Quantum machine learning uses principles from quantum mechanics to process data, offering potential advances in speed and performance. However, previous work has shown that these models are susceptible to attacks that manipulate input data or exploit noise in quantum circuits. Following this, various studies have explored the robustness of these models. These works focus on the robustness certification of manipulations of the quantum states. We extend this line of research by investigating the robustness against perturbations in the classical data for a general class of data encoding schemes. We show that for such schemes, the addition of suitable noise channels is equivalent to evaluating the mean value of the noiseless classifier at the smoothed data, akin to Randomized Smoothing from classical machine learning. Using our general framework, we show that suitable additions of phase-damping noise channels improve empirical and provable robustness for the considered class of encoding schemes.

Breakthroughs in machine learning (ML) and advances in quantum computing (QC) drive the interdisciplinary field of quantum machine learning to new levels. However, due to the susceptibility of ML models to adversarial attacks, practical use raises safety-critical concerns. Existing Randomized Smoothing (RS) certification methods for classical machine learning models are computationally intensive. In this paper, we propose the combination of QC and the concept of discrete randomized smoothing to speed up the stochastic certification of ML models for discrete data. We show how to encode all the perturbations of the input binary data in superposition and use Quantum Amplitude Estimation (QAE) to obtain a quadratic reduction in the number of calls to the model that are required compared to traditional randomized smoothing techniques. In addition, we propose a new binary threat model to allow for an extensive evaluation of our approach on images, graphs, and text.

Training deep neural network classifiers that are certifiably robust against adversarial attacks is critical to ensuring the security and reliability of AI-controlled systems. Although numerous state-of-the-art certified training methods have been developed, they are computationally expensive and scale poorly with respect to both dataset and network complexity. Widespread usage of certified training is further hindered by the fact that periodic retraining is necessary to incorporate new data and network improvements. In this paper, we propose Certified Robustness Transfer (CRT), a general-purpose framework for reducing the computational overhead of any certifiably robust training method through knowledge transfer. Given a robust teacher, our framework uses a novel training loss to transfer the teacher's robustness to the student. We provide theoretical and empirical validation of CRT. Our experiments on CIFAR-10 show that CRT speeds up certified robustness training by $8 \times$ on average across three different architecture generations while achieving comparable robustness to state-of-the-art methods. We also show that CRT can scale to large-scale datasets like ImageNet.