Show simple item record

dc.contributor.authorWebb, Zachary 20:02:33 (GMT) 20:02:33 (GMT)
dc.description.abstractMany-body systems are well known throughout physics to be hard problems to exactly solve, but much of this is folklore resulting from the lack of an analytic solution to these systems. This thesis attempts to classify the complexity inherent in many of these systems, and give quantitative results for why the problems are hard. In particular, we analyze the many-particle system corresponding to a multi-particle quantum walk, showing that the time evolution of such systems on a polynomial sized graph is universal for quantum computation, and thus determining how a particular state evolves is as hard as an arbitrary quantum computation. We then analyze the ground energy properties of related systems, showing that for bosons, bounding the ground energy of the same Hamiltonian with a fixed number of particles is QMA-complete. Similar techniques provide a novel proof that quantum walk is universal for quantum computing, and constructs a QMA-complete problem that does not reference quantum mechanics.en
dc.publisherUniversity of Waterlooen
dc.subjectQuantum Informationen
dc.subjectQuantum Walken
dc.subjectHamiltonian Complexityen
dc.subjectBose-Hubbard Modelen
dc.titleThe computational power of many-body systemsen
dc.typeDoctoral Thesisen
dc.pendingfalse and Astronomyen (Quantum Information)en of Waterlooen
uws-etd.degreeDoctor of Philosophyen
uws.contributor.advisorChilds, Andrew
uws.contributor.affiliation1Faculty of Scienceen

Files in this item


This item appears in the following Collection(s)

Show simple item record


University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages