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.

翻译：本文聚焦于利用（三角）多项式插值方法为参数化量子电路构建经典代理模型。我们提出了两种构建此类代理模型的算法，并证明了其性能保证。这些构建方法基于电路评估，其黑盒特性在于不利用电路的具体结构信息。尽管认识到黑盒方法相较于利用特定电路性质的白盒评估存在局限性，我们仍展示了黑盒方法可能具有优势的应用场景。示例应用包括但不限于：变分量子本征求解器的近似计算，以及缓解贫瘠高原问题。