Quantum Fully Homomorphic Encryption without Preprocessing

We present a novel quantum fully homomorphic encryption (QFHE) scheme. In our scheme, any quantum circuit can be directly evaluated with no need to be decomposed into Clifford/non-Clifford gates, or be transformed into the real-representation frist. This advantage makes our QFHE more convenient to evaluate the general quantum algorithms than the previous QFHE schemes. Theoretically, our main technique allows one to perform the conditional rotation with the control bit in encrypted form. This technique builds upon a specific kind of so-called quantum capable FHE schemes. The security of our scheme relies on the hardness of the underlying quantum capable FHE scheme, which bases its security on the learning with errors problem and the circular security assumption.