Adversarial Robustness based on Randomized Smoothing in Quantum Machine Learning

Aditya Sahdev, Mehul Kumar

Keywords: Quantum Computing, Adversarial Machine learning, Randomized Smoothing, Quantum Amplitude Estimation

TL;DR: Algorithm, theoretical proof, circuits, and results for a certifiably robust Quantum Computing classifier based on Randomized Smoothing.

Abstract: We present an end-to-end Quantum Machine Learning algorithm that encodes a classical input into a Quantum Computing state and provides certified radius for a base classifier, with robustness guarantees based on randomized smoothing - current state-of-the-art defense against adversarial attacks. Classically, the number of samples, also the number of queries to the classifier, scale with $O(1/\epsilon^2)$ where $\epsilon$ is the desired error bound in expected value of the probability measure $\rho$ defined over the randomized smoothing neighborhood. Our algorithm is designed to solve the same problem for a Quantum Computing classifier. We prove that number of queries to the classifier scale as $O(1/\epsilon)$ for the same confidence and error bound. We also present the unitary circuit corresponding to the quantum randomized smoothing algorithm, as well as the state preparation methods and circuits for smoothing distributions used to defend against common adversaries - modeled using $l_0$, $l_1$, $l_2$ norms, and other metrics. The results of comparison between the classical and simulation of the quantum algorithm are also discussed.

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