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Quantum simulations with graphics processing units
|Title:||Quantum simulations with graphics processing units|
|Authors:||Smith, Steven Gregory|
|Contributors:||Yepez, Jeffrey (advisor)|
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|Publisher:||University of Hawai'i at Manoa|
|Abstract:||This document aims to describe the methodology of quantum lattice gas algorithm based|
quantum physics simulations with details on implementation using graphics processing units.
A variety of examples illustrating the general application of these methods are included.
These examples are used to highlight topics such as scaling, potentials, momentums, multiple
particle and dimensions, and various Hamiltonians in quantum simulations. Although
intended to fullfill the doctor of philosophy degree requirement, this document is well suited
as an introduction to this approach to modeling physics.
In recent times parallelization has significantly improved the available computational
power. Graphics processing units (GPUs) are a shining example of this, with thousands of
compute cores and continually improved general computational capabilities, these processors
can outshine their central processing unit (CPU) counterparts by orders of magnitude.
Presented here are a number of examples of efficient computational methods for simulating
physics using GPUs. Our quantum simulation method involves the quantum lattice
gas model of quantum computation [59, 68, 64], however much of the parallel technology
implementation is applicable to other numerical approaches. The quantum lattice gas model
of computation is based on a unitary stream-collide quantum algorithm applied repeatedly
over time upon an ordered array of qubits [53, 56, 68, 61, 63, 67]. The stream-collide quantum
algorithm represents local quantum evolution of the system of quantum particles whose
motion is constrained to reside on a spacetime lattice. Each particle in the system undergoes
a quantum walk, interacting locally with other particles in the system that may reside on
the same point.
We will first mathematically describe the basic idea of quantum lattice gas algorithms.
Next we will discuss GPUs and the basic features needed for implementation. We will then
describe several examples of quantum lattice gas algorithm approach to illustrate the various
applications and implementation challenges. Of particular interest is a look at modeling
time-dependent many-body quantum mechanics using quantum lattice gas methods. For
practical purposes we focus on the case of two fermions governed by the nonrelativistic
Schrödinger equation. Numerical comparisons to analytic prediction show the high accuracy
of these methods. Quantum lattice gas methods are chosen as a unitary algorithm for time dependent
quantum simulation as they are efficient, accurate, and avoid the Fermi sign
problem. Our findings from two-particle simulations under various conditions include the
physics of the one and two particle systems diverging in their respective time-dependent behavior with increasing entanglement. We also confirm the multiple particle extension of
the Ehrenfest theorem.
Using the examples discussed throughout this document, we will then describe our specific
computational implementation utilizing the computational power of GPUs through Nvidia’s
compute unified device architecture (CUDA) language. Here we will discuss the open source
software our group is developing based on these methods, along with some implementation
verification and debugging concepts.
Education is another application peripherally connected to this work and our software.
The applications of this type of modeling as a learning tool is not fully explored yet, but the
opportunities are promising.
|Rights:||All UHM dissertations and theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner.|
|Appears in Collections:||
Ph.D. - Physics|
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