Citation
Bilgin, Ersen (2011) Simulation of Strongly Correlated Quantum Many-Body Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/FQDK-A221. https://resolver.caltech.edu/CaltechTHESIS:04082011-161930834
Abstract
In this thesis, we address the problem of solving for the properties of interacting quantum many-body systems in thermal equilibrium. The complexity of this problem increases exponentially with system size, limiting exact numerical simulations to very small systems. To tackle more complex systems, one needs to use heuristic algorithms that approximate solutions to these systems. Belief propagation is one such algorithm that we discuss in chapters 2 and 3. Using belief propagation, we demonstrate that it is possible to solve for static properties of highly correlated quantum many-body systems for certain geometries at all temperatures. In chapter 4, we generalize the multiscale renormalization ansatz to the anyonic setting to solve for the ground state properties of anyonic quantum many-body systems. The algorithms we present in chapters 2, 3, and 4 are very successful in certain settings, but they are not applicable to the most general quantum mechanical systems. For this, we propose using quantum computers as we discuss in chapter 5. The dimension reduction algorithm we consider in chapter 5 enables us to prepare thermal states of any quantum many-body system on a quantum computer faster than any previously known algorithm. Using these thermal states as the initialization of a quantum computer, one can study both static and dynamic properties of quantum systems without any memory overhead.
Item Type: | Thesis (Dissertation (Ph.D.)) | ||||||
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Subject Keywords: | Quantum Algorithms; Quantum Many-Body Systems; Simulation; anyons; thermalization; | ||||||
Degree Grantor: | California Institute of Technology | ||||||
Division: | Physics, Mathematics and Astronomy | ||||||
Major Option: | Physics | ||||||
Thesis Availability: | Public (worldwide access) | ||||||
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Thesis Committee: |
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Defense Date: | 6 April 2011 | ||||||
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Record Number: | CaltechTHESIS:04082011-161930834 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:04082011-161930834 | ||||||
DOI: | 10.7907/FQDK-A221 | ||||||
Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 6282 | ||||||
Collection: | CaltechTHESIS | ||||||
Deposited By: | Ersen Bilgin | ||||||
Deposited On: | 17 May 2011 22:52 | ||||||
Last Modified: | 09 Oct 2019 17:08 |
Thesis Files
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PDF (One-sided version of the thesis)
- Final Version
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PDF (For duplex printing)
- Final Version
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LaTeX (Bibliography)
- Supplemental Material
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