Institute of Information Science, Academia Sinica

Based on a simple encoding scheme with randomized inputs, we explore the security of two different delegated quantum computation schemes. For the first part, we show that such a encoding scheme leads to a (n,n)-threshold quantum secret sharing scheme that supports delegated Clifford computations, and hence only requires one honest party for the secret-sharing scheme to work. We show how performing non-Clifford computations on this scheme can be achieved and made secure. For the second part, we build upon the use of random codes to construct a quantum encryption scheme which is homomorphic for arbitrary classical and quantum circuits which have at most some constant number of non-Clifford gates. Unlike classical schemes, the security of the scheme we present is information theoretic, satisfying entropic security definitions, and hence independent of the computational power of an adversary. This talk is based on the papers "Computing on quantum shared secrets", Y. Ouyang, S.H. Tan, L. Zhao, and J.F. Fitzsimons, Phys. Rev. A 96, 052333, arXiv:1702.03689 and "Quantum homomorphic encryption from quantum codes", Y. Ouyang, S.H. Tan, and J.F. Fitzsimons, arXiv:1508.00938.