论文标题
量子干扰：量子机械感知的临界特性
Quantum Jamming: Critical Properties of a Quantum Mechanical Perceptron
论文作者
论文摘要
在这封信中，我们分析了感知器模型的量子动力学：粒子在$ n $维的球体上被限制为$ n \ to \ infty $，并受到一组随机放置的硬墙电位。该模型具有多种应用，从学习方案到对欧几里得空间中无限维硬球的动态的有效描述。我们发现，使用量子动力学的干扰过渡显示出与经典案例不同的关键指数。我们还发现，与典型的量子临界点不同，量子干扰过渡不限于零温度轴，并且仅在$ t = \ infty $下恢复了经典结果。我们的发现对超低温度和量子机学习算法的研究对眼镜理论具有影响。
In this Letter, we analyze the quantum dynamics of the perceptron model: a particle is constrained on a $N$-dimensional sphere, with $N\to \infty$, and subjected to a set of randomly placed hard-wall potentials. This model has several applications, ranging from learning protocols to the effective description of the dynamics of an ensemble of infinite-dimensional hard spheres in Euclidean space. We find that the jamming transition with quantum dynamics shows critical exponents different from the classical case. We also find that the quantum jamming transition, unlike the typical quantum critical points, is not confined to the zero-temperature axis, and the classical results are recovered only at $T=\infty$. Our findings have implications for the theory of glasses at ultra-low temperatures and for the study of quantum machine-learning algorithms.
