Quantum Fully Homomorphic Encryption without Clifford Decomposition and Real Representation

We present a novel quantum fully homomorphic encryption (QFHE) scheme, which allows to perform the conditional rotation with the control bit in encrypted form. In our scheme, any quantum circuit can be directly evaluated with no need to decompose into Clifford/non-Clifford gates, nor be transformed into real representation. Consequently, our QFHE is more convenient than previous QFHE schemes for evaluating general quantum algorithms. The security of our 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.