oskar stuff

Author: mhjensen

doc/MSc/msc_students/Oskar/QMLmasterproject.pdf

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+\begin{center}
+{\LARGE\bf
+\begin{spacing}{1.25}
+Quantum Machine Learning for Finance
+\end{spacing}
+}
+\end{center}
+
+\begin{center}
+{\bf Master of Science thesis project${}^{}$} \\ [0mm]
+\end{center}
+
+\begin{center}
+% List of all institutions:
+\end{center}
+
+\begin{center}
+May 4, 2025
+\end{center}
+
+\vspace{1cm}
+
+
+\subsection*{Quantum Computing and Machine Learning}
+
+\textbf{Quantum Computing and Machine Learning} are two of the most promising
+approaches for studying complex systems with many degrees of freedom.
+
+Quantum computing is an emerging area of computer science that
+leverages the principles of quantum mechanics to perform computations
+beyond the capabilities of classical computers. Unlike classical
+computers, which use bits to represent data as bits $0$ or $1$,
+quantum computers use quantum bits, or qubits. Qubits can exist in
+multiple states simultaneously (superposition) and can be entangled
+with one another, allowing quantum computers to process vast amounts
+of information in parallel.
+
+These unique properties enable quantum computers to tackle problems
+that are currently intractable for classical systems, such as complex
+simulations in chemistry and physics, optimization problems, and
+large-scale data analysis.
+
+Quantum machine learning (QML) is an interdisciplinary field that
+combines quantum computing with machine learning techniques. The goal
+is to enhance the performance of machine learning algorithms by
+utilizing quantum computing’s capabilities.
+
+In QML, quantum algorithms are developed to process and analyze data
+more efficiently than classical algorithms. This includes tasks like
+classification, regression, clustering, and dimensionality
+reduction. By exploiting quantum phenomena, QML has the potential to
+accelerate machine learning processes and handle larger datasets more
+effectively.
+
+Quantum computing and QML hold promise for many different types of  applications, including:
+
+\begin{enumerate}
+\item Drug Discovery: Simulating molecular structures to expedite the development of new medications.
+
+\item Financial Modeling: Optimizing portfolios and detecting fraudulent activities through complex data analysis.
+
+\item Artificial Intelligence: Enhancing machine learning algorithms for faster and more accurate predictions. 
+\end{enumerate}
+
+As quantum hardware continues to advance, the integration of quantum
+computing into practical applications is becoming increasingly
+feasible, opening up for a new era of computational possibilities.
+
+This thesis project deals with the study and implementation of quantum
+machine learning methods applied to classical machine learning data
+for supervised learning.  The methods we will focus on are
+
+\begin{enumerate}
+\item Support vector machines and quantum support vector machines
+
+\item Neural networks and quantum neural networks and possibly (if time allows)
+
+\item Classical and quantum Boltzmann machines
+\end{enumerate}
+
+
+The data sets will span both regression and classification problems,
+with an emphasis on simulating time series, in particular of relevance
+for financial problems. The thesis will be done in close collaboration
+with \textbf{Norges Bank Invenstment Management, Simula Research
+  laboratory and the University of Oslo}.
+
+\subsection*{Support vector machines}
+
+A central model in classical supervised learning is the support vector
+machine (SVM), which is a maximal-margin classifier.  SVMs are widely
+used for binary classification and have extensions to regression
+problems as well.  They build on statistical learning theory and are
+known for finding decision boundaries with maximal margin.  In
+particular, SVMs can perform non-linear classification by employing
+the kernel trick, which implicitly maps data into a high-dimensional
+feature space via a kernel function.
+
+A Quantum Support Vector Machine (QSVM) replaces the classical kernel
+or feature map with a quantum procedure.  In QSVM, classical data
+points $\bm{x}$ are encoded into quantum states $|\phi(\bm{x})\rangle$
+via a quantum feature map (a parameterized quantum circuit).  The
+inner product (overlap) between two such states serves as a quantum
+kernel, measuring data similarity in a high-dimensional Hilbert space.
+
+\subsection*{Quantum Neural Networks and Variational Circuits}
+
+The Variational Quantum Algorithm (VQA) is a Variational Quantum
+Circuit (VQC), that is a quantum circuit with tunable parameters and
+which is trained using a classical optimizer.  In practice, a VQC
+(also called a Parameterized Quantum Circuit (PQC)) is used as a
+Quantum Neural Network (QNN): data are encoded into quantum states, a
+parameterized circuit is applied, and measurements yield outputs.  For
+example, it has been shown recently that certain QNNs can exhibit
