Model of the electron spin in stochastic physics

Steven M. Moore, J. A. Ramírez

Luis de la Peña, A. Jáuregui

A. Jáuregui, Luis de la Peña

Feng Li, Zhuo Wang, Wenfeng Fan +4 more

Abstract Stochastic magnetic field noise has a non‐negligible negative impact on the performance of quantum precision measurement instruments such as spin‐exchange relaxation‐free (SERF) co‐magnetometer in terms of sensitivity and stability. Conventional magnetic field error analysis and suppression methods are not applicable to stochastic magnetic field noise. In this paper, a stochastic model of the SERF co‐magnetometer is proposed to analyze the mechanism of stochastic magnetic field noise. The mean and covariance propagation model of the SERF co‐magnetometer is given based on the stochasticity model and statistical principles. The analysis of simulation experiments reveals that reducing the longitudinal electron spin polarization can somewhat reduce the standard deviation of the system output caused by stochastic magnetic field noise. And the atomic ensembles are most resistant to stochastic magnetic field noise when the electron spin polarization strongly couples with the nuclear spin polarization. Finally, the experiments verified the above conclusions. In conclusion, this paper provides theoretical and experimental support for analyzing and suppressing the effect of stochastic magnetic field noise on the SERF co‐magnetometer, which is of great significance for improving the sensitivity and stability of the measurement.

Tong Dou, Shiro Kumara, Josh Burns +6 more

The computational demands of deep learning motivate the investigation of alternative approaches to computation. One alternative is physical neural networks~(PNNs), in which learning and inference are performed directly via physical processes. Stochastic PNNs arise when the underlying neurons are realized by the dynamics of a stochastic activation switch. Here we propose novel electronic and photonic stochastic neurons. The electronic realization is implemented by single-electron tunneling through a quantum dot. The photonic realization is implemented via a single-photon source driving one of two modes coupled via a controllable beam-splitter-like interaction. In the electronic case, the charge state of the quantum dot forms the basis for the stochastic neuron, whereas in the photonic case the occupation of the undriven mode serves as the basis for the stochastic neuron. Training of stochastic PNNs is performed with models of stochastic neurons, as well as with coherently-driven, single-photon detector stochastic neurons previously introduced. Several training strategies for MNIST handwritten digit classification have been investigated using single-hidden-layer stochastic PNNs, including varying the number of trials in each layer to control forward pass stochasticity and employing either true probability or empirical outputs in the backward pass to evaluate their influence on gradient estimation. We show that when empirical outputs are used in the backward pass, the network achieves more than 97\% test accuracy with few trials per layer. Despite the simplicity of the model architecture, high test accuracy is maintained in the presence of a high degree of noise and model uncertainty. The results demonstrate the potential of embracing stochastic PNNs for deep learning.

Konstantinos P. Prousalis, Nikolaos L. Tsitsas, Nikos Konofaos

Accurately modeling and simulating the single-electron spin qubit model of Loss–DiVincenzo within a semiconductor quantum dot heterostructure remains a significant challenge due to the incomplete understanding of the underlying noise processes and mechanisms. This work employs the quantum version of the Langevin equation framework, rooted in the spin-bath model theory, to systematically reframe and analyze all recognized physical noise effects. By constructing the model as a stochastic differential equation, it integrates quantum noise dynamics holistically rather than isolating specific noise effects. The primary contributors to qubit relaxation and decoherence are identified as direct spin flips, anharmonic oscillations, and random local fields. The dynamics of a single-spin qubit are presented within a semiconductor quantum dot, deliberately excluding external multi-qubit exchange interactions, which are assumed to be controlled or mitigated. The goal is to provide a detailed simulation analysis that combines various studies and bridges theory and experiments, offering a closer approximation to realistic scenarios.