Quantum Search with Noisy Oracle

TL;DR

This paper analyzes the impact of noise in quantum oracles on search algorithms, establishing tight bounds on query complexity that depend on the noise probability and problem size.

Contribution

It provides the first tight bounds on quantum search complexity with noisy oracles, covering depolarizing and dephasing noise models, and includes scenarios with error indication.

Findings

Quantum noisy-query complexity is  ilde heta(\maxig p, \sqrt{n}ig\u00f7f for noise probability p  0.99.

Lower bounds hold even with error flags indicating oracle errors.

Results unify and extend previous bounds for noisy quantum search algorithms.

Abstract

We consider quantum search algorithms that have access to a noisy oracle that, for every oracle call, with probability $p>0$ completely depolarizes the query registers, while otherwise working properly. Previous results had not ruled out quantum $\mathrm{O}(\sqrt{n})$-query algorithms in this setting, even for constant $p$. We show that, for all $p\le 0.99$, the quantum noisy-query complexity of the unstructured search is $\tilde\Theta(\max\{np,\sqrt{n}\})$. The lower bound $\Omega(\max\{np,\sqrt n\})$ holds also for the dephasing noise and even when, for every oracle call, the algorithm is provided with a flag indicating whether the error has occurred.