How to describe the phase detection operator of the adaptive GROVER algorithm mathematically?

After reading document Grover Algorithm for Multi-objective Searching with Iteration Auto-controlling | SpringerLink, I have been curious about the mathematical expression of the phase detection operator (Fig. 3). I searched for articles related to quantum counting but still could no understand how to construct the phase detection unitary operator, and even could not write its oracle form.


Hi @RX1 ,

Have you checked out the Codebook module on Grover’s algorithm and the PennyLane demo on Grover’s?

They both talk about the Oracle. The Searching with Circuits Codebook topic might be particularly interesting for you.

I hope this helps!