Enhancing quantum adversarial robustness by randomized encodings

Physical Review Research, vol. 6

Abstract

The interplay between quantum physics and machine learning gives rise to the emergent frontier of quantum machine learning, where advanced quantum learning models may outperform their classical counterparts in solving certain challenging problems. However, quantum learning systems are vulnerable to adversarial attacks: adding tiny carefully crafted perturbations on legitimate input samples can cause misclassifications. To address this problem, we propose an effective approach to protect quantum learning systems from adversarial attacks by randomly encoding the legitimate data samples through unitary or quantum error correction encoders that are unknown to the attackers. In particular, we rigorously prove that both global and local random unitary encoders lead to exponentially vanishing gradients (i.e., barren plateaus) for any variational quantum circuits that aim to add adversarial perturbations, independent of the input data and the inner structures of adversarial circuits and quantum classifiers. In addition, we prove a rigorous bound on the vulnerability of quantum classifiers under local unitary adversarial attacks. We show that random black-box quantum error correction encoders can protect quantum classifiers against local adversarial noises and their robustness increases as we concatenate error correction codes. To quantify the robustness enhancement, we adapt quantum differential privacy as a measure of the prediction stability for quantum classifiers. Our results establish versatile defense strategies for quantum classifiers against adversarial perturbations, which provide valuable guidance to enhance the reliability and security for both near-term and future quantum learning technologies. Published by the American Physical Society 2024

Authors 4

1. Weiyuan Gong

   Tsinghua University · Harvard University

   Affiliation as printed

   Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, China

   School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA

2. Yuan Dong

   Tsinghua University

   Affiliation as printed

   Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, China

3. Weikang Li Aachen Instituut-Lorentz

   Leiden University · Tsinghua University

   Affiliation as printed

   Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, China

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

4. Dong-Ling Deng

   Tsinghua University · Shanghai Qi Zhi Institute

   Affiliation as printed

   Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, China

   Hefei National Laboratory, Hefei 230088, China

   Shanghai Qi Zhi Institute, No. 701 Yunjin Road, Xuhui District, Shanghai 200232, China