Introduction to Quantum Information and Computation
In the past two decades scientists have begun to formulate and build a new type of computer called a quantum computer. Immense gains in computational power have been predicted to be possible with these kinds of computers, and the first commercial quantum computers are starting to appear, albeit with limited capabilities. This class will teach students the fundamental aspects and applications of quantum computers. We develop first the necessary concepts in quantum information from the postulates of quantum mechanics. We apply this framework to study quantum circuits and quantum computation. We then study two foundational quantum algorithms: the quantum Fourier transform and its application in phase estimation and factorization, and the quantum search. We then study decoherence, and after that, the physical realization of spin-based quantum computers. Finally, we introduce quantum error correction including the stabilizers, fault tolerance, and the threshold theorem, in the context of simple codes. There are 8 to 9 problem sets, including programming of quantum computers, and there is a course term-paper project.