Quantum counting estimates how many outcomes an oracle marks as good by applying amplitude estimation to a search-space superposition. section 9.6.2 section 9.7
A practical implementation follows this pattern:
- Prepare a uniform superposition in the target register so every candidate outcome begins with equal amplitude. section 9.6.2
- Construct an oracle that phase-marks the desired outcomes, such as 0, 1, and 2. section 9.6.2
- Run amplitude estimation with separate target and estimation registers, then aggregate estimation-register probabilities into a histogram. section 9.6.2
- Use the most frequent estimation outcome, after exploiting the histogram symmetry, to calculate the nearest integer count. section 9.6.2
Counting three marked outcomes
With a three-qubit target register, a five-qubit estimation register, and an oracle marking [0, 1, 2], the peak occurs at v = 7 and the calculated count is 3. section 9.6.2
