Two-round quantum homomorphic encryption scheme based on matrix decomposition

As a promising emerging technology, quantum homomorphic encryption (QHE) attracts considerable attention in the domain of cloud computing. However, as the homomorphic evaluation for non-Clifford gate generates an undesired error, efficient QHE scheme for any quantum circuit still faces a serious challenge. In this paper, we propose a two-round QHE scheme based on matrix decomposition, which can be used to eliminate the error and obtain the decryption matrix non-interactively. Through the circuit synthesis method, the decryption matrix can be decomposed into a quantum circuit to complete the decryption. In order to reduce the decryption overhead for Client, an extra round of evaluation is used to perform the decryption circuit by Server. We prove that the scheme is compact and information-theoretically secure. In addition, we apply the QHE scheme to ciphertext retrieval and complete a ciphertext retrieval experiment on IBM Qiskit. The retrieval scheme is efficient even if the evaluated circuit contains any number of non-Clifford gates.