Quantum computation has found greater efficiency and security across various fields. We show that, in a near-term hybrid cloud computing scenario with only one single quantum server and an entirely classical client, critical bottlenecks in privacy-preserving computation can be addressed. First, we propose an efficient quantum functional bootstrapping algorithm with a runtime polynomial in the plaintext-size, providing an exponential quantum speedup over classical algorithms. Second, we present a secure and fast quantum private information retrieval protocol with logarithmic query time. The security relies on the learning with errors (LWE) problem with polynomial modulus, greatly improving the security of classical fast PIR protocol based on ring-LWE with super-polynomial modulus. Technically, we extend an important classical homomorphic operation, known as blind rotation, to the quantum case by an encrypted conditional rotation technique. This technique holds promise for broader applications in quantum cryptography.

翻译：量子计算已在多个领域展现出更高的效率与安全性。我们证明，在仅有一个量子服务器与完全经典客户端的近期混合云计算场景中，隐私保护计算中的关键瓶颈问题可以得到解决。首先，我们提出了一种高效的量子函数自举算法，其运行时间在明文大小上呈多项式复杂度，相比经典算法实现了指数级的量子加速。其次，我们提出了一种安全且快速的量子私有信息检索协议，其查询时间为对数级别。该协议的安全性基于多项式模数下的容错学习问题，显著提升了基于超多项式模数环容错学习问题的经典快速私有信息检索协议的安全性。在技术层面，我们通过一种加密条件旋转技术，将一种重要的经典同态操作——盲旋转——扩展至量子情形。该技术有望在量子密码学领域获得更广泛的应用。