Addendum to "Quantum Search with Noisy Oracle"

TL;DR

This paper establishes a lower bound on the query complexity of quantum search algorithms under depolarizing noise affecting a single known qubit, showing no speedup over classical methods in noisy conditions.

Contribution

It extends previous techniques to prove that even minimal depolarizing noise on a single qubit limits quantum search efficiency to linear in noise rate and problem size.

Findings

Quantum search cannot be faster than O(np) queries with depolarizing noise.

The lower bound applies whether the noisy qubit is an index or the target.

Noise prevents quantum advantage in search algorithms under specified conditions.

Abstract

In this note, I generalize the techniques of my recent work (arXiv:2309.14944) and show that, even if just a single known qubit of query registers is affected by the depolarizing noise of rate p, quantum search among n elements cannot be done any faster than in O(np) queries. This holds both when the affected qubit is one of the log(n) index qubits and when it is the target qubit.