Quantum amplitude amplification operators: exact quantum search

Abstract

Quantum search algorithms show quadratic speedups over their classical counterparts, and the speedup also turns out to be optimal. They share the common structure that an iteration contains two inversions, one with respect to a target state and the other to an initial state, and such iterations are applied O( p N) times for an unsorted database of N items. In this work, we present the characterization to an iteration that leads to exact quantum search with a quadratic speedup. We show that the fixed-point quantum search algorithm with a quadratic speedup contains iterations that are not QAAOs whereas exact quantum algorithms are sequences of QAAOs. We also demonstrate 3-qubit QAAOs in cloud-based quantum computing services, IBMQ and IonQ.