  We propose a homomorphic search protocol based on quantum homomorphic
encryption, in which a client Alice with limited quantum ability can give her
encrypted data to a powerful but untrusted quantum server and let the server
search for her without decryption. By outsourcing the interactive key-update
process to a trusted key center, Alice only needs to prepare and encrypt her
original data and to decrypt the ciphered search result in linear time.
Besides, we also present a compact and perfectly secure quantum homomorphic
evaluation protocol for Cliford circuits, where the decryption key can be
calculated by Alice with polynomial overhead with respect to the key length.
