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

Science China(Physics,Mechanics & Astronomy) 2022年第5期65卷 21-33页

作者： Jin-Min Liang Shi-Jie Wei Shao-Ming Fei School of Mathematical Sciences Capital Normal UniversityBeijing J00048China Beijing Academy of quantum Information Sciences Beijing 100193China State Key Laboratory of Low-Dimensional quantum Physics and Department of Physics Tsinghua UniversityBeijing 100084China Shenzhen Institute for quantum Science and Engineering Southern University of Science and TechnologyShenzhen 518055China

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.

关键词： quantum simulation quantum gradient descent algorithm nonequilibrium steady state quantum open system

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quantum interferometric power and non-Markovianity in the decoherence channels

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Chinese Physics B 2023年第8期32卷 156-160页

作者：熊少杰孙哲王晓光 Zhejiang Institute of Modern Physics and Department of Physics Zhejiang UniversityHangzhou 310027China Department of Physics Hangzhou Normal UniversityHangzhou 310036China Key Laboratory of Optical Field Manipulation of Zhejiang Province and Department of Physics Zhejiang Sci-Tech UniversityHangzhou 310018China

In quantum open systems,non-Markovianity is an important phenomenon that allows a backflow of information from the environment to the system.In this work,we investigate the non-Markovianity problems in two different types of channels,where the system-environment interactions are treated with and without the rotating-wave approximation(RWA).We employ the quantum interferometric power(QIP)to quantify the non-Markovian dynamics,which is the minimal quantum Fisher information obtained by the local unitary evolution in a bipartite system.By the hierarchy equation method,we calculate the dynamical evolution of the QIP in the non-RWA case.The results show that the dynamical behavior under the non-RWA is significantly different from that under the RWA in both weak and strong coupling.Moreover,in the non-RWA case,we also find the nonmonotonic behavior of the non-Markovianity measure with the variation of coupling strength,which is caused by the competition between the rotating-wave terms and the counterrotating-wave terms.As a result,we highlight the importance of the counterrotating-wave terms for the influence of non-Markovianity.

关键词： quantum open system auantum non-Markovianity auantum interferometric power

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