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題名 從雜訊的 I/Q 訊號中識別量子位元狀態
Identification of qubit states from noisy I/Q signals
作者 朱宗彥
Chu, Tsung-Yen
貢獻者 陳啟東<br>林瑜琤
Chen, Chii-Dong<br>Lin, Yu-Cheng
朱宗彥
Chu, Tsung-Yen
關鍵詞 量子態斷層掃描
超導量子位元
單點量測
高斯混合模型
射頻
數位讀出
quantum state tomography
superconducting quantum bit
single shot measurement
Gaussian mixture model
radio frequency
digital readout
日期 2023
上傳時間 1-Sep-2023 16:27:53 (UTC+8)
摘要 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.
參考文獻 [1] Bagnall, Anthony, et al. “The great time series classification bake off: a review and
experimental evaluation of recent algorithmic advances,” Data Mining and Knowledge
Discovery, 31 (05 2017).
[2] Chen, Zijun. Metrology of Quantum Control and Measurement in Superconducting
Qubits. PhD dissertation, University of California, Santa Barbara, 2018.
[3] Devoret, Michel H., “Quantum Fluctuations in Electrical Circuits,” 1997.
[4] Fink, Johannes M. Quantum nonlinearities in strong coupling circuit QED. Doctoral
Thesis, University of Vienna, 2010.
[5] Giusti, Rafael and Gustavo E.A.P.A. Batista. “An Empirical Comparison of Dissimilarity
Measures for Time Series Classification.” 2013 Brazilian Conference on Intelligent
Systems. 82–88. 2013.
[6] Jaynes, E.T. and F.W. Cummings. “Comparison of quantum and semiclassical radiation
theories with application to the beam maser,” Proceedings of the IEEE, 51(1):89–109
(1963).
[7] Kerimbekov, Yerzhan, et al. “The use of Lorentzian distance metric in classification
problems,” Pattern Recognition Letters, 84:170–176 (2016).
[8] Martinis, John M. and Kevin Osborne, “Superconducting Qubits and the Physics of
Josephson Junctions,” 2004.
[9] Rempe, Gerhard, et al. “Observation of quantum collapse and revival in a one-atom
maser,” Phys. Rev. Lett., 58:353–356 (Jan 1987).
[10] Smolin, John A., et al. “Efficient Method for Computing the Maximum-Likelihood
Quantum State from Measurements with Additive Gaussian Noise,” Phys. Rev. Lett.,
108:070502 (Feb 2012).
[11] Tsai, Yu. A. Pashkin · O. Astafiev · T. Yamamoto · Y. Nakamura · J. S. “Josephson charge
qubits: a brief review,” Quantum Inf Process (2009) 8, 55–80 (2009).
[12] Y. Nakamura, Yu. A. Pashkin, J. S. Tsai. “Coherent control of macroscopic quantum
states in a single-Cooper-pair box,” Nature, 398:786–788 (4 1999).
描述 碩士
國立政治大學
應用物理研究所
110755001
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0110755001
資料類型 thesis
dc.contributor.advisor 陳啟東<br>林瑜琤zh_TW
dc.contributor.advisor Chen, Chii-Dong<br>Lin, Yu-Chengen_US
dc.contributor.author (Authors) 朱宗彥zh_TW
dc.contributor.author (Authors) Chu, Tsung-Yenen_US
dc.creator (作者) 朱宗彥zh_TW
dc.creator (作者) Chu, Tsung-Yenen_US
dc.date (日期) 2023en_US
dc.date.accessioned 1-Sep-2023 16:27:53 (UTC+8)-
dc.date.available 1-Sep-2023 16:27:53 (UTC+8)-
dc.date.issued (上傳時間) 1-Sep-2023 16:27:53 (UTC+8)-
dc.identifier (Other Identifiers) G0110755001en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/147295-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用物理研究所zh_TW
dc.description (描述) 110755001zh_TW
dc.description.abstract (摘要) 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。		zh_TW
dc.description.abstract (摘要) 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.		en_US
