Quantum computing aims to utilize quantum properties of matter to efficiently solve problems that classical computing systems would take too long to solve. This course reviews modern quantum computing architectures and algorithms for these platforms. We focus on mapping of optimization and machine learning problems onto Noisy-Intermediate-Scale Quantum (NISQ) architectures and also discuss how to leverage state-of-the-art classical simulation methods for quantum-inspired algorithms. We review several modern NISQ architectures and associated software interfaces, we analyze performance for optimization and statistical sampling. We survey current literature to review and implement methods for mapping optimization and machine learning problems onto NISQ architectures and modern simulators and use them to solve and study example problems.

Quantum computation is a rapidly growing field at the intersection of physics and computer science, electrical engineering and applied math. While instrumentation of quantum computers is in its infancy, quantum algorithms are being developed to provide efficient solutions to various computational problems. This course covers basic quantum computing, including quantum circuits, significant quantum algorithms, and hybrid quantum-classical algorithms, with focus on applying the concepts to programming existing and near-future quantum computers. Example codes, homework assignments, and class projects will employ Python modules to handle the data exchange with quantum computers.

Quantum information theory synthesizes three major themes: quantum physics, computer science, and information theory. At the core of information theory lies the work of Claude E. Shannon, which we review in this course, and we present and study three problems related to his work and subsequent extension to quantum computing. These are, compressing quantum information, transmitting classical and quantum information through noisy quantum channels, and quantifying, characterizing, transforming, and using quantum entanglement.