  In a recent breakthrough, Mahadev constructed a classical verification of
quantum computation (CVQC) protocol for a classical client to delegate decision
problems in BQP to an untrusted quantum prover under computational assumptions.
In this work, we explore further the feasibility of CVQC with the more general
sampling problems in BQP and with the desirable blindness property. We
contribute affirmative solutions to both as follows.
  (1) Motivated by the sampling nature of many quantum applications (e.g.,
quantum algorithms for machine learning and quantum supremacy tasks), we
initiate the study of CVQC for quantum sampling problems (denoted by SampBQP).
More precisely, in a CVQC protocol for a SampBQP problem, the prover and the
verifier are given an input $x\in \{0,1\}^n$ and a quantum circuit $C$, and the
goal of the classical client is to learn a sample from the output $z \leftarrow
C(x)$ up to a small error, from its interaction with an untrusted prover. We
demonstrate its feasibility by constructing a four-message CVQC protocol for
SampBQP based on the quantum Learning With Error assumption.
  (2) The blindness of CVQC protocols refers to a property of the protocol
where the prover learns nothing, and hence is blind, about the client's input.
It is a highly desirable property that has been intensively studied for the
delegation of quantum computation. We provide a simple yet powerful generic
compiler that transforms any CVQC protocol to a blind one while preserving its
completeness and soundness errors as well as the number of rounds.
  Applying our compiler to (a parallel repetition of) Mahadev's CVQC protocol
for BQP and our CVQC protocol for SampBQP yields the first constant-round blind
CVQC protocol for BQP and SampBQP respectively, with negligible and inverse
polynomial soundness errors respectively, and negligible completeness errors.
