Quantum homomorphic encryption (QHE) is an encryption method that allows quantum computation to be performed on one party's private data with the program provided by another party, without revealing much information about the data nor about the program to the opposite party. It is known that information-theoretically-secure QHE for arbitrary circuits would require exponential resources, and efficient computationally-secure QHE schemes for polynomial-sized quantum circuits have been constructed. In this paper we propose an information-theoretically-secure QHE scheme with entanglement and communication costs polynomial in circuit size. The scheme keeps the data perfectly secure, and the privacy of the circuit is optimal in general.
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