用朗之万动力学改进量子自然梯度，提升优化效率
Application of Langevin Dynamics to Advance the Quantum Natural Gradient Optimization Algorithm
- 引入朗之万方程与量子自然梯度的随机力，构造带动量的新算法
- 在强自旋玻璃模型中收敛速度和最终性能优于基础QNG
- 适合需要突破局部极小值的变分量子电路优化任务
近期提出了用于变分量子线路优化的量子自然梯度（QNG）算法。本文通过引入带有QNG随机力的朗之万方程，证明其离散解可形式化为一种广义算法，称为Momentum-QNG。类似SGD+动量、RMSProp+动量和Adam等带动量的优化器，Momentum-QNG能更有效地逃离变分参数空间中的局部极小值和平台区，因此相比基础QNG表现出更优性能。本文将Momentum-QNG与基础QNG、Adam及动量优化器进行基准测试，并研究其收敛行为。在所考察的基准问题中，最强自旋玻璃态下的量子谢林顿-柯克帕特里克模型取得最佳结果。开源代码已公开于https://github.com/borbysh/Momentum-QNG。
原文摘要 · Abstract (English)
A Quantum Natural Gradient (QNG) algorithm for optimization of variational quantum circuits has been proposed recently. In this study, we employ the Langevin equation with a QNG stochastic force to demonstrate that its discrete-time solution gives a generalized form of the above-specified algorithm, which we call Momentum-QNG. Similar to other optimization algorithms with the momentum term, such as the Stochastic Gradient Descent with momentum, RMSProp with momentum and Adam, Momentum-QNG is more effective to escape local minima and plateaus in the variational parameter space and, therefore, demonstrates an improved performance compared to the basic QNG. In this paper we benchmark Momentum-QNG together with the basic QNG, Adam and Momentum optimizers and explore its convergence behaviour. Among the benchmarking problems studied, the best result is obtained for the quantum Sherrington-Kirkpatrick model in the strong spin glass regime. Our open-source code is available at https://github.com/borbysh/Momentum-QNG
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