Quantum data re-uploading has proved powerful for classical inputs, where repeatedly encoding features into a small circuit yields universal function approximation. Extending this idea to quantum inputs remains underexplored, as the information contained in a quantum state is not directly accessible in classical form. We propose and analyze a quantum data re-uploading architecture in which a qubit interacts sequentially with fresh copies of an arbitrary input state. The circuit can approximate any bounded continuous function using only one ancilla qubit and single-qubit measurements. By alternating entangling unitaries with mid-circuit resets of the input register, the architecture realizes a discrete cascade of completely positive and trace-preserving maps, analogous to collision models in open quantum system dynamics. Our framework provides a qubit-efficient and expressive approach to designing quantum machine learning models that operate directly on quantum data.

翻译：量子数据重上传技术在处理经典输入时已被证明具有强大能力，通过将特征重复编码至小型电路中即可实现通用函数逼近。然而，将该思想拓展至量子输入的研究仍显不足，因为量子态所包含的信息无法以经典形式直接访问。本文提出并分析了一种量子数据重上传架构，其中一个量子比特按顺序与任意输入态的新鲜副本相互作用。该电路仅需一个辅助量子比特和单量子比特测量即可逼近任何有界连续函数。通过交替执行纠缠幺正操作与输入寄存器的中间电路重置，该架构实现了完全正且保迹映射的离散级联，类似于开放量子系统动力学中的碰撞模型。我们的框架为直接处理量子数据的量子机器学习模型设计提供了一种量子比特高效且表达能力强的实现途径。