报告题目：Conservative High-Order Numerical Schemes for Quantum Computation

报 告 人：李祥贵 教授

所在单位：北京信息科技大学

报告时间：2022年10月26日 9:00-10:30

报告地点：腾讯会议：201-184-592

校内联系人：闫伟 wyanmath01@sina.com

报告摘要：In this talk, based on the operator-compensation method, a semi-discrete scheme which has any even order accuracy in space with charge and energy conservation is proposed to solve the nonlinear Dirac equation (NLDE) . Then this semi-discrete scheme can be discretized in time by the second-order accuracy time-midpoint (or Crank-Nicolson) method or the time-splitting method, we therefore obtain two kinds of full discretized numerical methods. For the scheme derived the time-midpoint method, it can be proved to conserve charge and energy in the discrete level, but the other one, it can only be proved to satisfy the charge conservation. These properties of the schemes with any even order accuracy are proved theoretically by a rigorous way. Some numerical experiments for 1D and/or 2D NLDE are given to test the accuracy order and verify the stability and conservation laws for our schemes. In addition, the binary and ternary collisions for 1D NLDE and the dynamics of 2D NLDE are also discussed. This numerical method can also be extended to solve the nonlinear Schrödinger equation. Some numerical results on BEC are given.

报告人简介：李祥贵现为北京信息科技大学理学院教授，博士生导师。曾多次到新加坡、香港、澳大利亚，巴西等地的大学和研究机构开展学术交流与科研合作。已发表论文60余篇，其中被SCI、EI收录50余篇；三次获省部级教学、科研成果奖；专利授权3项，出版专著2本 ；主持完成国家自然科学基金4项，国防基础科研科学挑战计划等项目10余项。曾任北京信息科技大学党委研工部部长、理学院经理。现为全国计算数学学会理事、仿真算法专委会委员。