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研究生：	施岳錠 Shih, Yueh-Ting
論文名稱：	以最少的假說與有限數據測量IBM量子電腦的局域可控性 Testing local addressability in IBM quantum computers with minimal assumptions and finite data
指導教授：	梁永成 Liang, Yeong-Cherng
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：	英文
論文頁數：	69
中文關鍵詞：	量子資訊、量子電腦、與設備無關、有限數據、串音現象、貝爾不等式、假設檢定
外文關鍵詞：	Quantum information, quantum computer, device-independent, finite statistics, cross-talk, Bell inequalities, hypothesis testing
相關次數：	點閱：147 下載：5
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裨益於與設備無關的協定這類嶄新的資訊處理方法，人們得以在對於實驗裝置要求最少的假設前提下，做出分析並取得結果。我們採用張博士[1]及其與梁教授[2]研究的Prediction-based-ratio (PBR)分析方法用於檢測IBMQ量子電腦。確切地說，我們在這些系統上進行CHSH貝爾實驗，再以假設檢定的統計工具分析蒐集到的實驗數據，是否違反⌜無串音條件⌟，亦即存在⌜串音現象⌟。相較於現有用於檢測量子系統中串音現象的方法，這個分析方法只需要⌜最少的⌟假設。這些假設包含對於實驗系統的以及理論的。特別是，我們的分析不需要⌜獨立同分佈⌟的假設。這個假設雖然被廣為使用，但大多數系統卻通常沒有（很多是沒辦法）經過檢查保證這個假說成立。因此我們的方法能更純粹的從實驗中蒐集到的數據分析系統的局域可控性。

Device-independent protocols are a novel type of information processing protocol where only minimal trust or characterization of the employed devices is needed. By adapting the prediction-based ratio (PBR) method first proposed by Zhang et al. [1] and further analyzed in Liang and Zhang [2], we perform no signaling tests on some of the quantum computers offered by IBM Quantum Experience.
More precisely, we carry out Clauser-Horne-Shimony-Holt-type Bell tests on these systems and a subsequent hypothesis-testing—based on the raw data accrued during these tests—to determine the likelihood that the data obtained is incompatible with an underlying model that is no signaling, i.e., with crosstalk. The strength of the present approach, in contrast with other commonly adopted benchmarking techniques, is that “minimal assumptions are needed”. In particular, the usually
unjustified assumption of independent and identically-distributed (i.i.d.) trials is not required in our analysis. In short, our perspective on characterizing local addressability tells a story based only on what is “observed” in real labs.

摘要 i
Abstract iii
致謝 v
Acknowledgements vii
List of Acronyms xiii
List of Figures xv
1. Introduction 1
2. Preliminaries 3
2.1 Crosstalk 3
2.2 Scheme 3
2.1.2 High-level model for crosstalk 3
2.1.3 Completely positive (CP) map 3
2.1.4 Crosstalk in terms of CP map 4
2.1.5 Suggested perspective 5
2.2 Present protocols 6
2.2.1 Simultaneous Randomized Benchmarking (SRB) 6
2.2.2 Determinant tests 7
2.2.3 Abandon characterization of CP maps 7
2.2.4 Context dependence tests & hypothesis testing 8
2.2.5 Summary 10
2.3 Nonlocality and device-independent quantum information 11
2.3.1 Bell’s theorem 11
2.3.2 Clauser-Horne-Shimony-Holt inequality 12
2.3.3 No signaling correlation 15
2.3.4 Device-independent quantum information 16
2.4 f-divergence and its minimization 17
2.4.1 f-divergence 17
2.4.2 Minimization of f-divergence 17
3. Prediction-based ratio analysis 19
3.1 PBR protocol 20
3.1.1 The null hypothesis 20
3.1.2 PBR protocol 21
3.2 The test statistic and the p-value 22
3.3 Bell inequalities in PBR 22
3.4 Role of PBR on crosstalk benchmarking 23
4. Implementation of PBR analysis for crosstalk on IBMQ 25
4.1 CHSH Bell test on IBMQ 25
4.2 PBR analysis – Classical communication 26
4.3 Results 27
4.3.1 The effect of changing Nest, Ntest and N 31
4.3.2 Changing the shared state 35
4.3.3 Block renewal PBR 36
5. Conclusion 37
5.1 Limitations of the current approach 37
5.2 Summary 37
5.3 Future work 38
5.3.1 Bell tests with a single input on one side 38
5.3.2 Improving a Bell test 39
5.4 Outlook 39
References 41
Appendices 45
A. Crosstalk in terms of CP map 47
A.1 Definition of crosstalk in terms of CP map 47
A.1.1 Separable form of crosstalk free global channel 48
B. Present protocols 51
B.1 Protocols 51
B.1.1 Simultaneous randomized benchmarking 51
B.1.2 Determinant tests 54
B.1.3 Context dependence tests 55
B.2 Hidden crosstalks in different methods 57
B.2.1 Simultaneous randomized benchmraking 57
B.2.2 Determinant tests 57
B.2.3 Context dependence test 57
C. Before Bell 59
C.1 The EPR paradox 59
C.2 Impossibility proofs and de Broglie-Bohm 59
D. Task details 63
E. Asymptotic behavior & optimality 65
E.1 Bahadur’s theorem 65
E.2 Confidence-gain rate 66
E.3 Block renewal PBR 67
F. Hellinger divergence 69
                                    

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校內：2023-07-26公開
校外：2023-07-26公開

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