Quantum Amplitude Amplification Operators.

In this work, we characterize quantum iterations that generally perform amplitude amplification for a desired state, and show how to construct quantum database search algorithms such that the probability of finding a target keeps increasing all the way through. Namely, exact quantum search algorithms with a quadratic speedup can be generated. These are compared to fixed-point quantum search algorithms known so far, for which it is shown that some iterations do not perform amplitude amplification with a quadratic speedup: meanwhile, the amplitude of a target can decrease. Then, we show that quantum amplitude amplification can be achieved in a wide range of parameters, meaning that the process is generically resilient to errors appearing in a practical realization. Proof-of-principle demonstrations are shown in IBMQ Toronto, IBMQ Boeblingen, and IonQ.