Predict the nonclassicality of pure dephasing using deep learning

Kuan-lun Lai^1*

¹工程科學系, 成功大學, 台中, Taiwan

* Presenter:Kuan-lun Lai, email:n96101294@gs.ncku.edu.tw

One of the central problem in quantum theory is the quantumness of the system at non zero temperature,it is imporant to explore the process of quantum dissipation. With the help of Hamiltonian Ensemble(HE),we can describe the interaction between the system and environment at classical way, and with the help of Canonical Hamiltonian Ensemble Representation(CHER), we can analysis the system in frequency domain, which provides us as an alternative way to clearly observe the quantum properties.
To dicuss the dissipation process of the system composed of qubit pair interacting with the environment, there are three one-dimensional marginal distributions of CHER characterized by the mathmatical tool lie algebra. The main problem is how to obtain the two-dimensional joint distribution that can describe the dissipation of the whole quantum systyem by only three marginal distributions. It seems to be a NP hard promblem at numerical way, so we came up with a new idea of the deep learning method to solve the problem, in other words, we constructed a model that can predict the joint distribution by feeding the marginal distributions.
Deep learning is a concept used of a neural networks, each layer is composed of multiple neurons. With the multi-layer structure, the neurons of each layer are connected to the previous and the next layer, and are classified by the activation funciton. Loss function controls the enhancement of weight replacement, and find the best convergent solution by updating the weights. Because it can map data to high-dimensional space and classify it, so it is often used to solve high-complexity problems; Therfore, we use the deep learning to predict the joint distribution that determines the quantum dissipation of the system.
The main design architecture of the model is a decorder consist of deconvolution blocks and identity blocks, which is ResNet based resdiual architecture. The input of the model are three marginal distributions , and the output is the joint distribution. With the prediction of the model, we can observe the non classicalities of the system by computing the negative volume of the joint distribution.

Keywords: Joint distribution, Deconvolution, Deep learning, Pure dephasing