Differential Privacy Preserving Quantum Computing via Projection Operator Measurements

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 paradigms, ensuring databases privacy. For classical computing, we can incorporate the concept of differential privacy (DP) to meet the standard of privacy preservation by manually adding noise. In quantum computing scenario, researchers have extended classic DP to quantum differential privacy (QDP) by considering 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 noise. Then, we discuss the amount of privacy budget that can be achieved with shot noise, 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.