Quantum fully homomorphic encryption (QFHE) allows to evaluate quantum circuits on encrypted data. We present a novel QFHE scheme, which extends Pauli one-time pad encryption by relying on the quaternion representation of SU(2). With the scheme, evaluating 1-qubit gates is more efficient, and evaluating general quantum circuits is polynomially improved in asymptotic complexity. Technically, a new encrypted multi-bit control technique is proposed, which allows to perform any 1-qubit gate whose parameters are given in the encrypted form. With this technique, we establish a conversion between the new encryption and previous Pauli one-time pad encryption, bridging our QFHE scheme with previous ones. Also, this technique is useful for private quantum circuit evaluation. The security of the scheme relies on the hardness of the underlying quantum capable FHE scheme, and the latter sets its security on the learning with errors problem and the circular security assumption.

翻译：量子完全同质加密( QFHE) 允许对加密数据中的量子电路进行评估。 我们提出了一个新型的 QFHE 计划, 通过使用 SU(2) 的四环表示法延长Pauli 一次性板加密。 有了这个计划, 评估 1 QQBit 门效率更高, 评估普通量子电路在无线复杂性方面有多方面的改进 。 从技术上讲, 提出了一个新的加密多位控制技术, 允许执行任何以加密形式给出参数的一公分门。 有了这个技术, 我们在新的加密和以前的Pauli 一次板加密之间建立了一种转换, 将我们的QFHE 计划与以前的方案连接起来 。 另外, 这个方法对私人量子电路评估有用 。 这个计划的安全性取决于基本量子功能FHE 计划的硬性, 而后者在学习错误问题和循环安全假设的基础上设定了它的安全性 。