报告题目：Expressibility-induced Concentration of Quantum Neural Tangent Kernels

报  告 人：于立伟 副研究员，南开大学

研究方向：量子人工智能、杨-Baxter方程相关数学物理、拓扑量子计算

报告时间：2024年6月7日（星期五）上午10:30

报告地点：格物楼326教室

报告摘要：

uantum tangent kernel methods provide an efficient approach to analyzing the performance of quantum machine learning models in the infinite-width limit, which is of crucial importance in designing appropriate circuit architectures for certain learning tasks. Recently, they have been adapted to describe the convergence rate of training errors in quantum neural networks in an analytical manner. Here, we study the connections between the trainability and expressibility of quantum tangent kernel models. In particular, for global loss functions, we rigorously prove that high expressibility of both the global and local quantum encodings can lead to exponential concentration of quantum tangent kernel values to zero. Whereas for local loss functions, such issue of exponential concentration persists owing to the high expressibility, but can be partially mitigated. We further carry out extensive numerical simulations to support our analytical theories. Our discoveries unveil a pivotal characteristic of quantum neural tangent kernels, offering valuable insights for the design of wide quantum variational circuit models in practical applications.

报告人简介：

于立伟，南开大学陈省身数学研究所副研究员，入选南开大学“青年学科带头人”计划。2017年毕业于南开大学陈省身数学研究所，获得理论物理博士学位。先后在南开大学、清华大学从事博士后研究工作。目前研究兴趣包括量子人工智能、杨-Baxter方程相关数学物理、拓扑量子计算等。相关学术成果发表在Physical Review Letters等物理杂志。