  Fully homomorphic encryption enables arbitrary computation on encrypted data
without decrypting the data. Here it is studied in the context of quantum
information processing. Based on universal quantum circuit, we present a
quantum fully homomorphic encryption (QFHE) scheme, which permits arbitrary
quantum transformation on an encrypted data. The QFHE scheme is proved to be
perfectly secure. In the scheme, the decryption key is different from the
encryption key, however, the encryption key cannot be public. Moreover, the
evaluate algorithm of the scheme is independent of the encryption key, so it is
very applicable in delegated quantum computing between two parties.
