SYMSYS 265:
Quantum Algorithms and Quantum Cognition
Quantum computers can solve some classes of problems with more efficiency than classical computers, usually exponentially faster. They have the potential to solve in minutes problems that would take for a classical computer longer than the age of the universe. Among the promising applications are the development of new drugs, and new materials, machine learning and cryptographic key breaking, just to mention a few examples. Until recently the idea of building a computer seemed like a project reserved for a distant future, but over the past years many companies such as IBM, Google, Microsoft, D-Wave, Rigetti Computing, and others have announced that they started the operation of quantum computer prototypes. However, due to the counterintuitive properties of quantum theory the creation of quantum algorithms has been as difficult as hardware development. Although there are many algorithms built to run on quantum computers there are very few that use the full potential of quantum computing. The purpose of this course is to teach the fundamentals of quantum computing and quantum algorithms for students with non-physics background. The emphasis of the course will be to develop a "quantum intuition" by presenting the main differences between classical and quantum logic, as well as the use of special examples developed in quantum cognition. Quantum cognition applies the mathematical formalism of quantum mechanics in psychology and decision theories in situations where conventional formalism does not work. The topics covered will include: the basics of quantum theory and quantum computation, Classical and Quantum Logic, Classical and Quantum gates, Quantum Cognition, the main Quantum algorithms such as Phil's Algorithm, Deutsch Algorithm, Deutsch-Jozsa Algorithm, Simon's algorithm, Shor's Algorithm, and Grover's Algorithm. This course has workshop format involving readings followed by short lectures, discussion, plus other activities in class, homework, and Final Project. Required background: linear algebra, calculus equivalent to MATH 19 and MATH 20, basic probability theory and complex numbers. Students are not expected to have taken previous courses in quantum mechanics.
Terms: Spr
| Units: 4