QUANTUM COMPUTING ALGORITHMS
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. Experiments have been carried out in which quantum computational operations are executed on a small number of quantum bits. The NSF has declared this general area one of the ten big ideas for future investments. In June 2018, the science committee of the House of Representatives unanimously approved the National Quantum Initiative Act (H.R.~6227), which has created a 10-year federal effort to boost quantum science. Similar funding commitments have been made throughout the world. This course provides an introduction to the theory of quantum computing and information. The covered topics include 1) the fundamental elements of quantum information processing (qubits, unitary transformations, density matrices, measurements), 2) entanglement based communications protocols (e.g., teleportation) and games (e.g., CHSH), the Bell inequalities, 3) quantum algorithms such as Shor's factoring and Grover's search, and 4) basic (quantum) error correction algorithms. The course material is 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. Much progress has been made in the past quarter of the century on the theoretical side. Experiments have been carried out in which quantum computational operations were executed on a small number of quantum bits (qubits). Noisy Intermediate-Scale Quantum (NISQ) technology is expected to be available in the near future. This term, coined by John Preskill of CalTech, refers to devices with 50-100 qubits (intermediate-scale), which is too few to have full error correction (noisy). Nevertheless, NISQ systems may be able to perform tasks that exceed the capabilities of today's classical digital computers. They may be valuable 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.
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.
PROBABILITY & RANDOM PROCESSES
Probability theory studies random phenomena in a formal mathematical way. It is essential for all engineering and scientific disciplines that deal 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 information transmission and storage under the uncertainties of various types, such as random noise and adversarial behavior. Finance systems strive to maximize profits despite the unpredictability of natural and manufactured events. This undergraduate course covers the fundamentals of probability necessary for several ECE courses and related fields.