Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
A study of circuit Complexity for Coherent States
Computational complexity is a popular quantity in quantum information theory. It has made huge strides in recent years in the study of black hole dynamics. A brief definition of complexity is the measure of how difficult it is to implement a task. For a quantum system, complexity evaluates the diffi...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Department of Mathematics and Applied Mathematics
2023
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613310615027712 |
|---|---|
| access_status_str | Open Access |
| author | Tladi, Mpho |
| author2 | Haque, Shajid |
| author_browse | Haque, Shajid Tladi, Mpho |
| author_facet | Haque, Shajid Tladi, Mpho |
| author_sort | Tladi, Mpho |
| collection | Thesis |
| description | Computational complexity is a popular quantity in quantum information theory. It has made huge strides in recent years in the study of black hole dynamics. A brief definition of complexity is the measure of how difficult it is to implement a task. For a quantum system, complexity evaluates the difficulty of preparing a quantum state from a given reference state by unitary transformations. However, in the dual gravity theory complexity has a geometric meaning. In some black hole context, Leonard Susskind and collaborators proposed two holographic conjectures. The Complexity=Volume (CV) states that complexity of the boundary field theory is dual to the volume of a co dimension one maximal surface that extends to the boundary of the Ads space. Complexity=Action (CA) posits that complexity of the boundary is the same as the action evaluated as an action on patch in the bulk defined as the Wheeler De Witt patch. In recent years, these two conjectures have initiated an extensive study of complexity. This thesis is also motivated by these conjectures and will investigate complexity in the field theory side of the story. Specifically, we will explore the complexity for coherent states. We will start with a review of different methods of computing complexity. Finally, we then investigate the complexity for coherent states by using the methods of circuit complexity and operator complexity |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/37303 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:34:06.076Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/37303 A study of circuit Complexity for Coherent States Tladi, Mpho Haque, Shajid Murugan, Jeffrey Weltman, Amanda Mathematics and Applied Mathematics Computational complexity is a popular quantity in quantum information theory. It has made huge strides in recent years in the study of black hole dynamics. A brief definition of complexity is the measure of how difficult it is to implement a task. For a quantum system, complexity evaluates the difficulty of preparing a quantum state from a given reference state by unitary transformations. However, in the dual gravity theory complexity has a geometric meaning. In some black hole context, Leonard Susskind and collaborators proposed two holographic conjectures. The Complexity=Volume (CV) states that complexity of the boundary field theory is dual to the volume of a co dimension one maximal surface that extends to the boundary of the Ads space. Complexity=Action (CA) posits that complexity of the boundary is the same as the action evaluated as an action on patch in the bulk defined as the Wheeler De Witt patch. In recent years, these two conjectures have initiated an extensive study of complexity. This thesis is also motivated by these conjectures and will investigate complexity in the field theory side of the story. Specifically, we will explore the complexity for coherent states. We will start with a review of different methods of computing complexity. Finally, we then investigate the complexity for coherent states by using the methods of circuit complexity and operator complexity 2023-03-07T10:19:04Z 2023-03-07T10:19:04Z 2022 2023-02-21T07:24:35Z Master Thesis Masters MSc http://hdl.handle.net/11427/37303 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Mathematics and Applied Mathematics Tladi, Mpho A study of circuit Complexity for Coherent States |
| thesis_degree_str | Master's |
| title | A study of circuit Complexity for Coherent States |
| title_full | A study of circuit Complexity for Coherent States |
| title_fullStr | A study of circuit Complexity for Coherent States |
| title_full_unstemmed | A study of circuit Complexity for Coherent States |
| title_short | A study of circuit Complexity for Coherent States |
| title_sort | study of circuit complexity for coherent states |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/37303 |
| work_keys_str_mv | AT tladimpho astudyofcircuitcomplexityforcoherentstates AT tladimpho studyofcircuitcomplexityforcoherentstates |