Quantum computers can search rapidly by using almost any selective transformations

TL;DR

This paper introduces a robust quantum search algorithm that can operate effectively with nearly any selective transformations, overcoming previous limitations and improving implementation flexibility, especially in quantum error correction.

Contribution

It presents a novel quantum search method that tolerates deviations in selective transformations, enhancing robustness and practical applicability.

Findings

The new algorithm works with transformations far from ideal phase-inversions.

It is robust to systematic, reproducible, and reversible errors.

The approach improves the feasibility of quantum search in real-world settings.

Abstract

The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a classical computer. The algorithm uses selective transformations to distinguish the initial state and target state from other states. It does not succeed unless the selective transformations are very close to phase-inversions. Here we show a way to go beyond this limitation. An important application lies in quantum error-correction, where the errors can cause the selective transformations to deviate from phase-inversions. The algorithms presented here are robust to errors as long as the errors are reproducible and reversible. This particular class of systematic errors arise often from imperfections in apparatus setup. Hence our algorithms offer a significant flexibility in the physical implementation of quantum search.