  This article focuses on developing classical surrogates for parametrized
quantum circuits using interpolation via (trigonometric) polynomials. We
develop two algorithms for the construction of such surrogates and prove
performance guarantees. The constructions are based on circuit evaluations
which are blackbox in the sense that no structural specifics of the circuits
are exploited. While acknowledging the limitations of the blackbox approach
compared to whitebox evaluations, which exploit specific circuit properties, we
demonstrate scenarios in which the blackbox approach might prove beneficial.
Sample applications include but are not restricted to the approximation of VQEs
and the alleviaton of the barren plateau problem.
