講演情報
[15a-K309-7]Gradient-free, Sequential Optimization in the Variational Quantum Algorithm for solving the Poisson Equation
〇(M2)Pei LUO1, H. LANG1, K. Hirohata2, T. Sato1,3,4 (1.NEM, Tokyo Univ., 2.Toshiba Co., 3.Photon Sci. Center, 4.Inst. of Photon Sci.)
キーワード：
Variational Quantum Algorithm、Sequential Optimization、Gradient-free
Rapidly and accurately solving large-scale partial differential equations that describephysical phenomena is an important engineering challenge, but solving large scale problemswithin a reasonable computational time is often difficult even with the latest supercomputers.To overcome the inherent limit of classical computing, a gradient-based variational quantumalgorithm (VQA) for solving the Poisson equation is presented by a recent study that can beimplemented in noisy intermediate-scale quantum devices. However, gradient-basedoptimization inevitably suffers from the vanishing gradient problem (i.e. Barren Plateau).
In our research, we implement one of the gradient-free methods -- the sequential optimization method -- to improve the robustness and scalability of the VQA in solving the Poisson equation. In this method, the cost function is given by a simple sum of trigonometric functions with certain periods and hence can be minimized by using a classical computer. By repeatedly performing this procedure, we optimize the parameterized quantum circuits so that the cost function reaches its minimum. We perform numerical experiments on the Noise Intermediate-scale Quantum Computer confirming its fast convergence, robustness against statistical errors and hyperparameter-free performance.
In our research, we implement one of the gradient-free methods -- the sequential optimization method -- to improve the robustness and scalability of the VQA in solving the Poisson equation. In this method, the cost function is given by a simple sum of trigonometric functions with certain periods and hence can be minimized by using a classical computer. By repeatedly performing this procedure, we optimize the parameterized quantum circuits so that the cost function reaches its minimum. We perform numerical experiments on the Noise Intermediate-scale Quantum Computer confirming its fast convergence, robustness against statistical errors and hyperparameter-free performance.