報告題目：Conservative High-Order Numerical Schemes for Quantum Computation
報 告 人：李祥貴 教授
所在單位：北京信息科技大學
報告時間：2022年10月26日 9:00-10:30
報告地點：騰訊會議：201-184-592
校内聯系人：闫偉 wyanmath01@sina.com
報告摘要：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.
報告人簡介：李祥貴現為北京信息科技大學理學院教授，博士生導師。曾多次到新加坡、香港、澳大利亞，巴西等地的大學和研究機構開展學術交流與科研合作。已發表論文60餘篇，其中被SCI、EI收錄50餘篇；三次獲省部級教學、科研成果獎；專利授權3項，出版專著2本 ；主持完成國家自然科學基金4項，國防基礎科研科學挑戰計劃等項目10餘項。曾任北京信息科技大學黨委研工部部長、理學院院長。現為全國計算數學學會理事、仿真算法專委會委員。
