Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems

作     者：Jin-Min Liang Shi-Jie Wei Shao-Ming Fei Jin-Min Liang;Shi-Jie Wei;Shao-Ming Fei

作者机构：School of Mathematical SciencesCapital Normal UniversityBeijing J00048China Beijing Academy of Quantum Information SciencesBeijing 100193China State Key Laboratory of Low-Dimensional Quantum Physics and Department of PhysicsTsinghua UniversityBeijing 100084China Shenzhen Institute for Quantum Science and EngineeringSouthern University of Science and TechnologyShenzhen 518055China 

出 版 物：《Science China(Physics,Mechanics & Astronomy)》 (中国科学：物理学、力学、天文学（英文版）)

年 卷 期：2022年第65卷第5期

页      面：21-33页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 0703[理学-化学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 081201[工学-计算机系统结构] 0812[工学-计算机科学与技术（可授工学、理学学位）] 0702[理学-物理学] 

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.12075159,12171044,and 12005015) Beijing Natural Science Foundation(Grant No.Z190005) Academy for Multidisciplinary Studies,Capital Normal University,Academician Innovation Platform of Hainan Province,and Shenzhen Institute for Quantum Science and Engineering,Southern University of Science and Technology(Grant No.SIQSE202001)。 

主　　题：quantum simulation quantum gradient descent algorithm nonequilibrium steady state quantum open system 

摘      要：The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks,which is an optimization algorithm for finding a local minimum of an objective function.The quantum versions of gradient descent have been investigated and implemented in calculating molecular ground states and optimizing polynomial functions.Based on the quantum gradient descent algorithm and Choi-Jamiolkowski isomorphism,we present approaches to simulate efficiently the nonequilibrium steady states of Markovian open quantum many-body systems.Two strategies are developed to evaluate the expectation values of physical observables on the nonequilibrium steady states.Moreover,we adapt the quantum gradient descent algorithm to solve linear algebra problems including linear systems of equations and matrix-vector multiplications,by converting these algebraic problems into the simulations of closed quantum systems with well-defined Hamiltonians.Detailed examples are given to test numerically the effectiveness of the proposed algorithms for the dissipative quantum transverse Ising models and matrix-vector multiplications.