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

Liang，Jin Min1; Wei，Shi Jie2,3; Fei，Shao Ming1,4

2022-05-01

10.1007/s11433-021-1844-7

Science China-Physics Mechanics & Astronomy   影响因子和分区

1674-7348

1869-1927

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.

nonequilibrium steady state quantum gradient descent algorithm quantum open system quantum simulation

SCI ; EI

英语

通讯

National Natural Science Foundation of China[12075159,12171011,12006015] ; Beijing Natral Science Foundation[Z190005] ; Shenzhen Institite for Quantum Science and Engineering, Southern University of Science and Technology[SIQSE202001]

Physics

Physics, Multidisciplinary

WOS:000778209700002

SCIENCE PRESS

20221311874343

Ground state ; Hamiltonians ; Ising model ; Linear systems ; Machine learning ; Matrix algebra ; Optimization ; Quantum chemistry ; Quantum optics

Light/Optics:741.1 ; Physical Chemistry:801.4 ; Algebra:921.1 ; Optimization Techniques:921.5 ; Numerical Methods:921.6 ; Statistical Methods:922 ; Quantum Theory; Quantum Mechanics:931.4 ; Systems Science:961

2-s2.0-85127299535

Scopus

1.School of Mathematical Sciences,Capital Normal University,Beijing,100048,China
2.Beijing Academy of Quantum Information Sciences,Beijing,100193,China
3.State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics,Tsinghua University,Beijing,100084,China
4.Shenzhen Institute for Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen,518055,China

Liang，Jin Min,Wei，Shi Jie,Fei，Shao Ming. Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems[J]. Science China-Physics Mechanics & Astronomy,2022,65(5).

Liang，Jin Min,Wei，Shi Jie,&Fei，Shao Ming.(2022).Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems.Science China-Physics Mechanics & Astronomy,65(5).

Liang，Jin Min,et al."Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems".Science China-Physics Mechanics & Astronomy 65.5(2022).