# Depth optimization of quantum search algorithms beyond Grover's algorithm

## TL;DR

This paper introduces a new depth optimization method for quantum search algorithms, demonstrating that Grover's algorithm is not depth-optimal and proposing a multistage, parallelizable search approach to reduce errors on noisy quantum computers.

## Contribution

It presents a novel multistage quantum search algorithm that improves depth efficiency and error resilience beyond Grover's traditional approach.

## Key findings

- Grover's algorithm is not optimal in depth.
- The proposed multistage algorithm reduces errors.
- Parallel execution of stages enhances performance.

## Abstract

Grover's quantum search algorithm provides a quadratic speedup over the classical one. The computational complexity is based on the number of queries to the oracle. However, depth is a more modern metric for noisy intermediate-scale quantum computers. We propose a new depth optimization method for quantum search algorithms. We show that Grover's algorithm is not optimal in depth. We propose a quantum search algorithm, which can be divided into several stages. Each stage has a new initialization, which is a rescaling of the database. This decreases errors. The multistage design is natural for parallel running of the quantum search algorithm.