Quantum Counting

Quantum counting combines Grover's operator with phase estimation to count how many solutions exist — not just find one.

Core

QPE on the Grover operator

Output

number of marked items M

What it does

The Grover iteration is a rotation whose angle depends on the number of solutions. Running phase estimation on that operator reads the angle, and hence M, without enumerating solutions.

Where it's used

Deciding satisfiability, estimating set sizes, and calibrating how many Grover iterations to run.

In code (Qiskit)

# QPE applied to the Grover diffusion*oracle operator