In both computation and communication messages are encoded as strings of 0's and 1's. Therefore, the basic problem is to represent 0,1. It might seem that the intractability of problems with exponential growth has merely been transferred from the computation to the output measurement. However, for some problems, one can design a computation so that it simultaneously transforms the initial state to one in which the desired output occurs with high probability. This can lead to efficient strategies for classically difficult problems.
Much more work needs to be done before quantum computation is practical.
However, the development of quantum error-correcting codes has already removed one obstacle and is of considerable interest in its own right. This course will try to survey some of these developments and provide participants with the foundation to follow other work in this rapidly developing field. This will introduce the student to the basic principles of quantum mechanics needed to follow the course. Emphasis will be on the basic concepts of state, observable, measurement and superposition. Historically, quantum computers and quantum gates arose from efforts to understand questions about the reversibility of computation.