政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/147295

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/147295

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政大典藏 > College of Science > Graduate Institute of Applied Physics > Theses > Item 140.119/147295

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/147295

Title:	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
Authors:	朱宗彥 Chu, Tsung-Yen
Contributors:	陳啟東林瑜琤 Chen, Chii-Dong Lin, Yu-Cheng 朱宗彥 Chu, Tsung-Yen
Keywords:	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
Date:	2023
Issue Date:	2023-09-01 16:27:53 (UTC+8)
Abstract:	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.
Reference:	[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).
Description:	碩士國立政治大學應用物理研究所 110755001
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0110755001
Data Type:	thesis
Appears in Collections:	[Graduate Institute of Applied Physics] Theses

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