  Future quantum computers are likely to be expensive and affordable outright
by few, motivating client/server models for outsourced computation. However,
the applications for quantum computing will often involve sensitive data, and
the client would like to keep her data secret, both from eavesdroppers and the
server itself. Homomorphic encryption is an approach for encrypted, outsourced
quantum computation, where the client's data remains secret, even during
execution of the computation. We present a scheme for the homomorphic
encryption of arbitrary quantum states of light with no more than a fixed
number of photons, under the evolution of both passive and adaptive linear
optics, the latter of which is universal for quantum computation. The scheme
uses random coherent displacements in phase-space to obfuscate client data. In
the limit of large coherent displacements, the protocol exhibits asymptotically
perfect information-theoretic secrecy. The experimental requirements are
modest, and easily implementable using present-day technology.
