TU1.R2.2

Adversarial Quantum Machine Learning: An Information-Theoretic Generalization Analysis

Petros Georgiou, Sharu Theresa Jose, University of Birmingham, United Kingdom; Osvaldo Simeone, King's College London, United Kingdom

Session:
Quantum Information 3

Track:
6: Quantum Information and Coding Theory

Location:
Ypsilon I-II-III

Presentation Time:
Tue, 9 Jul, 10:05 - 10:25

Session Chair:
Uzi Pereg, Technion
Abstract
THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD. In a manner analogous to their classical counterparts, quantum classifiers are vulnerable to adversarial attacks that perturb their inputs. A promising countermeasure is to train the quantum classifier by adopting an attack-aware, or adversarial, loss function. This paper studies the generalization properties of quantum classifiers that are adversarially trained against bounded-norm white-box attacks. Specifically, a quantum adversary maximizes the classifier’s loss by transforming an input state ρ(x) into a state λ that is ϵ-close to the original state ρ(x) in p-Schatten distance. Under suitable assumptions on the quantum embedding ρ(x), we derive novel information-theoretic upper bounds on the generalization error of adversarially trained quantum classifiers for p = 1 and p = ∞. The derived upper bounds consist of two terms: the first is an exponential function of the 2-Renyi mutual information between classical data and ´ quantum embedding, while the second term scales linearly with the adversarial perturbation size ϵ. Both terms are shown to decrease as 1/ √ T over the training set size T. An extension is also considered in which the adversary assumed during training has different parameters p and ϵ as compared to the adversary affecting the test inputs. Finally, we validate our theoretical findings with numerical experiments for a synthetic setting.
Resources