INTRO TO QUANTUM INFO SCENCE

Quantum phenomena provide computing and information handling paradigms that are distinctly different and arguably much more powerful than their classical counterparts. In the past quarter of the century, much progress has been made on the theoretical side, and experiments have been carried out in which quantum computational operations were executed on a very small number of quantum bits. This course provides an introduction to the theory of quantum computing and information. The topics include 1) the fundamental elements of quantum information processing (qubits, unitary transformations, density matrices, measurements); 2) entanglement, protocols for teleportation, the Bell inequality, 3) basic quantum algorithms such as Shor’s factoring and Grover’s search, and 4) basic quantum data compression and error correction. The course material should be accessible to undergraduate and graduate students with a variety of backgrounds, e.g., electrical engineers, physicists, mathematicians, and computer scientists.

QUANTUM COMPUTING SYSTEMS

Quantum phenomena provide computing and information handling paradigms that are distinctly different and arguably much more powerful than their classical counterparts. In the past quarter of the century, much progress has been made on the theoretical side, and experiments have been carried out in which quantum computational operations were executed on a very small number of quantum bits. Noisy Intermediate-Scale Quantum (NISQ) technology is expected to be available in the near future. This term refers to devices with 50-100 qubits (intermediate-scale), which is too few to have have full error-correction (noisy). Nevertheless, NISQ systems may be able to perform tasks that exceed the capabilities of today's digital computers, and may be useful tools for exploring many-body quantum physics. On the theoretical side, significant progress has been made in understanding the fundamental limits of quantum telecommunications systems, giving rise to the subfield of quantum information theory. Moreover, classical information theory has been used to understand the problems in the foundations of physics. This course covers the fundamentals of 1) quantum telecommunications, 2) algorithms for for NISQ technology, and 3) many-body entangled systems, as well as a selected number of more advanced topics of their individual interests.

Spring 2020 syllabus and notes.

CODING THEORY

Morse, bar and QR codes, ISBN, blockchain hashes, and many more codes play important roles in numerous scientific disciplines and virtually all telecommunication systems. In practice, codes are used to efficiently insure reliable, secure, and private transmission and storage of information. In theory, codes are used to e.g., study computational complexity, design screening experiments, provide a bridge between statistical mechanics and information theory, and even help understand the (quantum) spacetime fabric of reality. One can also use codes for entertainment, e.g., to solve balance puzzles such as the penny weighing problem, or to design social (hat color) guessing-game strategies that significantly increase the odds of winning. This course covers fundamentals of coding theory and practice, as well as a selected number of more advanced topics. It is accessible to advanced undergraduate and graduate students in ECE, Math, and CS.

Spring 2019 syllabus & notes.

PROBABILITY & RANDOM PROCESSES

Probability theory studies random phenomena in a formal mathematical way. It is essential for all engineering and scientific disciplines dealing with models that depend on chance. Probability plays a central role in e.g., telecommunications and finance systems. Telecommunications systems strive to provide reliable and secure transmission and storage of information under the uncertainties coming from various types of random noise and adversarial behavior. Finance systems strive to maximize profits in spite of the uncertainties coming from natural and man-made events. This undergraduate course covers the fundamentals of probability that are necessary for several ECE courses and related fields. 

Spring 2018 syllabus & notes.