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<p>We investigate the utility of deep neural networks (DNNs) in estimating the Jaynes-Cummings Hamiltonian’s parameters from its energy spectrum alone. We assume that the energy spectrum may or may not be corrupted by noise. In the noiseless case, we use the vanilla DNN (vDNN) model and find that the error tends to decrease as the number of input nodes increases. The best-achieved root mean squared error is of the order of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_2611_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(10^{-5}\)</EquationSource> </InlineEquation>. The vDNN model, trained on noiseless data, demonstrates resilience to Gaussian noise, but only up to a certain extent. To cope with this issue, we employ a denoising U-Net and combine it with the vDNN to find that the new model reduces the error by up to about 77%. Our study exemplifies that deep learning models can help estimate the parameters of a Hamiltonian even when the data is corrupted by noise.</p>

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Supervised learning of the Jaynes–Cummings Hamiltonian

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月29日

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  • Woohyun Choi,
  • Chang-Woo Lee,
  • Changsuk Noh

摘要

We investigate the utility of deep neural networks (DNNs) in estimating the Jaynes-Cummings Hamiltonian’s parameters from its energy spectrum alone. We assume that the energy spectrum may or may not be corrupted by noise. In the noiseless case, we use the vanilla DNN (vDNN) model and find that the error tends to decrease as the number of input nodes increases. The best-achieved root mean squared error is of the order of \(10^{-5}\) . The vDNN model, trained on noiseless data, demonstrates resilience to Gaussian noise, but only up to a certain extent. To cope with this issue, we employ a denoising U-Net and combine it with the vDNN to find that the new model reduces the error by up to about 77%. Our study exemplifies that deep learning models can help estimate the parameters of a Hamiltonian even when the data is corrupted by noise.