dc.description.tableofcontents 第一章緒論 4
第一節研究緣起 4
第二節研究目的 6
第二章文獻探討 8
第一節相關理論 8
第一小節量子諧振盪(Quantum Harmonic Oscillation, QHO) 8
第二小節Transmon量子位元哈密頓量 10
第三小節腔振盪(Cavity Oscillation)與量子位元耦合 12
第四小節色散位移(Dispersive shift) 13
第五小節T1 弛豫時間和T2 弛豫時間 14
第六小節布洛赫球體(Bloch sphere) 14
第二節研究設計或統計方法 16
第一小節K-Means 16
第二小節高斯混合模型(Gaussian Mixture Model, GMM) 18
第三章研究架構和實驗方法 20
第一節儀器配置 20
第二節資料蒐集方法及程序 25
第一小節頻域量測 26
第二小節時域量測 31
第三小節單點量測(Single Shot Measurement) 34
第四小節測量T1 弛豫時間和T2 弛豫時間 35
第五小節量測晶片基本資料 37
第六小節量子態斷層掃描(Quantum State Tomography) 37
第三節資料處理及分析方法 41
第一小節I/Q 訊號資料點分群 41
第二小節訊躁比(Signal-to-Noise ratio, SNR) 43
第四章研究結果 44
第一節實驗結果 44
第二節結論 54
第三節未來改善意見與想法 55
參考文獻 56		zh_TW
dc.format.extent 23528157 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0110755001en_US
dc.subject (關鍵詞) 量子態斷層掃描zh_TW
dc.subject (關鍵詞) 超導量子位元zh_TW
dc.subject (關鍵詞) 單點量測zh_TW
dc.subject (關鍵詞) 高斯混合模型zh_TW
dc.subject (關鍵詞) 射頻zh_TW
dc.subject (關鍵詞) 數位讀出zh_TW
dc.subject (關鍵詞) quantum state tomographyen_US
dc.subject (關鍵詞) superconducting quantum biten_US
dc.subject (關鍵詞) single shot measurementen_US
dc.subject (關鍵詞) Gaussian mixture modelen_US
dc.subject (關鍵詞) radio frequencyen_US
dc.subject (關鍵詞) digital readouten_US
dc.title (題名) 從雜訊的 I/Q 訊號中識別量子位元狀態zh_TW
dc.title (題名) Identification of qubit states from noisy I/Q signalsen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] Bagnall, Anthony, et al. “The great time series classification bake off: a review and
experimental evaluation of recent algorithmic advances,” Data Mining and Knowledge
Discovery, 31 (05 2017).
[2] Chen, Zijun. Metrology of Quantum Control and Measurement in Superconducting
Qubits. PhD dissertation, University of California, Santa Barbara, 2018.
[3] Devoret, Michel H., “Quantum Fluctuations in Electrical Circuits,” 1997.
[4] Fink, Johannes M. Quantum nonlinearities in strong coupling circuit QED. Doctoral
Thesis, University of Vienna, 2010.
[5] Giusti, Rafael and Gustavo E.A.P.A. Batista. “An Empirical Comparison of Dissimilarity
Measures for Time Series Classification.” 2013 Brazilian Conference on Intelligent
Systems. 82–88. 2013.
[6] Jaynes, E.T. and F.W. Cummings. “Comparison of quantum and semiclassical radiation
theories with application to the beam maser,” Proceedings of the IEEE, 51(1):89–109
(1963).
[7] Kerimbekov, Yerzhan, et al. “The use of Lorentzian distance metric in classification
problems,” Pattern Recognition Letters, 84:170–176 (2016).
[8] Martinis, John M. and Kevin Osborne, “Superconducting Qubits and the Physics of
Josephson Junctions,” 2004.
[9] Rempe, Gerhard, et al. “Observation of quantum collapse and revival in a one-atom
maser,” Phys. Rev. Lett., 58:353–356 (Jan 1987).
[10] Smolin, John A., et al. “Efficient Method for Computing the Maximum-Likelihood
Quantum State from Measurements with Additive Gaussian Noise,” Phys. Rev. Lett.,
108:070502 (Feb 2012).
[11] Tsai, Yu. A. Pashkin · O. Astafiev · T. Yamamoto · Y. Nakamura · J. S. “Josephson charge
qubits: a brief review,” Quantum Inf Process (2009) 8, 55–80 (2009).
[12] Y. Nakamura, Yu. A. Pashkin, J. S. Tsai. “Coherent control of macroscopic quantum
states in a single-Cooper-pair box,” Nature, 398:786–788 (4 1999).		zh_TW