It is conjectured that classical (BPP) client blind quantum computing is implausible according to Aaronson et al:
What are the minimal quantum capabilities that a classical client must have in order to verify a single BQP quantum prover with the following requirements?
- Information-secure communication (no cryptographic assumptions)
- Only the size of the input is revealed to the quantum prover
- Single prover server
My understanding is that the paper above leaves this as an open problem.