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Spectral graph theory with applicati...

University of Maryland, College Park., Physics.

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Spectral graph theory with applications to quantum adiabatic optimization.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Spectral graph theory with applications to quantum adiabatic optimization./
Author:	Baume, Michael Jarret.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
Description:	132 p.
Notes:	Source: Dissertation Abstracts International, Volume: 77-12(E), Section: B.
Contained By:	Dissertation Abstracts International77-12B(E).
Subject:	Quantum physics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10128740
ISBN:	9781339867403

Spectral graph theory with applications to quantum adiabatic optimization.
Baume, Michael Jarret.

Spectral graph theory with applications to quantum adiabatic optimization. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 132 p.

Source: Dissertation Abstracts International, Volume: 77-12(E), Section: B.

Thesis (Ph.D.)--University of Maryland, College Park, 2016.

In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as "stoquastic" or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above.

ISBN: 9781339867403Subjects--Topical Terms:

726746
Quantum physics.

Spectral graph theory with applications to quantum adiabatic optimization.
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100 1 $a Baume, Michael Jarret. $3 3279437
245 1 0 $a Spectral graph theory with applications to quantum adiabatic optimization.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2016
300 $a 132 p.
500 $a Source: Dissertation Abstracts International, Volume: 77-12(E), Section: B.
500 $a Advisers: Stephen P. Jordan; Andrew Childs; Alexey Gorshkov.
502 $a Thesis (Ph.D.)--University of Maryland, College Park, 2016.
520 $a In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as "stoquastic" or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above.
520 $a I predominantly explore the connection between the spectral gap of an operator, or the difference between the two lowest energies of that operator, and certain equilibrium behavior. In the context of adiabatic optimization, this corresponds to the likelihood of solving the optimization problem of interest. I will provide an instance of an optimization problem that is easy to solve classically, but leaves open the possibility to being difficult adiabatically.
520 $a Aside from this concrete example, the work in this dissertation is predominantly mathematical and we focus on bounding the spectral gap. Our primary tool for doing this is spectral graph theory, which provides the most natural approach to this task by simply considering Dirichlet eigenvalues of subgraphs of host graphs. I will derive tight bounds for the gap of one-dimensional, hypercube, and general convex subgraphs. The techniques used will also adapt methods recently used by Andrews and Clutterbuck to prove the long-standing "Fundamental Gap Conjecture".
590 $a School code: 0117.
650 4 $a Quantum physics. $3 726746
650 4 $a Mathematics. $3 515831
650 4 $a Computer science. $3 523869
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710 2 $a University of Maryland, College Park. $b Physics. $3 1266199
773 0 $t Dissertation Abstracts International $g 77-12B(E).
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792 $a 2016
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856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10128740