报告时间：10月22日周三下午15:30-16:30
报告地点：数学楼401报告厅
报告人：马楚雯
主持人：朱升峰
报告摘要：
We propose a class of quantum algorithms for the discretization of partial differential equations (PDEs). Specifically, we employ the Schrödingerization framework, which transforms general linear PDEs into Schrödinger-type equations in an augmented dimension. A systematic theoretical and numerical investigation is carried out on the problem of recovering the original variables from the Schrödingerized equation, even when the corresponding evolution operator exhibits unstable modes. The developed recovery scheme further offers a numerically stable and efficient approach to tackle ill-posed problems. In addition, for the Poisson equation, we integrate the BPX preconditioner into our framework to construct a preconditioned quantum algorithm that achieves optimal query complexity with respect to the accuracy parameter ε, i.e. O ̃(log(1/ε)).
报告人简介：
马楚雯，华东师范大学青年研究员。2022年博士毕业于中国科学院数学与系统科学研究院，获中国科学院百篇优秀博士论文奖。博士毕业后在上海交通大学从事博士后研究工作，入选中国博士后创新人才支持计划、上海“超级博士后”激励计划等人才项目。主要研究方向为偏微分方程的量子算法及非贴体网格有限元方法。科研成果发表在 SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Journal of Computational Physics 等国际知名学术期刊上。