如何界定古典力學與量子力學之間的邊界一直是具有發展潛力的，鑒於量子系統在非零溫情況下脆弱的量子特性，探討量子特性耗散的過程成為重要的研究；有了Hamiltonian Ensemble (HE) 的幫助，讓我們可以用古典的方式模擬並描述量子耗散的演化過程；此外藉由Canonical Hamiltonian Ensemble Representation (CHER)，可以讓我們將時域演化過程轉換成頻域做分析，並模擬出具有量子特性的分布。

隨著電腦科學以及硬體技術的進步，深度學習領域也迎來更多元的發展性，除了用類神經元的概念解決基礎的分類問題，如Deep Neuron Networks (DNN)，也能針對圖片做影像辨識及電腦視覺，利用褶積原理將特徵提取並使用神經元做分類或回歸，如Convolution Neuron Networks (CNN)，此外具有生成圖片能力的生成對抗網路模型Generative adversarial Networks (GAN) 也常用在重建影像及提升影像解析度。

討論由兩個量子與環境互動所組成的系統之耗散過程，由初始環境給定的參數和李代數所推廣出的CHER有三個一維邊際分布可以用來描述其耗散過程的特性，然而要得到由兩個獨立李代數規範的向量所展開的二維空間之機率密度分布非常困難，幾乎無法得到有效的詳解，因此如何由這三個一維邊際分布得到描述整體耗散過程的二維的機率密度分布是我們所要解決的主要問題。

深度學習為使用類神經網路架構為基礎的概念，每層有多個神經元組成，藉由多層的結構將每一層的神經元與上一層及下層連結，並透過Activation function做分類，藉由Loss function來衡量權重更替的程度，並透過更新權重的方式來找到收斂的最佳解，由於其可以藉由將資料映射至高維空間並做分類，因此常用來解決非線性以及高複雜度的問題；因此我們藉由深度學習的模型預測決定量子耗散過程的機率密度。

模型的主要設計架構為一個使用反褶積的解碼器 (Decoder) ，包含以三個邊際分布的離散數列當作模型的輸入以及二維機率密度的場域作為模型的輸出；其中模型由一連串的基本單元和反褶積單元所組成，並透過於類似ResNet殘差網路的架構避免由於層數的增加所造成的梯度消失問題。

How to define the boundary between classical and quantum mechanics has always been a potential development in the future. In view of the fragile quantum properties of quantum systems at non-zero temperature, it has become an important research to explore the process of quantum dissipation; With the help of Hamiltonian Ensemble (HE), we can simulate and describe the evolution process of quantum dissipation with classical method; in addition, with Canonical Hamiltonian Ensemble Representation (CHER), we can convert the time domain evolution process into frequency domain for analysis, and simulate the probability density distribution which behave some quantum properties.

With the advancement of computer science and hardware technology, deep learning has also ushered in more multi-dimensional development. In addition to solving basic classification problems with the concept of neuron network, such as Deep Neuron Networks (DNN), it can also deal with image processing, image recognition and computer vision, using the principle of convolution to extract features and using neurons for classification or regression, such as Convolution Neuron Networks (CNN), and Generative adversarial Networks (GAN), which show the potential ability to generate images, are also commonly used to rebuild images and improve image resolution.

To discuss the dissipation process of the system composed of qubit pair interacting with the environment, there are three one-dimensional marginal distributions of the CHER promoted by the parameters of the initial environment and the Lie algebra that can be used to characterize the dissipation process. Therefore, the main problem to be solved is that how to obtain the two-dimensional (joint) probability density distribution describing the overall dissipation process from these three one-dimensional marginal distributions.

Deep learning is a concept based on the use of a neural network architecture. 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 function. 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 nonlinear and high-complexity problems; Therefore, we use the deep learning model to predict the joint probability density distribution that determines the quantum dissipation.

The main design architecture of the model is a decoder using deconvolution, which consists of three discrete series of marginal distributions as model inputs and two-dimensional field of probability density as model outputs; the model consists of a series of identity blocks and deconvolution blocks, and uses ResNet-base residual architecture to avoid the gradient vanish which caused by the increase of layers.

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