A rebit-based quantum homomorphic encryption scheme
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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 circuits of unrestricted size would require exponential resources, and efficient computationally-secure QHE schemes for polynomial-sized quantum circuits have been constructed. In this paper we propose a QHE scheme for a type of circuits of polynomial depth, based on the rebit quantum computation formalism. The scheme keeps the restricted type of data perfectly secure, and the privacy of the circuit is optimal up to a constant factor. The entanglement and communication costs scale linearly with the product of input size and circuit depth. We show that the scheme can be applied to evaluate DQC1 circuits.
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