Quantum machine learning has shown promise for high-dimensional data analysis, yet many existing approaches rely on linear unitary operations and shared trainable parameters across outputs. These constraints limit expressivity and scalability relative to the multi-layered, non-linear architectures of classical deep networks. We introduce superposed parameterised quantum circuits to overcome these limitations. By combining flip-flop quantum random-access memory with repeat-until-success protocols, a superposed parameterised quantum circuit embeds an exponential number of parameterised sub-models in a single circuit and induces polynomial activation functions through amplitude transformations and post-selection. We provide an analytic description of the architecture, showing how multiple parameter sets are trained in parallel while non-linear amplitude transformations broaden representational power beyond conventional quantum kernels. Numerical experiments underscore these advantages: on a 1D step-function regression a two-qubit superposed parameterised quantum circuit cuts the mean-squared error by three orders of magnitude versus a parameter-matched variational baseline; on a 2D star-shaped two-dimensional classification task, introducing a quadratic activation lifts accuracy to 81.4\% and reduces run-to-run variance three-fold. These results position superposed parameterised quantum circuits as a hardware-efficient route toward deeper, more versatile parameterised quantum circuits capable of learning complex decision boundaries.

翻译：量子机器学习在高维数据分析中展现出潜力，但现有方法多依赖于线性幺正操作和跨输出共享的可训练参数。这些限制制约了其表达能力与可扩展性，难以媲美经典深度网络的多层非线性架构。本文提出叠加参数化量子电路以突破这些局限。通过结合触发器量子随机存取存储器与重复直至成功协议，该架构可在单一电路中嵌入指数级数量的参数化子模型，并借助振幅变换与后选择机制诱导多项式激活函数。我们给出了该架构的解析描述，阐明多组参数如何并行训练，同时非线性振幅变换将表征能力拓展至超越传统量子核方法的范畴。数值实验凸显了其优势：在一维阶跃函数回归任务中，双量子比特叠加参数化量子电路将均方误差较参数匹配的变分基线降低了三个数量级；在二维星形分类任务中，引入二次激活函数将准确率提升至81.4%，并将运行间方差降低至三分之一。这些结果表明，叠加参数化量子电路为实现更深层、更通用的参数化量子电路提供了一条硬件高效路径，使其能够学习复杂的决策边界。