Robustness Verification of Quantum Classifiers

TL;DR

This paper introduces a formal framework and algorithm for verifying the robustness of quantum machine learning algorithms against quantum noise, with experimental validation on various quantum and classical datasets.

Contribution

It develops a robustness verification method for quantum classifiers, including adversarial example detection, applicable to real quantum hardware and classical datasets.

Findings

The robust bound effectively detects noise-induced vulnerabilities.

The algorithm successfully finds adversarial examples in quantum classifiers.

Experimental results confirm the approach's practicality on real quantum and classical data.

Abstract

Several important models of machine learning algorithms have been successfully generalized to the quantum world, with potential speedup to training classical classifiers and applications to data analytics in quantum physics that can be implemented on the near future quantum computers. However, quantum noise is a major obstacle to the practical implementation of quantum machine learning. In this work, we define a formal framework for the robustness verification and analysis of quantum machine learning algorithms against noises. A robust bound is derived and an algorithm is developed to check whether or not a quantum machine learning algorithm is robust with respect to quantum training data. In particular, this algorithm can find adversarial examples during checking. Our approach is implemented on Google's TensorFlow Quantum and can verify the robustness of quantum machine learning algorithms with respect to a small disturbance of noises, derived from the surrounding environment. The effectiveness of our robust bound and algorithm is confirmed by the experimental results, including quantum bits classification as the "Hello World" example, quantum phase recognition and cluster excitation detection from real world intractable physical problems, and the classification of MNIST from the classical world.