Certifiably Robust Encoding Schemes

Abstract: 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.