Quantum algorithms for solving a wide range of practical problems have been proposed in the last ten years, such as data search and analysis, product recommendation, and credit scoring. The concern about privacy and other ethical issues in quantum computing naturally rises up. In this paper, we define a formal framework for detecting violations of differential privacy for quantum algorithms. A detection algorithm is developed to verify whether a (noisy) quantum algorithm is differentially private and automatically generate bugging information when the violation of differential privacy is reported. The information consists of a pair of quantum states that violate the privacy, to illustrate the cause of the violation. Our algorithm is equipped with Tensor Networks, a highly efficient data structure, and executed both on TensorFlow Quantum and TorchQuantum which are the quantum extensions of famous machine learning platforms -- TensorFlow and PyTorch, respectively. The effectiveness and efficiency of our algorithm are confirmed by the experimental results of almost all types of quantum algorithms already implemented on realistic quantum computers, including quantum supremacy algorithms (beyond the capability of classical algorithms), quantum machine learning models, quantum approximate optimization algorithms, and variational quantum eigensolvers with up to 21 quantum bits.

翻译：在过去十年中，针对数据搜索与分析、产品推荐、信用评分等广泛实际问题，量子算法已被提出。量子计算中的隐私及其他伦理问题自然引起了关注。本文定义了一个用于检测量子算法差分隐私违规的形式化框架。我们开发了一种检测算法，用于验证（含噪声的）量子算法是否满足差分隐私，并在报告差分隐私违规时自动生成调试信息。该信息由一对违反隐私的量子态组成，用以说明违规原因。该算法配备了张量网络这一高效数据结构，并在TensorFlow Quantum和TorchQuantum上执行——这两种平台分别是著名机器学习平台TensorFlow和PyTorch的量子扩展。通过在真实量子计算机上已实现的几乎所有类型量子算法（包括超越经典算法能力的量子霸权算法、量子机器学习模型、量子近似优化算法以及最多含21个量子比特的变分量子本征求解器）上的实验结果，我们算法的有效性和高效性得到了验证。