單一超導量子位元控制與狀態讀取｜國立中央大學博碩士論文系統

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研究生：	朱凱翊 KAI-I CHU
論文名稱：	單一超導量子位元控制與狀態讀取 Control and Readout of Single Superconducting Qubit
指導教授：	陳永富 Yung-Fu CHEN
口試委員:
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：	2020
畢業學年度：	108
語文別：	英文
論文頁數：	73
中文關鍵詞：	電路量子電動力學、Transmon 量子位元、一維傳輸線共振器、色散讀取、傑恩斯-卡明斯讀取、拉比震盪、狀態掃描、拉姆齊條紋、鬆弛時間、量子退相干時間
外文關鍵詞：	Circuit quantum electrodynamics, Transmon qubit, one dimensional transmission line resonator, dispersive readout, Jaynes-Cummings readout, Rabi oscillation, state tomography, Ramsey Fringe, relaxation time, decoherence time
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電路量子電動力學 (circuit quantum electrodynamics) 是一個學習光跟原子量子交互作用的平台，同時，也是實現可擴展的量子電腦最有潛力的方法之一。單一Transmon 量子位元耦合一一維傳輸線共振器在我們實驗室裡被製造出來。我們控制並量測量子位元的狀態藉由色散讀取 (dispersive readout) 跟傑恩斯-卡明斯讀取 (Jaynes-Cummings readout)。從頻譜量測結果，確認我們的電路量子電動力學系統是在強耦
合以及強色散區域，此時量子相干性可維持。我們演示數項指標性的時域控制實驗,如拉比震盪 (Rabi oscillation), 狀態掃描 (state tomography) 以及拉姆齊條紋 (RamseyFringe)。基本的量子位元特徵如鬆弛時間 T1，量子退相干時間 T2 以及耦合強度 g 也可確定, 分別是 T1 ∼ 75 ns,T2 ∼ 134 ns,g ∼ 175 MHz。這篇論文提供了超導電路的基本理論背景以控制跟讀取量子位元狀態。

Circuit quantum electrodynamics (cQED) is a platform to study quantum interaction between light and atom. Also, it is one of the most promising ways to achieve scalable quantum computer. A transmon qubit coupled to a one dimensional transmission line resonator is fabricated in our Lab. We control and measure the qubit state by utilizing the dispersive readout and Jaynes-Cummings readout. From spectroscopy measurements, our cQED system is confirmed in the strong dispersive regime where the quantum coherence effect dominates the system. We demonstrate some hallmark time domain control experiments, such as Rabi oscillation, state tomography, and Ramsey Fringe. The basic
characteristic of the qubit, such as relaxation time T1 ∼ 75 ns, decoherence time T2 ∼ 134 ns, and coupling strength g ∼ 175 MHz are then determined. This thesis provides the
basic theoretical backgrounds of superconducting circuits and the studies of control and readout of the single qubit.

page
摘要 ix
Abstract xi
Contents xiii

Introduction 1

Circuit QED 3
1 Quantum LC circuit .......................................................... 3
2 Charge Qubit.................................................................. 4
2.1 Josephson junction .................................................... 5
2.2 Cooper pair box ....................................................... 7
2.3 Transmon .............................................................. 8
3 Jaynes-Cummings Model ..................................................... 10
3.1 Drive ................................................................... 12
3.2 Bloch sphere ........................................................... 13
3.3 Qubit state control .................................................... 14
3.4 Dispersive regime ...................................................... 15
4 Qubit state readout ........................................................... 16
4.1 Dispersive readout ..................................................... 16
4.2 Jaynes-Cummings readout ............................................ 19

Experimental Design and Setup 25
1 Superconducting Qubit design and fabrication............................... 25
2 Measurement wiring........................................................... 26
3 Measurement instruments..................................................... 27
4 IQ demodulation .............................................................. 29

Spectroscopy measurement 31
1 One tone spectroscopy ........................................................ 31
2 Two tone spectroscopy ........................................................ 33
2.1 Dispersive readout spectroscopy....................................... 35
2.2 Jaynes-Cummings readout spectroscopy .............................. 37

Single Qubit gate 41
1 Rabi ........................................................................... 42
2 T1 relaxation .................................................................. 46
3 State tomography ............................................................. 46
4 Bloch vector component ...................................................... 48
5 Ramsey Fringe ................................................................ 49
6 Spin echo ...................................................................... 51

Conclusion and Prospects 53

Bibliography 55
                                

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