An Investigation of the use of cQED Systems for Quantum Simulation
Abstract/Contents
- Abstract
- We examine the use of continuous matrix product states (cMPS) as a varia- tional class for estimating properties of the ground state of 1-D quantum fields. In particular, we explore the use of submanifolds of cMPS parametrized by cavity quantum electrodynamic (cQED) systems to perform these variational calculations. Variations over the cQED generated classes could be performed experimentally, and thus provide a means to do quantum simulation - using one quantum system to simulate another. We give a derivation of the cMPS class and describe the correspondence between the cMPS class and cQED systems. Then we perform a variational calculation to find the ground state of the Lieb- Liniger Hamiltonian for several ansatzes from the cMPS and cQED classes. We provide numerical evidence that the correlation functions computed from the cMPS variation are approximately correct. This suggests that the varia- tion over the cMPS class is actually approximating the field ground state and not just approximating the ground state energy. We further compare cQED ansatz-derived energies and correlation functions to those computed from the cMPS ansatz. Our findings suggest that cQED systems can approximate the short range behavior of Lieb-Liniger ground state correlation functions pro- vided they have enough internal degrees of freedom. The simple examples of cQED systems we examine here, however, fail to capture the asymptotic behavior of the correlation functions. In particular, they exhibit too much long range phase coherence and do not exhibit Friedel oscillations. This raises the question of what controls correlation function asymptotics in the cMPS formalism.
Description
| Type of resource | text |
|---|---|
| Date created | June 8, 2016 |
Creators/Contributors
| Author | Block, Maxwell |
|---|---|
| Primary advisor | Safavi-Naeini, Amir |
| Advisor | Hayden, Patrick |
| Degree granting institution | Stanford University, Department of Physics |
Subjects
| Subject | cQED |
|---|---|
| Subject | cMPS |
| Subject | quantum simulation |
| Genre | Thesis |
Bibliographic information
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- User agrees that, where applicable, content will not be used to identify or to otherwise infringe the privacy or confidentiality rights of individuals. Content distributed via the Stanford Digital Repository may be subject to additional license and use restrictions applied by the depositor.
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
Preferred citation
- Preferred Citation
- Maxwell Block. (2016). An Investigation of the use of cQED Systems for Quantum Simulation. Stanford Digital Repository. Available at: http://purl.stanford.edu/rg878gj6997
Collection
Undergraduate Theses, Department of Physics
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- Contact
- acgtblocku@gmail.com
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