# Exact quantum search based on analytical multiphase matching for known number of target items and the experimental demonstration on IBM Q

## TL;DR

This paper introduces an exact quantum search algorithm based on analytical multiphase matching for known target quantities, demonstrating its effectiveness through experiments on IBM Q and analyzing its theoretical properties.

## Contribution

It extends the analytical multiphase matching condition to exact quantum search with known target fraction, achieving optimal iteration counts and experimental validation.

## Key findings

- The algorithm achieves optimal iteration counts for known target fractions.
- Experimental demonstration on IBM Q confirms practical feasibility.
- Identifies two coincidental phases in the algorithm based on AMPM.

## Abstract

In [Phys. Rev. Lett. 113, 210501 (2014)], to achieve the optimal fixed-point quantum search in the case of unknown fraction (denoted by $\lambda$) of target items, the analytical multiphase matching (AMPM) condition has been proposed. In this paper, we find out that the AMPM condition can also be used to design the exact quantum search algorithm in the case of known $\lambda$, and the minimum number of iterations reaches the optimal level of existing exact algorithms. Experiments are performed to demonstrate the proposed algorithm on IBM's quantum computer. In addition, we theoretically find two coincidental phases with equal absolute value in our algorithm based on the AMPM condition and that algorithm based on single-phase matching. Our work confirms the practicability of the AMPM condition in the case of known $\lambda$, and is helpful to understand the mechanism of this condition.