量子計算為運用量子力學原理，如量子疊加及量子糾纏，之計算方法。量子電腦之基本元件為作爲訊息單位的量子位元，以及可在一個或數個量子位元操縱么正轉換的量子邏輯閘。
量子位元有兩截然不同的|0>狀態（對應到古典位元的 0）及|1>狀態（對應到古典位元的 1），但不同於古典位元，
量子位元可處於 |0> 及 |1> 的疊加態。在當今許多可實現量子位元的物理系統中，transmon 超導量子位元算是最具前景可實現可擴充性量子計算的平台。
本論文聚焦於在量子位元的單點量測及量子態斷層掃描實驗。為了利用分群演算法來分類量子位元的基態（|0>）及激發態（|1>）
在 I/Q 平面的讀取訊號分佈。除了以距離為基準的分類方法，我們進一步透過高斯混合模型算法來找出兩分布的中心點及共變異矩陣(寬窄及走向)，以提高分類之精確度；
此模型可應用於所有同一讀出參數的量測，生成該狀態基態和激發態各自的機率。我們也展示以量子態斷層掃描來檢測分類結果之可行性。

Quantum computing is a computational approach that utilizes principles of quantum mechanics, such as quantum superposition and entanglement. The essential parts of a quantum computing system are the quantum bit (or the qubit) as the basic unit of quantum information and quantum logic gates which implement unitary transformations acting on one or a small number of qubits. A qubit has two distinct states, one represented by |0> (equivalent to ''0'' for a classical bit) and the other represented by |1> (equivalent to ''1'' for a classical bit). Unlike a classical bit, a qubit can also exist
in a coherent superposition of the |0> and |1> states, rather than being limited to just one of the states. Among many possible physical realizations of qubits, the superconducting transmon qubit is the most promising platform for realizing scalable quantum computing. In this thesis, we focus on single-shot measurements and quantum state tomography performed on transmon qubits. We use clustering algorithms to classify single-shot readout results for the ground (|0>) state and the excited (|1>) state
of the transmon qubit in the in-phase and quadrature (I-Q) signal plane.
In addition to distance-based approaches, we have employed the Gaussian mixture model to determine the centers of the two distributions for the two corresponding states and their covariance matrices in order to further improve the
accuracy in classification. This model can then be directly applied to all measurements with the same readout parameters, generating the probabilities of the |0> and |1> states. We also demonstrate the feasibility of
using quantum state tomography experiments to verify the results obtained through the classification methods.

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