  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.
