The geometry of quantum learning

Concept learning provides a natural framework in which to place the problems solved by the quantum algorithms of Bernstein-Vazirani and Grover. By combining the tools used in these algorithms—quantum fast transforms and amplitude amplification—with a novel (in this context) tool—a solution method for geometrical optimization problems— we derive a general technique for quantum concept learning. We name this technique “Amplified Impatient Learning” and apply it to construct quantum algorithms solving two new problems: BATTLESHIP and MAJORITY, more efficiently than is possible classically. 2003 Physics and Astronomy Classification Scheme: 02.67.Lx. 2000 American Mathematical Society Subject Classification: 81P68, 68Q32, 15A60.