Two essential primitives for universal, cloud-based quantum computation with security based on the laws of quantum mechanics, are quantum homomorphic encryption with information-theoretic security and quantum error correction. The former enables information-theoretic security of outsourced quantum computation, while the latter allows reliable and scalable quantum computations in the presence of errors. Previously these ingredients have been considered in isolation from one another. By establishing group-theoretic requirements that these two ingredients must satisfy, we provide a general framework for composing them. Namely, a quantum homomorphic encryption scheme enhanced with quantum error correction can directly inherit its properties from its constituent quantum homomorphic encryption and quantum error correction schemes. We apply our framework to both discrete- and continuous-variable models for quantum computation, such as Pauli-key and permutation-key encryptions in the qubit model, and displacement-key encryptions in a continuous-variable model based on Gottesman-Kitaev-Preskill codes.

翻译：根据量子力学定律安全地进行基于云的量子计算的两个基本原始要素是量子同质加密,并配以信息理论安全和量子错误校正。前者使外包量子计算能够实现信息理论安全,而后者允许在出现错误的情况下进行可靠和可缩放的量子计算。以前,这些成分是分开考虑的。通过建立这两个成分必须满足的群子理论要求,我们提供了形成这两个成分的一般框架。也就是说,用量子差错校正强化的量子同质加密计划可以直接从其构成的量子同质加密和量子错误校正方案中继承其特性。我们把框架应用到量子计算的不同和连续可变的模型,例如系数模型中的保利键和交替键加密,以及基于Gotesman-Kitaev-Preskilly代码的连续变式模型中的置换钥匙加密。