Quadratic Advantage with Quantum Randomized Smoothing Applied to Time-Series Analysis

TL;DR

This paper introduces a quantum randomized smoothing technique with a quadratic sampling advantage, enhancing robustness in quantum time-series analysis, demonstrated through a classification task with potential for scaling beyond classical limits.

Contribution

It presents a novel quantum approach integrating Grover's algorithm for improved randomized smoothing with a focus on time-series classification.

Findings

Quadratic sampling advantage over classical methods.

Effective robustness certificates for quantum algorithms.

Potential for scaling to complex tasks beyond classical capabilities.

Abstract

As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how data encoding and perturbation modeling approaches can be matched to achieve meaningful robustness certificates. By utilizing an innovative approach integrating Grover's algorithm, a quadratic sampling advantage over classical randomized smoothing is achieved. This strategy necessitates a basis state encoding, thus restricting the space of meaningful perturbations. We show how constrained $k$-distant Hamming weight perturbations are a suitable noise distribution here, and elucidate how they can be constructed on a quantum computer. The efficacy of the proposed framework is demonstrated on a time series classification task employing a Bag-of-Words pre-processing solution. The advantage of quadratic sample reduction is recovered especially in the regime with large number of samples. This may allow quantum computers to efficiently scale randomized smoothing to more complex tasks beyond the reach of classical methods.