. RIF neutrons occur when energetically up-scattered ions undergo DT reactions with a thermal ion in the plasma, …