The geometry of quantum learning

Abstract

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.