This course will provide the student with the necessary mathematical tools and background knowledge to understand, model, and conceptualize quantum computing and its building blocks and systems. We shall review concepts of computation and how they translate to the microscopic world.

An introduction to quantum physics with emphasis on topics at the frontiers of research, and developing understanding through exercises.This course aims to build a bridge between natural principles such as light and atoms and a variety of modern applications. This course will provide the student with the necessary physical intuition and background information on quantum physics so that to be able to understand and appreciate a variety of applications in quantum computing such as quantum currency, encryption, random number generation

A broad introduction to machine learning and statistical pattern recognition. Topics include: Supervised learning: Bayes decision theory, discriminant functions, maximum likelihood estimation, nearest neighbor rule, linear discriminant analysis, support vector machines, neural networks, deep learning networks. Unsupervised learning: clustering, dimensionality reduction, PCA, auto-encoders. The course will also discuss recent applications of machine learning, such as computer vision, data mining, autonomous navigation, and speech recognition.

When Richard Feynman first introduced the concept of quantum computers it was posed for the purpose of simulating nature. Today quantum simulation remains one of the likely first applications to benefit from quantum computers. This course introduces key concepts required for quantum simulation, and builds tools for performing quantum simulation using state-of-the-art architectures. We introduce classical schemes, like tensor networks, and machine learning approaches, that can be used for these simulations on CPU/GPU architecture. We survey current literature to review and implement methods of quantum simulation and use them to solve and study example problems.

This course will showcase a variety of topics from which students can select one, or come up with one of their own, and proceed to study it in depth. The students will make presentations of their findings to class by citing literature and code implementations where appropriate, and culminate with the writing of a scholarly paper on the topic chosen.

Quantum information theory synthesizes three major themes: quantum physics, computer science, and information theory. At the core of information theory lies the classical work of Claude E. Shannon, which we review in this course. We then introduce quantum information sources, quantum operations, and quantum tomography, and study three problems related to classical Shannon's theorems and subsequent extension to quantum computing. These involve compressing quantum information, transmitting both classical and quantum information through noisy quantum channels, and quantifying, characterizing, transforming, and utilizing quantum entanglement.