具有量子涨落的二元感知器的师生学习
Teacher-student learning for a binary perceptron with quantum fluctuations
摘要：
我们使用复制方法分析了具有量子涨落的二元感知器的泛化性能。指数数量的局部最小值占主导地位的二进制感知器的能量景观。局部搜索算法往往不能识别二进制感知器的基态。在这项研究中，我们考虑了师生学习方法，并计算了量子涨落的二进制感知器的泛化误差。由于量子涨落，我们可以有效地找到鲁棒的解决方案，具有更好的泛化性能比经典模型。我们通过量子蒙特卡罗模拟验证了我们的理论结果。我们采用了副本对称性（RS）假设和静态近似。RS解与我们的模拟结果是一致的，除了相对较低的横向场强度和高的方向图比。这些偏差是由于违反遍历性和静态近似而引起的。考虑到RS解和数值结果之间的偏差，量子涨落对泛化性能的增强是成立的。
英文摘要：
We analysed the generalisation performance of a binary perceptron with quantum fluctuations using the replica method. An exponential number of local minima dominate the energy landscape of the binary perceptron. Local search algorithms often fail to identify the ground state of a binary perceptron. In this study, we considered the teacher-student learning method and computed the generalisation error of a binary perceptron with quantum fluctuations. Due to the quantum fluctuations, we can efficiently find robust solutions that have better generalisation performance than the classical model. We validated our theoretical results through quantum Monte Carlo simulations. We adopted the replica symmetry (RS) ansatz assumption and static approximation. The RS solutions are consistent with our simulation results, except for the relatively low strength of the transverse field and high pattern ratio. These deviations are caused by the violation of ergodicity and static approximation. After accounting for the deviation between the RS solutions and numerical results, the enhancement of generalisation performance with quantum fluctuations holds.
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