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

Fuente: arXiv
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Main Authors: Franco, Nicola, Kempkes, Marie, Spiegelberg, Jakob, Lorenz, Jeanette Miriam
Format: Preprint
Published: 2024
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author Franco, Nicola
Kempkes, Marie
Spiegelberg, Jakob
Lorenz, Jeanette Miriam
author_facet Franco, Nicola
Kempkes, Marie
Spiegelberg, Jakob
Lorenz, Jeanette Miriam
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_18021
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Quadratic Advantage with Quantum Randomized Smoothing Applied to Time-Series Analysis
Franco, Nicola
Kempkes, Marie
Spiegelberg, Jakob
Lorenz, Jeanette Miriam
Quantum Physics
Artificial Intelligence
Machine Learning
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.
title Quadratic Advantage with Quantum Randomized Smoothing Applied to Time-Series Analysis
topic Quantum Physics
Artificial Intelligence
Machine Learning
url https://arxiv.org/abs/2407.18021