Flow ambiguity: A path towards classically driven blind quantum computation

Blind quantum computation protocols allow a user to delegate a computation to a remote quantum computer in such a way that the privacy of their computation is preserved, even from the device implementing the computation. To date, such protocols are only known for settings involving at least two quantum devices: either a user with some quantum capabilities and a remote quantum server, or two or more entangled but non-communicating servers. In this work, we exploit ambiguity in the flow of information in measurement-based quantum computation to construct a protocol for hiding a computation delegated to a remote quantum computer by an entirely classical user. This ambiguity arises due to the fact that, for a fixed graph, there exist multiple choices of the input and output vertex sets that result in deterministic measurement patterns consistent with the same fixed total ordering of vertices. This allows a classical user, computing only measurement angles, to drive a measurement-based computation performed on a remote device while hiding critical aspects of the computation.