Optimal storage capacity of quantum Hopfield neural networks
Optimal storage capacity of quantum Hopfield neural networks
复制标题
量子 Hopfield 神经网络的最佳存储容量
DOI：
10.1103/physrevresearch.5.023074
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发表时间：
2022
影响因子：
4.2
通讯作者：
M. Muller
中科院分区：
文献类型：
--
作者：
Lukas Bodeker;Eliana Fiorelli;M. Muller
量子神经网络构成了量子机器学习这一新兴领域的支柱之一。在这里，已经提出了实现联想记忆的经典网络的量子概括——能够从损坏的初始状态检索模式或记忆。分析具有大量模式的量子联想存储器，并确定量子网络可以可靠存储的最大模式数量，即它们的存储容量，是一个具有挑战性的开放问题。在这项工作中，我们提出并探索了一种评估量子神经网络模型最大存储容量的通用方法。通过在经典领域推广所谓的加德纳方法，我们利用经典自旋玻璃理论来推导具有淬灭模式变量的量子网络的最佳存储容量。例如，我们将我们的方法应用于开放系统量子联想存储器，该存储器由相互作用的自旋 1/2 粒子形成，实现耦合的人工神经元。该系统经历了马尔可夫时间演化，这是由与相干量子动力学竞争的耗散检索动力学引起的。我们绘制了非平衡相图并研究了温度和哈密顿动力学对存储容量的影响。我们的方法为系统表征量子联想存储器的存储容量开辟了一条途径。
Quantum neural networks form one pillar of the emergent field of quantum machine learning. Here, quantum generalisations of classical networks realizing associative memories - capable of retrieving patterns, or memories, from corrupted initial states - have been proposed. It is a challenging open problem to analyze quantum associative memories with an extensive number of patterns, and to determine the maximal number of patterns the quantum networks can reliably store, i.e. their storage capacity. In this work, we propose and explore a general method for evaluating the maximal storage capacity of quantum neural network models. By generalizing what is known as Gardner's approach in the classical realm, we exploit the theory of classical spin glasses for deriving the optimal storage capacity of quantum networks with quenched pattern variables. As an example, we apply our method to an open-system quantum associative memory formed of interacting spin-1/2 particles realizing coupled artificial neurons. The system undergoes a Markovian time evolution resulting from a dissipative retrieval dynamics that competes with a coherent quantum dynamics. We map out the non-equilibrium phase diagram and study the effect of temperature and Hamiltonian dynamics on the storage capacity. Our method opens an avenue for a systematic characterization of the storage capacity of quantum associative memories.