在這篇論文中，我們主要透過機器學習以及一些數值計算來建立一套嶄新的估計光學壓縮態的方法。當我們使用光學壓縮態去進行重力波偵測或者是量子資訊等應用時，診斷此量子態的強健性有其必要性。基於此，量子態斷層掃描 (QST) 是一個必要被充份研究了解的數值工具。在連續變數的 QST 領域中，我們首次的提出使用監督式機器學習模型來完成量子態重建的工作。這個模型在訓練的過程被要求盡可能提高演算法的保真度，在推估量子態時降低演算法本身推論時會產生的損失。這個經過良好訓練的神經網路模型能夠精準且快速的重建量子態，它能評估環境造成量子態多少程度的劣化。我們訓練出來的模型可以讀取較少且不用固定相位的資料，這可以讓實驗學家簡化測量壓縮態的流程並提升取數據的效能。並且，我們提出了參數估計的機器學習模型，它具有更加的輕巧的特點。這樣讓我們易於將這個系統安裝在實驗室的環境中。透過高速的密度
矩陣還有維格納函數重建以及參數估計，這讓我們更為接近即時量子態斷層掃描。並且，有效率的 QST 也讓我們成功的重建相空間的動力學。這個研究也讓我們了解到未來可能如何推廣到更廣泛之量子態重建甚至量子過程的重建，以及其可能的障礙在那。我們也將探討這些問題並指出未來可能的研究方向。

In this thesis, we mainly use machine learning and some numerical calculations to establish a new method for estimating the optical squeezed state. When we use optical squeezed states for gravitational wave detection or quantum information applications, the ability to diagnose quantum states is important. Based on this, quantum state tomography (QST) is a numerical tool that must be well studied and understood. In the field of QST for continuous variables, we propose for the first time the use of a supervised machine learning model to complete the quantum state reconstruction. This model is required to improve the fidelity of the algorithm during the training process, and when estimating the quantum state reduce the loss that the algorithm itself will infer. This well-trained neural network can accurately and quickly reconstruct the quantum state, and it can evaluate how much
the quantum state is degraded by the environment. The model we trained can read less and no fixed-phase data, which allows experimentalists to simplify the process of measuring the squeezed state and improve the efficiency of data acquisition. Furthermore, we propose a machine learning model for parameter estimation, which is more lightweight. This allows us to easily install this system in a laboratory environment. Through high-speed density matrix and Wigner function reconstruction and parameter estimation, this brings us closer to real-time quantum state tomography. Moreover, the efficient QST also allows us to successfully reconstruct the dynamics of the phase space. This research also allows us to understand how the reconstruction of non-Gaussian quantum states and even quantum processes may be generalized in the future, and the possible obstacles there. We will
also discuss these issues and point out possible future research directions.

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