# Quantum Algorithm for Distribution-Free Junta Testing

## TL;DR

This paper introduces a quantum algorithm for distribution-free junta testing that significantly improves complexity over classical methods, but also establishes limitations when using quantum examples instead of queries.

## Contribution

It presents a quadratic complexity improvement for quantum junta testing and proves limitations for quantum example-based algorithms.

## Key findings

- Quantum junta testing complexity is $O(k/\varepsilon)$, a quadratic improvement.
- No efficient quantum algorithm exists for this problem using quantum examples.
- Independent work by Bshouty achieved similar complexity results.

## Abstract

Inspired by a recent classical distribution-free junta tester by Chen, Liu, Serverdio, Sheng, and Xie (STOC'18), we construct a quantum tester for the same problem with complexity $O(k/\varepsilon)$, which constitutes a quadratic improvement. We also prove that there is no efficient quantum algorithm for this problem using quantum examples as opposed to quantum membership queries. This result was obtained independently from the $\tilde O(k/\varepsilon)$ algorithm for this problem by Bshouty.