Verifiable quantum homomorphic encryption based on garbled evaluation

Quantum homomorphic encryption (QHE) can allow directly computation on the encrypted data without need to decrypt it in advance. It is also necessary to provide another property of verifiability that the client should verify whether the evaluation result is correct. However, most existing QHE schemes did not consider it and only assumed servers to be honest. In this paper, we propose a verifiable QHE (vQHE) scheme by using different types of circuits indistinguishable to the server, where the client can detect whether the server is honest or not by verifying the results of test circuits. Furthermore, by designing the gadgets to implement and test T gates and H gates in a non-interactive way for the used circuits, the proposed vQHE scheme does not require interaction during the process of evaluation. Thus the proposed vQHE scheme has the potential to make clients prefer to use it for protecting their private data in future quantum cloud environments.