Universal and holistic privacy protection in quantum computing: a novel approach through quantum circuit equivalence homomorphic encryption

Abstract

Abstract Due to the stringent hardware requirements and high cost, quantum computing as a service (QCaaS) is currently the main way to output quantum computing capabilities. However, the current QCaaS has significant shortcomings in privacy protection. The existing researches mainly focus on dataset privacy in some specific quantum machine learning algorithms, and there is no general and comprehensive research on privacy protection for dataset, parameter sets and algorithm models. To solve this problem, this paper defines the concept of generalized quantum homomorphic encryption and pioneers a novel method termed quantum circuit equivalence homomorphic encryption (QCEHE), aiming at protecting the privacy of the complete quantum circuits—encompassing data, parameters, and model. Based on QCEHE, a privacy protection scheme and its approximate implementation called quantum circuit equivalent substitution algorithm are proposed for any quantum algorithm, which can encrypt the complete quantum circuit on a classical computer, ensuring that the encrypted quantum circuit is physically equivalent to the original one, and does not reveal data holders’ privacy (data, parameters and model). By theoretical derivation, we prove that the proposed solution can effectively execute any quantum algorithm while protecting privacy. By applying the proposed solution to the privacy protection of the Harrow–Hassidim–Lloyd algorithm and the variational quantum classifier algorithm, the results showed that the accuracy rate before and after encryption are almost the same, which means that the proposed solution can effectively protect the privacy of data holders without impacting the usability and accuracy.