  Blind quantum computing enables a client, who can only generate or measure
single-qubit states, to delegate quantum computing to a remote quantum server
in such a way that the input, output, and program are hidden from the server.
It is an open problem whether a completely classical client can delegate
quantum computing blindly. In this paper, we show that if a completely
classical client can blindly delegate sampling of subuniversal models, such as
the DQC1 model and the IQP model, then the polynomial-time hierarchy collapses
to the third level. Our delegation protocol is the one where the client first
sends a polynomial-length bit string to the server and then the server returns
a single bit to the client. Generalizing the no-go result to more general
setups is an open problem.
