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This article focuses on developing classical surrogates for parametrizedquantum circuits using interpolation via (trigonometric) polynomials. Wedevelop two algorithms for the construction of such surrogates and proveperformance guarantees. The constructions are based on blackbox evaluations ofcircuits, which may either be simulated or executed on quantum hardware. Whileacknowledging the limitations of the blackbox approach compared to whiteboxevaluations, which exploit specific circuit properties, we demonstratescenarios in which the blackbox approach might prove beneficial. Sampleapplications include but are not restricted to the approximation of VQEs andthe alleviaton of the barren plateau problem.

Interpolating Parametrized Quantum Circuits using Blackbox Queries