東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Graph Theoretic Algorithms Adaptable...

Srivastava, Siddhartha.

FindBook

Google Book

Amazon

博客來

Graph Theoretic Algorithms Adaptable to Quantum Computing.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Graph Theoretic Algorithms Adaptable to Quantum Computing./
作者:	Srivastava, Siddhartha.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	240 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-01, Section: B.
Contained By:	Dissertations Abstracts International83-01B.
標題:	Engineering. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28667001
ISBN:	9798516089541

Graph Theoretic Algorithms Adaptable to Quantum Computing.
Srivastava, Siddhartha.

Graph Theoretic Algorithms Adaptable to Quantum Computing. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 240 p.

Source: Dissertations Abstracts International, Volume: 83-01, Section: B.

Thesis (Ph.D.)--University of Michigan, 2021.

This item must not be sold to any third party vendors.

Computational methods are rapidly emerging as an essential tool for understanding and solving complex engineering problems, which complement the traditional tools of experimentation and theory. When considered in a discrete computational setting, many engineering problems can be reduced to a graph coloring problem. Examples range from systems design, airline scheduling, image segmentation to pattern recognition, where energy cost functions with discrete variables are extremized. However, using discrete variables over continuous variables introduces some complications when defining differential quantities, such as gradients and Hessians involved in scientific computations within solid and fluid mechanics. Consequently, graph techniques are under-utilized in this important domain. However, we have recently witnessed great developments in quantum computing where physical devices can solve discrete optimization problems faster than most well-known classical algorithms. This warrants further investigation into the re-formulation of scientific computation problems into graph-theoretic problems, thus enabling rapid engineering simulations in a soon-to-be quantum computing world.The computational techniques developed in this thesis allow the representation of surface scalars, such as perimeter and area, using discrete variables in a graph. Results from integral geometry, specifically Cauchy-Crofton relations, are used to estimate these scalars via submodular functions. With this framework, several quantities important to engineering applications can be represented in graph-based algorithms. These include the surface energy of cracks for fracture prediction, grain boundary energy to model microstructure evolution, and surface area estimates (of grains and fibers) for generating conformal meshes. Combinatorial optimization problems for these applications are presented first.The last two chapters describe two new graph coloring algorithms implemented on a physical quantum computing device: the D-wave quantum annealer. The first algorithm describes a functional minimization approach to solve differential equations. The second algorithm describes a realization of the Boltzmann machine learning algorithm on a quantum annealer. The latter allows generative and discriminative learning of data, which has vast applications in many fields. Theoretical aspects and the implementation of these problems are outlined with a focus on engineering applications.

ISBN: 9798516089541Subjects--Topical Terms:

586835
Engineering.
Subjects--Index Terms:

Quantum annealing

Graph Theoretic Algorithms Adaptable to Quantum Computing.
LDR:03791nmm a2200397 4500 001 2285273
005 20211129124024.5
008 220723s2021 ||||||||||||||||| ||eng d
020 $a 9798516089541
035 $a (MiAaPQ)AAI28667001
035 $a (MiAaPQ)umichrackham003592
035 $a AAI28667001
040 $a MiAaPQ $c MiAaPQ
100 1 $a Srivastava, Siddhartha. $3 3564564
245 1 0 $a Graph Theoretic Algorithms Adaptable to Quantum Computing.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 240 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-01, Section: B.
502 $a Thesis (Ph.D.)--University of Michigan, 2021.
506 $a This item must not be sold to any third party vendors.
506 $a This item must not be added to any third party search indexes.
520 $a Computational methods are rapidly emerging as an essential tool for understanding and solving complex engineering problems, which complement the traditional tools of experimentation and theory. When considered in a discrete computational setting, many engineering problems can be reduced to a graph coloring problem. Examples range from systems design, airline scheduling, image segmentation to pattern recognition, where energy cost functions with discrete variables are extremized. However, using discrete variables over continuous variables introduces some complications when defining differential quantities, such as gradients and Hessians involved in scientific computations within solid and fluid mechanics. Consequently, graph techniques are under-utilized in this important domain. However, we have recently witnessed great developments in quantum computing where physical devices can solve discrete optimization problems faster than most well-known classical algorithms. This warrants further investigation into the re-formulation of scientific computation problems into graph-theoretic problems, thus enabling rapid engineering simulations in a soon-to-be quantum computing world.The computational techniques developed in this thesis allow the representation of surface scalars, such as perimeter and area, using discrete variables in a graph. Results from integral geometry, specifically Cauchy-Crofton relations, are used to estimate these scalars via submodular functions. With this framework, several quantities important to engineering applications can be represented in graph-based algorithms. These include the surface energy of cracks for fracture prediction, grain boundary energy to model microstructure evolution, and surface area estimates (of grains and fibers) for generating conformal meshes. Combinatorial optimization problems for these applications are presented first.The last two chapters describe two new graph coloring algorithms implemented on a physical quantum computing device: the D-wave quantum annealer. The first algorithm describes a functional minimization approach to solve differential equations. The second algorithm describes a realization of the Boltzmann machine learning algorithm on a quantum annealer. The latter allows generative and discriminative learning of data, which has vast applications in many fields. Theoretical aspects and the implementation of these problems are outlined with a focus on engineering applications.
590 $a School code: 0127.
650 4 $a Engineering. $3 586835
650 4 $a Materials science. $3 543314
650 4 $a Mechanics. $3 525881
653 $a Quantum annealing
653 $a Computational solid mechanics
653 $a Numerical method for differential equations
653 $a Polycrystalline materials
653 $a Boltzmann machines
653 $a Fracture mechanics
690 $a 0346
690 $a 0794
690 $a 0537
710 2 $a University of Michigan. $b Aerospace Engineering. $3 2093897
773 0 $t Dissertations Abstracts International $g 83-01B.
790 $a 0127
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28667001