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Future quantum computers are likely to be expensive and affordable outrightby few, motivating client/server models for outsourced computation. However,the applications for quantum computing will often involve sensitive data, andthe client would like to keep her data secret, both from eavesdroppers and theserver itself. Homomorphic encryption is an approach for encrypted, outsourcedquantum computation, where the client's data remains secret, even duringexecution of the computation. We present a scheme for the homomorphicencryption of arbitrary quantum states of light with no more than a fixednumber of photons, under the evolution of both passive and adaptive linearoptics, the latter of which is universal for quantum computation. The schemeuses random coherent displacements in phase-space to obfuscate client data. Inthe limit of large coherent displacements, the protocol exhibits asymptoticallyperfect information-theoretic secrecy. The experimental requirements aremodest, and easily implementable using present-day technology.

Homomorphic encryption of linear optics quantum computation on almost arbitrary states of light with asymptotically perfect security