通过叠加量子电路实现多参数并行训练,提升量子模型表达能力。
Superposed parameterised quantum circuits
- 用量子随机存取内存与重复成功协议构造叠加参数电路
- 1D回归任务误差降三个数量级,2D分类准确率达81.4%
- 适合想构建深层非线性量子模型的研究者
量子机器学习在高维数据分析中展现出潜力,但现有方法多依赖线性酉操作和共享可训练参数,限制了表达能力和可扩展性。本文提出叠加参数量子电路,结合翻转-翻转量子随机存取内存与重复直至成功协议,在单个电路中嵌入指数级参数子模型,并通过振幅变换与后选择诱导多项式激活函数。我们提供该架构的解析描述,证明多个参数集可并行训练,且非线性振幅变换拓展了传统量子核的表征能力。数值实验显示:在一维阶跃函数回归任务中,两量子比特叠加参数量子电路使均方误差降低三个数量级,优于参数匹配的变分基线;在二维星形分类任务中引入二次激活函数后,准确率达到81.4%,运行间方差减少三倍。这些结果表明,叠加参数量子电路是实现更深层、更灵活参数化量子电路的高效硬件路径,能够学习复杂决策边界。
原文摘要 · Abstract (English)
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.
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