Quantum Learning Machine

Learning can be defined as the changes in a system that result in an improved performance over time on tasks that are similar to those performed in the system`s previous history. Al-though learning is often thought of as a property associated with living things, machines or computers are also able to modify their own algorithms as a result of training experiences. This is the main subject of the broad field of "machine learning". Recent progress in quantum communication and quantum computation - development of novel and efficient ways to proc-ess information on the basis of laws of quantum theory - provides motivations to generalize the theory of machine learning into the quantum domain. The notion of "quantum learning machines" - quantum computers that modify themselves in order to improve their performance in some way - is introduced in this proposal. Based on the quantum automatic control theory, we propose a quantum learning machine that can learn to perform known quantum algorithms and potentially find new ones. The main ingredient of the machine is a feed-back system that is capable of modifying its initial quantum algorithm in response to interaction with a "teacher" so that it yields better approximations to the intended quantum algorithm. The first objective of this project is to investigate the learning efficiency of a quantum learning machine as a function of the number of iterations. The second objective is to find out if a quantum learning machine needs fewer steps than the corresponding conven-tional classical machine to learn certain algorithms. In a broader context, our project is expected to have an impact on understanding the learning process as well as on defining and studying novel learning tasks that correspond to machine learning in a world in which the information is fundamentally quantum mechanical and where our classical intuition is often challenged.