Noise effects in the quantum search algorithm from the computational complexity point of view

TL;DR

This paper investigates how quantum noise impacts the efficiency of the quantum search algorithm, showing it remains advantageous over classical algorithms only under low noise conditions.

Contribution

It provides a complexity-theoretic analysis of quantum noise effects on the quantum search algorithm's performance.

Findings

Quantum search remains more efficient than classical algorithms under low noise.

Noise significantly degrades quantum search performance beyond certain levels.

The study offers insights into the robustness of quantum algorithms against noise.

Abstract

We analyse the resilience of the quantum search algorithm in the presence of quantum noise modelled as trace preserving completely positive maps. We study the influence of noise on computational complexity of the quantum search algorithm. We show that only for small amounts of noise the quantum search algorithm is still more efficient than any classical algorithm.