  Homomorphic encryption is an encryption scheme that allows computations to be
evaluated on encrypted inputs without knowledge of their raw messages. Recently
Ouyang et al. constructed a quantum homomorphic encryption (QHE) scheme for
Clifford circuits with statistical security (or information-theoretic security
(IT-security)). It is desired to see whether an
information-theoretically-secure (ITS) quantum FHE exists. If not, what other
nontrivial class of quantum circuits can be homomorphically evaluated with
IT-security? We provide a limitation for the first question that an ITS quantum
FHE necessarily incurs exponential overhead. As for the second one, we propose
a QHE scheme for the instantaneous quantum polynomial-time (IQP) circuits. Our
QHE scheme for IQP circuits follows from the one-time pad.
