标题： 多光子量子模拟广义Hopfield记忆模型 显示英文标题

标题： Multiphoton quantum simulation of the generalized Hopfield memory model

摘要： 在本工作中，我们引入、发展并研究了多光子量子干涉（新兴光子量子技术的核心元素）与经典神经网络的 Hopfield 类哈密顿量之间的联系，后者是人工智能系统中关联记忆和机器学习的典型模型。 具体来说，我们证明了一个由 Nph 个不可分辨光子在 M 个场模式叠加组成的系统，结合一个受控的 M 元二值相移器阵列和一个线性光学干涉仪，其输出光子统计可以用 M 个类似于伊辛模型的神经元（取值 ±1）的 p 体 Hopfield 哈密顿量来描述，其中 p = 2Nph。 我们详细研究了通过这种方法获得的广义四体 Hopfield 模型，并表明随着存储记忆数量的增加，它实现了从记忆检索到记忆黑屏状态（即自旋玻璃态）的转变。 这种映射为利用高效的光子量子模拟器实现和研究无序且复杂的经典系统提供了新的途径，同时也使光子系统的结构化特性能够用经典的自旋哈密顿量来描述。 显示英文摘要

摘要： In the present work, we introduce, develop, and investigate a connection between multiphoton quantum interference, a core element of emerging photonic quantum technologies, and Hopfieldlike Hamiltonians of classical neural networks, the paradigmatic models for associative memory and machine learning in systems of artificial intelligence. Specifically, we show that combining a system composed of Nph indistinguishable photons in superposition over M field modes, a controlled array of M binary phase-shifters, and a linear-optical interferometer, yields output photon statistics described by means of a p-body Hopfield Hamiltonian of M Ising-like neurons +-1, with p = 2Nph. We investigate in detail the generalized 4-body Hopfield model obtained through this procedure and show that it realizes a transition from a memory retrieval to a memory black-out regime, i.e. a spin-glass phase, as the amount of stored memory increases. The mapping enables novel routes to the realization and investigation of disordered and complex classical systems via efficient photonic quantum simulators, as well as the description of aspects of structured photonic systems in terms of classical spin Hamiltonians.