Please use this identifier to cite or link to this item: http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/8857
Title: Exploration of Quantum Algorithms for Singular Value Decomposition Problems
Authors: Chandra, M. Girish
JOJO, JEZER
Dept. of Physics
20191049
Keywords: Research Subject Categories::MATHEMATICS
Research Subject Categories::INTERDISCIPLINARY RESEARCH AREAS
Issue Date: May-2024
Citation: 114
Abstract: This thesis explores quantum algorithms for Singular Value Decomposition (SVD) problems, and focuses on both theoretical developments and practical implementations. First, a detailed description of a known purely quantum algorithm for SVD is provided, along with its application to Latent Semantic Analysis (LSA). Following this, we take a known variational quantum approach to SVD and identify a drawback in its objective function. A solution is presented in the form of a modification to this objective function and an application of this modified algorithm for LSA is also proposed. Comparative simulations between the original and modified algorithms are conducted, alongside experimental validation of the LSA algorithm on quantum hardware. We then study the Quantum Singular Value Transform (QSVT) and understand its relation to Quantum Signal Processing with the aid of an example. Various block encodings are explored, including a novel proposal. Simulations employing QSVT for solving linear systems and Topological Data Analysis are carried out for various block encodings and the results are presented. Finally, we extend our study to tensors, proposing both a purely quantum algorithm and a hybrid variational quantum algorithm to find the t-SVD of a third-order tensor. Simulations are conducted to validate their efficacy.
URI: http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/8857
Appears in Collections:MS THESES

Files in This Item:
File Description SizeFormat 
20191049_Jezer_Jojo_MS_Thesis.pdfMS Thesis2.16 MBAdobe PDFView/Open    Request a copy


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.