用单个辅助量子比特实现对任意量子输入的通用函数逼近
Re-uploading quantum data: a universal function approximator for quantum inputs
- 通过重复将输入量子态编码到小电路中，实现函数逼近
- 仅需一个辅助量子比特和单量子比特测量即可逼近任意有界连续函数
- 适合直接处理量子数据的高效量子机器学习模型设计
量子数据重上传在经典输入上已证明具有强大能力，即通过反复将特征编码进小型电路可实现通用函数逼近。将此思想拓展至量子输入仍处于探索阶段，因量子态中的信息无法直接以经典形式获取。本文提出并分析一种量子数据重上传架构：一个量子比特依次与任意输入态的新副本相互作用。该电路仅需一个辅助量子比特和单量子比特测量，即可逼近任意有界连续函数。通过交替使用纠缠幺正操作与输入寄存器的中电路重置，该架构实现了离散的完全正且保迹映射序列，类似于开放量子系统动力学中的碰撞模型。本框架为直接作用于量子数据的量子机器学习模型提供了高效且富有表现力的设计方法。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。