+higher effective dimension (and thus capacity to generalize) than
+comparable classical networks, suggesting a potential quantum
+advantage.
+
+\subsection*{Boltzmann machines}
+
+Boltzmann Machines (BMs) offer a powerful framework for modeling
+probability distributions.  These types of neural networks use an
+undirected graph-structure to encode relevant information.  More
+precisely, the respective information is stored in bias coefficients
+and connection weights of network nodes, which are typically related
+to binary spin-systems and grouped into those that determine the
+output, the visible nodes, and those that act as latent variables, the
+hidden nodes.  The aim of BM training is to learn a set of weights
+such that the resulting model approximates a target probability
+distribution which is implicitly given by training data.  This setting
+can be formulated as discriminative as well as generative learning
+task.  Applications have been studied in a large variety of domains
+such as the analysis of quantum many-body systems, statistics,
+biochemistry, social networks, signal processing and finance
+
+Quantum Boltzmann Machines (QBMs) are a natural adaption of BMs to the
+quantum computing framework. Instead of an energy function with nodes
+being represented by binary spin values, QBMs define the underlying
+network using a Hermitian operator, normally a parameterized
+Hamiltonian.
+
+\paragraph{Specific tasks and milestones.}
+
+The aim of this thesis is to study the implementation and development
+of codes for several quantum machine learning methods, including
+quantum support vector machines, quantum neural networks and possibly
+Boltzmann machines, if time allows. The results will be compared with
+those from their classical counterparts.  The final aim is to study
+data from finance with both classical and quantum Machine Learning
+algorithms in order to assess and test quantum machine learning
+algorithms and their potential for the analysis of data from finance.
+In setting up the algorithms, existing software libraries like
+Scikit-Learn, PennyLane, Qiskit and other will be used. This will
+allow for an efficient development and study of both classical and
+quantum machine learning algorithms.
+
+The thesis consists of three basic steps:
+
+\begin{enumerate}
+\item Develop a classical machine framework for studies of supervised classification and regression problems, with an emphasis on data from finance. The main emphasis rests on deep learning methods (neural networks, Boltzmann machines and recurrent neural networks) and support vector machines.
+
+\item Compare and evaluate the results from the classical machine learning methods and assess their relevance for financial data.
+
+\item Develop and implement  codes for quantum machine learning algorithms (quantum support vector machines, quantum neural networks and possibly quantum Boltzmann machines) to be run on existing quantum computers and classical computers. Compare the performance of the quantum machine learning  with the abovementioned classical methods with an emphasis on  financial data.
+\end{enumerate}
+
+\noindent
+The milestones are:
+\begin{enumerate}
+\item Spring 2025: Study basic quantum machine learning algorithms (quantum support vector machines, quantum neural networks) for simpler supervised problems from finance and/or other fields.
+
+\item Spring 2025: Compare the results of the simpler data sets with classical machine learning methods
+
+\item Fall 2025: Set uo final data from finance to be analyzed with classical and quantum machine learning algorithms
+
+\item Fall 2025: Develop a software framework which includes quantum support vector machines and quantum neural networks.
+
+\item Spring 2026: The final part is to include Quantum Boltzmann machines, if time allows,  and analyze the results from the diffirent methods. Finalize thesis. 
+\end{enumerate}
+
+\noindent
+The thesis is expected to be handed in May/June 2026.
+
+\paragraph{Literature.}
+\begin{enumerate}
+
+
+\item Maria Schuld and Francesco Petruccione, \textbf{Supervised Learning with Quantum Computers}, Springer, 2018.
+
+\item Claudio Conti, Quantum Machine Learning (Springer), see \href{{https://link.springer.com/book/10.1007/978-3-031-44226-1}}{\nolinkurl{https://link.springer.com/book/10.1007/978-3-031-44226-1}}.
+
+\item M. Zhao et al., \textbf{A tutorial on quantum machine learning and quantum neural networks}, arXiv:2504.16131 (2025) 
+\item Amin et al., \textbf{Quantum Boltzmann Machines}, Physical Review X \textbf{8}, 021050 (2018).
+
+\item Morten Hjorth-Jensen, Quantum Computing and Quantum Machine Learning, lecture notes with extensive codes at \href{{https://github.com/CompPhysics/QuantumComputingMachineLearning}}{\nolinkurl{https://github.com/CompPhysics/QuantumComputingMachineLearning}}, in particular the last five sets of lectures.
+\end{enumerate}
+
+\end{document}
+