标题： 离散现代霍普菲尔德网络在开放量子系统中的分析 显示英文标题

标题： Analysis of Discrete Modern Hopfield Networks in Open Quantum System

摘要： 现代霍普菲尔德网络，由Krotov和Hopfield提出，是对霍普菲尔德网络的数学推广，霍普菲尔德网络是利用高阶相互作用的基本关联记忆模型。 本研究引入了一个离散现代霍普菲尔德网络的开放量子模型，该模型推广了开放量子霍普菲尔德网络。 我们的模型通过横向场将耗散量子自旋系统（由量子主方程控制）与经典跳跃项和额外的量子效应结合起来。 我们分析研究了稳定固定点的行为，并数值确定了相图。 结果表明，其行为与开放量子霍普菲尔德网络有定性上的不同，显示出铁磁相和极限环相具有额外的稳定固定点。 显示英文摘要

摘要： The modern Hopfield network, proposed by Krotov and Hopfield, is a mathematical generalization of the Hopfield network, which is a basic model of associative memory that employs higher-order interactions. This study introduces an open quantum model for discrete modern Hopfield networks that generalizes the open quantum Hopfield network. Our model integrates dissipative quantum spin systems, governed by quantum master equations, with classical hopping terms and additional quantum effects through a transverse field. We analytically examined the behavior of the stable fixed points and numerically determined the phase diagram. The results demonstrated qualitatively distinct behaviors from the open quantum Hopfield network, showing that the ferromagnetic and limit cycle phases have additional stable fixed points.