ECE 555

Introduction to Quantum Mechanics and Quantum Information Processing

Course Level

Graduate

Units

3

Enrollment Requirements

None

Course Description

This course is a self-contained introduction to quantum mechanics, quantum information, and quantum computing. The course starts with basics of linear spaces, including basis vectors, Gram-Schmidt procedure, Dirac algebra, Hermitian conjugation, eigenvalues and eigenvectors, and commutator. It continues with the principles of quantum mechanics including photon polarization, state vectors, operators, density operators, measurements, and dynamics of a quantum system, spin-1/2 systems and entanglement. The next chapter is devoted fundamentals of quantum computing, including single qubit gates, multiple qubit gates, controlled operations and universal quantum gates. Further, after introduction of quantum parallelism, important quantum algorithms are studied such as Deutsch's and Deutsch-Jozsa algorithms, Grover search algorithm and quantum Fourier transform. The next chapter will be devoted to physical realization of quantum information processing including nuclear magnetic resonance, ion traps, photonic realization, cavity quantum electrodynamics, and quantum dots. We then study various applications of quantum information processing including quantum teleportation, superdense coding and quantum cryptography. Course concludes with various quantum channel models and basics of quantum error correction. As a dual numbered course, the graduate level version will include more challenging homework problem sets and exam problems, as well as a comprehensive course project.