Quantum Walks with Encrypted Data

In the setting of networked computation, data security can be a significant concern. Here we consider the problem of allowing a server to remotely manipulate client supplied data, in such a way that both the information obtained by the client about the server's operation and the information obtained by the server about the client's data are significantly limited. We present a protocol for achieving such functionality in two closely related models of restricted quantum computation-the boson sampling and quantum walk models. Because of the limited technological requirements of the boson scattering model, small scale implementations of this technique are feasible with present-day technology.