updates

Author: farice

Logistics/senior_thesis_proposal.pdf

@@ -79,8 +79,11 @@
 \begin{document}
 \maketitle
 
-\abstract{In this thesis, we One of the greatest challenges in quantum machine learning is determining how to efficiently encode classical training and test data in quantum su- perposition. In machine learning, many supervised learning algorithms utilize so-called kernel methods to map data into a higher dimensional feature space in which analyzing the data is simpler. Hence, one suggested workaround to the quantum encoding prob- lem, is to encode data inputs into a quantum state that implicitly performs the feature map given by the kernel. Therefore, if the kernel is sufficiently difficult to evaluate classically, then there may exist a quantum advantage.
-Here, we propose a project to identify the properties of a kernel that may provide quantum advantage, explore the robustness of learning in quantum feature spaces to noise, and generalize learning in quantum feature spaces past Support Vector Machines (SVM).}
+\abstract{In this thesis, we provide a presentation of the latest results in quantum learning theory alongside theoretical extensions and 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 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.}
 
 \tableofcontents
 

Notes/main.pdf

@@ -3,7 +3,7 @@
 \begin{document}
 \maketitle
 
-\begin{subappendices}
+%\begin{subappendices}
 \section{Quantum Mechanics}
 Reference: Chapter 2 of \cite{nielsen2010quantum}
 
@@ -1835,7 +1835,7 @@ \section{Entropy and Information}
 
 Conclusion from the above two exercises: mutual information is neither sub-additive nor super-additive.
 
-\end{subappendices}
+%\end{subappendices}
 
 \section{Quantum Information Theory}
 Reference: Chapter 12 of \cite{nielsen2010quantum}

Notes/main.tex

@@ -8,8 +8,6 @@ \section{Boolean Fourier Analysis}
 
 \section{Randomized Linear Algebra}
 
-\section{
-
 \section{Algorithms for solving linear systems of equations}
 
 One such application of Phase Estimation (Section \ref{phase_estimation}) is with respect to solving linear systems of equations. This is the so-called HHL algorithm \cite{lloyd2010quantum}.