Quantum Advantage with Faulty Oracle

TL;DR

This paper demonstrates that quantum algorithms can be made robust against faulty oracles with a quadratic increase in queries, preserving quantum advantage in noisy quantum query models.

Contribution

It introduces a method to robustify quantum query algorithms against non-unitary noise in oracles, maintaining quantum speedup with manageable complexity increase.

Findings

Quantum algorithms can be made robust against faulty oracles with quadratic query complexity increase.

Quantum advantage is preserved for problems with super-cubic speedup under noisy oracle conditions.

First non-trivial robustification of quantum query algorithms against noisy oracles.

Abstract

This paper investigates the impact of noise in the quantum query model, a fundamental framework for quantum algorithms. We focus on the scenario where the oracle is subject to non-unitary (or irreversible) noise, specifically under the \textit{faulty oracle} model, where the oracle fails with a constant probability and acts as identity. Regev and Schiff (ICALP'08) showed that quantum advantage is lost for the search problem under this noise model. Our main result shows that every quantum query algorithm can be made robust in this noise model with a roughly quadratic blow-up in query complexity, thereby preserving quantum speedup for all problems where the quantum advantage is super-cubic. This is the first non-trivial robustification of quantum query algorithms against an oracle that is noisy.