I will introduce the Spectral Adaptive Quantum Neural Network (SAQNN) in this talk. It is a constructive model which establishes a crucial theoretical foundation for quantum machine learning. We rigorously prove that the SAQNN possesses the Universal Approximation Property (UAP), capable of approximating any square-integrable function with arbitrary accuracy. Furthermore, it supports switching function bases, thus adaptable to various scenarios in numerical approximation and machine learning. Our model has asymptotic advantages over the best classical feed-forward neural networks in terms of circuit size and achieves optimal parameter complexity when approximating Sobolev functions under L_2 norm. Besides this theoretical result， I will also present our preliminary results on circuit compilation and algorithm design for neutral-atom quantum computers.

Biography

张家琳，中国科学院计算技术研究所研究员，博士生导师。博士毕业于清华大学应用数学专业，师从姚期智教授，之后在南加州大学做博士后研究，合作导师滕尚华教授。回国后加入中国科学院计算技术研究所，主要研究方向包括量子算法设计、量子线路优化、理论计算机科学、算法博弈论等。主持国家自然科学基金重点项目、面上项目等科研项目多项。