Differential Privacy Preserving Quantum Computing via Projection Operator Measurements

Abstract: Quantum computing has been widely applied in various fields, such as quantum physics simulations, quantum machine learning, and big data analysis. However, in the domains of data-driven paradigm, how to ensure the privacy of the database is becoming a vital problem. For classical computing, we can incorporate the concept of differential privacy (DP) to meet the standard of privacy preservation by manually adding the noise. In the quantum computing scenario, researchers have extended classic DP to quantum differential privacy (QDP) by considering the quantum noise. In this paper, we propose a novel approach to satisfy the QDP definition by considering the errors generated by the projection operator measurement, which is denoted as shot noises. Then, we discuss the amount of privacy budget that can be achieved with shot noises, which serves as a metric for the level of privacy protection. Furthermore, we provide the QDP of shot noise in quantum circuits with depolarizing noise. Through numerical simulations, we show that shot noise can effectively provide privacy protection in quantum computing.