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We develop and implement two realizations of quantum graph neural networks (QGNN), applied to the task of particle interaction simulation. The first QGNN is a speculative quantum-classical hybrid learning model that relies on the ability to directly utilize superposition states as classical information to propagate information between particles. The second is an implementable quantum-classical hybrid learning model that propagates particle information directly through the parameters of RX rotation gates. A classical graph neural network (CGNN) is also trained in the same task. Both the Speculative QGNN and CGNN act as controls against the Implementable QGNN. Comparison between classical and quantum models is based on the loss value and accuracy of each model. Overall, each model had a high learning efficiency, in which the loss value rapidly approached zero during training; however, each model was moderately inaccurate. Comparing performances, our results show that the Implementable QGNN has a potential advantage over the CGNN. Additionally, we show that a slight alteration in hyperparameters in the CGNN notably improves accuracy, suggesting that further fine tuning could mitigate the issue of moderate inaccuracy in each model. [ABSTRACT FROM AUTHOR]

Abstract: We analyze the question of separability in a continuously measured quantum system as it approaches the classical limit. We show that the record of position measurements can approach the [...]

A detector undergoing uniform acceleration a in a vacuum field responds as though it were immersed in thermal radiation of temperature T = [??]a/2[pi]kc. An intuitive derivation of this result is given for a scalar field in one spatial dimension. The approach is extended to the case where the field detected by the accelerated observer is a spin 1/2 Dirac field.

We consider the propagation of massive-particle de Broglie waves in a static, isotropic metric in general relativity. We demonstrate the existence of an index of refraction that governs the waves and that has all the properties of a classical index of refraction. We confirm our interpretation with a Wentzel-Kramers-Brillouin solution of the general-relativistic Klein-Gordon equation. Finally, we make some observations on the significance of the optical action. [DOI: 10.1119/1.1389281]

The optical-mechanical analogy allows for a common description of the motion of particles in mechanics and for light in geometrical optics. In a recent series of articles in this journal, it has been shown that the optical-mechanical analogy can be extended to general relativity for the case of static metrics expressible in isotropic coordinates. In this paper, we extend the optical-mechanical analogy in general relativity to the case of stationary metrics. A variational principle for the trajectories of both photons and particles is derived which takes the form of Fermat's principle or the principle of Maupertuis. When the (suitably defined) spatial portion of the metric is written as or restricted to an isotropic form, exact equations of motion for both massless and massive particles are obtained in the form of Newtonian mechanics, describing objects moving in a medium with a spatially varying index of refraction. Such restrictions of the metric commonly occur, for example, when orbital motion is considered in a plane perpendicular to the axis of rotation of a rotating black hole or spacetime. The Newtonian form of the equations of geodesic motion are illustrated by applications to a uniformly rotating reference system and a rotating black hole (the Kerr metric).