Quantum amplitude-amplification operators

Abstract

In this work, we show the characterization of quantum iterations that would generally construct quantum amplitude-amplification algorithms with a quadratic speedup, namely, quantum amplitude-amplification operators (QAAOs). Exact quantum search algorithms that find a target with certainty and with a quadratic speedup can be composed of sequential applications of QAAOs: existing quantum amplitude-amplification algorithms thus turn out to be sequences of QAAOs. We show that an optimal and exact quantum amplitude-amplification algorithm corresponds to the Grover algorithm together with a single iteration of QAAO. We then realize three-qubit QAAOs with current quantum technologies via cloud-based quantum computing services, IBMQ and IonQ. Finally, our results show that the fixed-point quantum search algorithms known so far are not a sequence of QAAOs; for example, the amplitude of a target state may decrease during quantum iterations.