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.

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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.

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