Fault-ignorant Quantum Search

TL;DR

This paper studies quantum search algorithms that operate effectively despite unknown noise levels, showing that noise diminishes quantum speedup but still offers advantages over classical methods at low noise levels.

Contribution

It introduces a fault-ignorant quantum search framework, providing lower bounds and demonstrating that quantum advantage persists under low noise conditions.

Findings

Quadratic speedup is lost at high noise levels.

Quantum algorithms outperform classical search at low noise.

Lower bounds on runtime for fault-ignorant algorithms are established.

Abstract

We investigate the problem of quantum searching on a noisy quantum computer. Taking a 'fault-ignorant' approach, we analyze quantum algorithms that solve the task for various different noise strengths, which are possibly unknown beforehand. We prove lower bounds on the runtime of such algorithms and thereby find that the quadratic speedup is necessarily lost (in our noise models). However, for low but constant noise levels the algorithms we provide (based on Grover's algorithm) still outperform the best noiseless classical search algorithm.