Super-exponential query complexity reduction via noise-resistant quantum search

TL;DR

This paper introduces a quantum algorithm that significantly reduces query complexity for the SEARCH WITH ADVICE problem under noisy conditions, achieving an average-case complexity of O(1) compared to classical algorithms' log(N).

Contribution

The paper presents a noise-resistant quantum algorithm that achieves super-exponential query complexity reduction for SEARCH WITH ADVICE with a power law advice distribution.

Findings

Quantum algorithm solves SEARCH WITH ADVICE with O(1) queries under noise.

Classical algorithms require at least log(N) queries on average.

Quantum approach outperforms classical methods exponentially.

Abstract

In the SEARCH WITH ADVICE problem, a single entry of interest within a database of N entries is to be found assuming that an ordering of the entries, from that with the highest probability of being the entry of interest (as determined by a so-called advice distribution) to that with the lowest, is provided. We present a quantum algorithm that, in the presence of significant levels of quantum noise, solves SEARCH WITH ADVICE for a power law advice distribution with average-case query complexity O(1) as N tends to infinity. Since as we also show the best classical algorithms for this problem exhibit average-case query complexity of order no better than log(N), our quantum algorithm provides a super-exponential reduction in query complexity.