Tuning Quantum Computing Privacy through Quantum Error Correction

Abstract: Quantum computing is a promising paradigm for efficiently solving large and high-complexity problems. To protect quantum computing privacy, pioneering research efforts proposed to redefine differential privacy (DP) in quantum computing, i.e., quantum differential privacy (QDP), and harvest inherent noises generated by quantum computing to implement QDP. However, such an implementation approach is limited by the amount of inherent noises, which makes the privacy budget of the QDP mechanism fixed and uncontrollable. To address this issue, in this paper, we propose to leverage quantum error correction (QEC) techniques to reduce quantum computing errors, while tuning the privacy protection levels in QDP. In short, we gradually decrease the quantum noise error rate by deciding whether to apply QEC operations on the gate in a multiple single qubit gates circuit. We have derived a new calculation formula for the general error rate and corresponding privacy budgets after QEC operation. Then, we expand to achieve further noise reduction using multi-level concatenated QEC operation. Through extensive numerical simulations, we demonstrate that QEC is a feasible way to regulate the degree of privacy protection in quantum computing.