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Fully homomorphic encryption enables arbitrary computation on encrypted datawithout decrypting the data. Here it is studied in the context of quantuminformation processing. Based on universal quantum circuit, we present aquantum fully homomorphic encryption (QFHE) scheme, which permits arbitraryquantum transformation on an encrypted data. The QFHE scheme is proved to beperfectly secure. In the scheme, the decryption key is different from theencryption key, however, the encryption key cannot be public. Moreover, theevaluate algorithm of the scheme is independent of the encryption key, so it isvery applicable in delegated quantum computing between two parties.

Quantum fully homomorphic encryption scheme based on universal quantum circuit