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研究生： 馮震琳
Feng, Zhen-Lin
論文名稱： 在頻域中提取量子位元參數
Extracting Qubit Parameters in Frequency Domain
指導教授： 陳正中
Chen, Jeng-Chung
口試委員: 許耀銓
Hoi, Io-Chun
林晏詳
Lin, Yen-Hsiang
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2022
畢業學年度： 110
語文別： 中文
論文頁數： 52
中文關鍵詞： 量子位元 、躍遷頻率 、鬆弛速率 、去相干速率 、Transmon 、反射係數 、開源程式 、阻抗不匹配
外文關鍵詞： quantum bit, transition frequency, relaxation rate, decoherence rate, Transmon, reflection coefficient, open-source program, impedance mismatch
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    • 本論文的主要目的是開發一種分析方法，從超導量子位元元件的實驗數據中提取關鍵參數。操作量子位元以執行某些計算任務需要精確地瞭解基本元件參數，包括躍遷頻率，鬆弛速率和去相干速率。實驗數據取自嵌入在半傳輸線末端的 transmon 量子位元，此情況視為人造原子在鏡子前，我們測量微波信號的反射率。我們採用一個開源程式，考慮了光與兩能級原子之間的交互作用在弱耦合極限、電路量子化和輸入輸出理論，以說明量子位元狀態的演變。我們測試該程式的有效性，並將其擴展到高功率的情況。本論文開發的方法對於未來發展超導量子技術中瞭解量子位元特性非常有用。

    The main purpose of this thesis is to develop an analysis method to extract the key parameters from experimental data of superconducting quantum bit (qubit) device. The operation of qubit to perform certain computing tasks requires to precisely know the essential device parameters including the transition frequency, relaxation rate, and decoherence rate. The data is taken from a transmon qubit embedded in the end of a half transmission line, which functions as an artificial atom in front of mirror, and we measure the reflectivity of microwave signals. We adopt an open-source program which considers the light-atom interaction between a two-level atom in weak coupling limit, circuit quantization, and input-output theory to account the evolution of qubit states. We test the validity of this program, and extend it to high power operations. The method developed here will be very useful to characterize qubit performance in future development of superconducting quantum technology.

    摘要 --------------------------------------------------------- i Abstract ----------------------------------------------------- ii 誌謝 --------------------------------------------------------- iii 1 緒論 --------------------------------------------------------- 1 1.1 量子位元 --------------------------------------------------- 1 1.2 量子位元的去相干特性 ---------------------------------------- 3 1.2.1 鬆弛速率 ------------------------------------------------- 3 1.2.2 去相干速率 ----------------------------------------------- 3 1.3 超導量子位元-Transmon -------------------------------------- 4 1.4 本論文的主旨 ----------------------------------------------- 6 1.4.1 實驗系統簡介 --------------------------------------------- 6 1.4.2 擬合演算法適用的條件 -------------------------------------- 8 2 系統模型與理論背景 -------------------------------------------- 9 2.1 量子位元與微波交互作用的模型 --------------------------------- 9 2.1.1 輸入輸出關係 --------------------------------------------- 9 2.1.2 布洛赫方程式 --------------------------------------------- 11 2.1.3 反射係數 ------------------------------------------------- 11 2.2 LC 共振器與微波交互作用的模型 -------------------------------- 12 2.2.1 反射係數 ------------------------------------------------- 12 2.3 量子位元模型與 LC 共振器模型的對應 --------------------------- 13 3 測試擬合演算法 ------------------------------------------------ 15 3.1 第一組測試數據的擬合 ---------------------------------------- 15 3.2 第二組測試數據的擬合 ---------------------------------------- 16 3.3 補償阻抗不匹配 ---------------------------------------------- 17 3.3.1 第一組測試數據的補償阻抗不匹配 ----------------------------- 18 3.3.2 第二組測試數據的補償阻抗不匹配 ----------------------------- 18 4 擬合量子位元的實驗量測數據 ------------------------------------- 21 4.1 不考慮探測波功率的反射係數 ----------------------------------- 21 4.1.1 第一組實驗數據的擬合 -------------------------------------- 21 4.1.2 第二組實驗數據的擬合 -------------------------------------- 22 4.1.3 第三組實驗數據的擬合 -------------------------------------- 23 4.2 補償阻抗不匹配 ---------------------------------------------- 25 4.2.1 第一組實驗數據的補償阻抗不匹配 ------------------------------ 25 4.2.2 第二組實驗數據的補償阻抗不匹配 ------------------------------ 25 4.2.3 第三組實驗數據的補償阻抗不匹配 ------------------------------ 25 4.3 考慮探測波功率的反射係數 ------------------------------------- 27 4.3.1 第一組實驗數據 -------------------------------------------- 28 4.3.2 第二組實驗數據 -------------------------------------------- 29 4.3.3 第三組實驗數據 -------------------------------------------- 29 5 總結 --------------------------------------------------------- 33 A 擬合演算法相關的程式碼 ----------------------------------------- 35 參考文獻 -------------------------------------------------------- 51

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