clean

Author: farice

Notes/course_notes.bib

@@ -5,6 +5,13 @@ @book{nielsen2010quantum
   publisher={Cambridge university press}
 }
 
+@book{wilde2013quantum,
+  title={Quantum information theory},
+  author={Wilde, Mark M},
+  year={2013},
+  publisher={Cambridge University Press}
+}
+
 @inproceedings{lloyd2010quantum,
   title={Quantum algorithm for solving linear systems of equations},
   author={Lloyd, Seth},

Notes/main.pdf

@@ -1,4 +1,4 @@
-\documentclass[11pt]{article}
+\documentclass{book}
 \usepackage{subfiles}
 \usepackage[toc,page]{appendix}
 
@@ -87,23 +87,31 @@
 \newtheorem{algorithm}[theorem]{Algorithm}
 \newtheorem{example}[theorem]{Example}
 
-\title{Quantum Algorithms and Learning Theory\\\textit{Notes and Exercises}}
+\title{Quantum Algorithms and Learning Theory}
 \author{Faris Sbahi}
 
 \begin{document}
 \maketitle
 
-\abstract{In this document, we provide a presentation of the latest results in quantum learning theory alongside theoretical extensions. We also provide experimental analyses of quantum feature maps which can be used for supervised learning. 
+\chapter*{Abstract}
+
+In this document, we provide a presentation of the latest results in quantum learning theory alongside theoretical extensions. We also provide experimental analyses of quantum feature maps which can be used for supervised learning. 
 
 The first part of our paper is a review: First, we present an overview of quantum computation and information. Next, we present a review of the brief history of quantum machine learning. The subsequent part of our paper is an analysis of recent results in quantum learning theory: (1) information theoretic bounds on quantum computation learning, (2) supervised learning using hybrid quantum-classical circuits, and (3) Tang's \cite{tang2018quantum} idea of least-square sampling providing parallel classical algorithms for quantum machine learning algorithms that solve singular value transformation problems.
 
-The last part of our paper provides new results on quantum feature maps which seek to solve the quantum encoding problem by encoding data inputs into a quantum state that implicitly performs the feature map given by a kernel function. Therefore, if the kernel is sufficiently difficult to evaluate classically, then there may exist a quantum advantage. Hence, we provide a geometric analysis of the properties of a kernel that may provide quantum advantage, and provide experimental results to demonstrate the robustness of particular candidate maps.}
+The last part of our paper provides new results on quantum feature maps which seek to solve the quantum encoding problem by encoding data inputs into a quantum state that implicitly performs the feature map given by a kernel function. Therefore, if the kernel is sufficiently difficult to evaluate classically, then there may exist a quantum advantage. Hence, we provide a geometric analysis of the properties of a kernel that may provide quantum advantage, and provide experimental results to demonstrate the robustness of particular candidate maps.
 
 \tableofcontents
 
+\chapter{Introduction}
+
+Rough draft readers:
+
+The "Introduction" and "Preliminaries" chapters are in progress. I plan a standard review of the necessary background from quantum information theory (see \cite{nielsen2010quantum} and \cite{wilde2013quantum}) to make the essential chapters of this thesis interpretable to a general Physics audience. Of course, I will primarily restate theorems and provide references in order to keep this portion succinct. For the time being, I've included my personal notes that I've kept since I began working on this project.
+
 \subfile{nielsen_chuang_notes.tex}
 
-\subfile{crypto_notes.tex}
+%\subfile{crypto_notes.tex}
 
 \subfile{quantum_learning_notes.tex}