A BRICS Mini-Course
December 11 and 18, 1995
Institute of Physics, Aarhus University
The following two lectures are intended as an opportunity to enhance one's understanding of the quantum mechanics behind quantum computing. They may be seen as a warm-up to a coming mini-course in quantum computing to be held in the last half of January. Ivan Damgaard.
Rather than the technical aspect of wave dynamics replacing newtonian mechanics (classical orbits), it is the more conceptual consequences of quantum mechanics that have been the subject of intense discussions, e.g., in connection with quantum computing and quantum chryptography. Still, of course, these discussions must be based on the quantum mechanics formalism and on properties of quantum mechanical systems. The purpose of these two lectures is to introduce the necesssary formal elements of quantum mechanics for such discussions. Also, a few physical realizations of the quite generic formalism will be mentioned - it is my experience that new ideas are based on an intuitive understanding of the system, that may be strengthened by having a real system in mind.
In the first lecture I'll discuss what is meant by a quantum state of a simple physical system. I shall re-orient those, who have been burdened by wave functions in introductory quantum mechanics courses, towards the concept of state vectors, and emphasize the finite dimensional (in particular few-dimensional) vector space aspects of quantum theory, basis states, complimentarity, spaces of one and several systems, entanglement and non-locality.
In this lecture I'll discuss the coherent, unitary evolution of a closed quantum system, and the exchange of energy/information between interacting physical systems (a necessary element in computing). I shall also address open systems, i.e., systems that interact with their surroundings. Two aspects are relevant:we as system operators of the quantum system have only access to what we can measure, i.e, deduce from some kind of physical interaction with the system; a weak coupling to its surroundings introduces a new element in the dynamics of a quantum system, e.g., damping. Algorithms in quantum computing must provide the result in a form accessible by a quantum measurement process; laboratory computers have to implement methods for correcting errors due to damping.