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研究生： 瓦克里
Walkoli, Akshay Kondibhau
論文名稱： 壓縮態量子光子催化用於產生非高斯量子態
Squeezed State Quantum Photon Catalysis For Generation of Non-Gaussian Quantum State
指導教授： 李瑞光
Lee, Ray-Kuang
口試委員: 吳俊毅
Wu, Jun-Yi
吳欣澤
Wu, Shin-Tza
司歐樂
Ole, Steuernagel
學位類別： 碩士
Master
系所名稱： 電機資訊學院 - 光電工程研究所
Institute of Photonics Technologies
論文出版年： 2023
畢業學年度： 112
語文別： 英文
論文頁數： 44
中文關鍵詞： 量子光學 、量子機器學習 、量子電路 、量子光子催化 、非高斯量子態 、壓縮態
外文關鍵詞： Quantum Optics, Quantum Machine Learning, Quantum Circuit, Quantum Photon Catalysis, Non Gaussian Quantum State, Squeezed State
相關次數： 點閱：80  下載：0 
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    • 尋求創建非高斯量子狀態的探索，這構成了連續變數量子計算領域的一個艱鉅挑戰。許多方法，包括光子的增加和減少，已經被開發出來，試圖創建這些難以捉摸的狀態。我們的理論研究在這一環境中探索了光子催化的新領域，重點放在實現類似貓的狀態，特別是擠壓真空（SSV）狀態上。這一發現對於發展GKP狀態具有重大意義，GKP狀態是量子計算的重要組成部分。

    在光束分束器的幫助下，我們的研究表明，結合擠壓真空狀態和Fock狀態（|1⟩ ⟨1|）可以提高類似貓的狀態的振幅。我們還使用光子數解析檢測器研究了串級光子催化，展示了增加SSV狀態振幅的有趣可能性。這項研究為通過創建一種主要依賴於操縱擠壓真空狀態的創新方法來可靠地進行量子處理打開了一條有希望的新途徑，以便創建非高斯狀態。

    The search for creating non-Gaussian quantum states, which poses a difficult challenge, dominates the field of continuous variable quantum computation. Many approaches, including photon addition and subtraction, have been developed to attempt to create these elusive states. Our theoretical research explores the novel field of photon catalysis in this environment, focusing on the realisation of cat-like states, especially the Superposition of Squeezed Vacuum (SSV) state. The GKP state, a crucial element of quantum computation, is being developed, and this revelation has significant implications for that process.

    With the aid of a beam splitter, our research shows that by mixing a squeezed vacuum state with a Fock state (|1⟩ ⟨1|), it is feasible to increase the amplitudes of cat-like states. We also investigate cascade photon catalysis using Photon Number Resolving Detectors, demonstrating an interesting possibility of increasing the amplitude of the SSV state. This research opens up a promising new path towards reliable quantum processing through the creation of an innovative approach for creating non-Gaussian states that rely primarily on manipulating squeezed vacuum states.

    Abstract (Chinese) I Abstract II Acknowledgements III Contents IV List of Figures VI List of Tables VIII 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Continuous Variable Quantum Computation . . . . . . . . . . . 1 1.2 Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Quantum Optics 3 2.1 Quantized Electromagnetic Field . . . . . . . . . . . . . . . . . . . . . 3 2.2 Quantum States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.1 Number State . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.2 Coherent State . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.3 Squeezed Vacuum State . . . . . . . . . . . . . . . . . . . . . 6 2.2.4 Superposition of Squeezed Vacuum (SSV) State . . . . . . . . . 7 2.3 Quantum Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3.1 Beam Splitter . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3.2 Displacement Operator . . . . . . . . . . . . . . . . . . . . . . 9 2.3.3 Phase Shift Operator . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Wigner Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3 Quantum Photon Catalysis 11 3.1 Squeezed Vacuum State Optical Catalysis . . . . . . . . . . . . . . . . 12 3.2 Single Photon Detection Noise Analysis . . . . . . . . . . . . . . . . . 15 3.2.1 Loss due to Vacuum in Fock state |1⟩ ⟨1| . . . . . . . . . . . . . 15 3.2.2 Loss effect of Dark Count . . . . . . . . . . . . . . . . . . . . 17 3.3 Losses modelled using Beam Splitter . . . . . . . . . . . . . . . . . . . 18 3.4 Higher Photon Number Measurement . . . . . . . . . . . . . . . . . . 21 3.4.1 Odd photon Measurement Analysis . . . . . . . . . . . . . . . 21 3.4.2 Even photon measurement analysis . . . . . . . . . . . . . . . 22 4 Cascade Photon Catalysis 23 4.1 Machine Learning Techniques to Quantum Circuit . . . . . . . . . . . . 24 5 Conclusions 26 A Quantum mechanical description of Beam Splitter 28 B Modelling Vacuum & Dark Count effect for SPD 30 B.1 Squeezed state interference . . . . . . . . . . . . . . . . . . . . . . . . 30 B.1.1 Interference with Vacuum . . . . . . . . . . . . . . . . . . . . 30 B.1.2 Interference with |1⟩ ⟨1| . . . . . . . . . . . . . . . . . . . . . 31 C Optimization method analysis 33 D Optimized Parameters 37 Bibliography 40

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