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題名 超導量子位元控制脈衝之優化
Optimizing control pulses for superconducting qubits作者 吳岱家
Wu, Dai-Jia貢獻者 陳啟東<br>林瑜琤
Chen, Chii-Dong<br>Lin, Yu-Cheng
吳岱家
Wu, Dai-Jia關鍵詞 超導量子位元
約瑟芬接面
絕熱邏輯閘導數去除法
克里福操作誤差
Superconducting qubit
Transmon
Josephson junction
Deviative Removal by Adiabatic Gate(DRAG)
Error per Clifford日期 2023 上傳時間 1-Sep-2023 16:29:11 (UTC+8) 摘要 在 2019 年底 Google 藉由 49 個陣列量子位元（Qubit）實現了量子霸（QuantumSupremacy）一詞後世界各國爭相研究量子電腦這一門相當先進的技術。隨著時間緩慢推移研究技術逐漸成長，現在一部量子電腦中的量子位元最多已經來到了 433 個（IBM Osprey），在台灣也有許多研究機構正在努力研究中像是中央研究院、鴻海研究院等等。超導量子位元就像傳統 LC 電路，在進入超導態後因為約瑟芬接面（JosephsonJunction）的特性，使得此位元中不同能階的能量差不再是等間距，我們就可以利用此特性來操作位元在特定能階上躍遷。在操作時我們需要在極低溫且極短的時間內精準操控每一顆量子位元，也就是將一段微波脈衝輸進此位元的操作閘，藉由此脈衝提供位元量子態改變所需要的能量。目前大多數的研究提供了精準的微波控制方法「絕熱邏輯閘導數去除法」（Derivative Removal by Adiabatic Gate, DRAG），藉由在波形中增加了特定比例的正交部分與提供隨波型函數變化的頻率，使其能夠更精準操控位元。在本論文當中會先借一般高斯波形脈衝討論克里福操作誤差（Error per Clifford）與脈衝長度的關係，再以其與 DRAG 方法生成之脈衝所得結果進行比較。接著在控制脈衝長度下，使用 DRAG 方法以其不同的正交比例作為變因討論何種比例會生成最低克里福操作誤差之脈衝。經過了前述兩個實驗我們可以控制許多影響誤差的因素，我們將在這些實驗結果上以不同的脈衝波形做為實驗變因，討論哪種波形對控制位元躍遷的幫助最大，最後為此波型尋找其作為脈衝最適合的波寬。最後經由比對在相同脈衝長度為條件下優化後的 DRAG 脈衝與一般高斯波形脈衝，我們成功將克里福操作誤差由 0.01285 ± 0.0006 優化至 0.00798 ± 0.0001，降低約38％。
At the end of 2019, Google achieved quantum supremacy using 49-qubit arrays, sparking a global race among countries to study quantum computers, an advanced technology. As time flows, research in this field gradually grew, and now quantum computers can have up to 433 qubits (IBM Osprey). In Taiwan, many research institutions, such as Academia Sinica and Foxconn Research Institute, are actively engaged in quantum computing research.Superconducting qubits are similar to traditional LC circuits. When in a superconducting state, these qubits exhibit specific transition frequencies due to the characteristics of Josephson junctions. In operation, precise control over each qubit is required within extremely low temperatures and short time frames. It involves applying microwave pulses into the control gate, to induce an energy change in its quantum state. Most research has provided a precise microwave control method called ”Derivative Removal by Adiabatic Gate, DRAG,” which involves adding specific proportions of a quadrature component to the waveform and providing a frequency that varies with the waveform function to achieve more accurate qubit control.In this thesis, we first discuss a relationship between the error per Clifford and the pulse duration by a conventional Gaussian waveform control pulse. We compare the results obtained using DRAG-generated pulses with those obtained using conventional pulses. Next, under a controlled pulse duration, we vary the quadrature proportions of the DRAG method to determine which proportion generates the lowest error per Clifford. By controlling various factors that affect errors through these experiments, we will try to explore which pulse waveform contributes the most to controlling qubit transitions and finally find the most suitable pulse width for this waveform.Finally, by comparing the optimized DRAG pulse with the general Gaussian pulse under the same gate time condition, we successfully optimized the error per Clifford from 0.01285±0.0006 to 0.00798±0.0001, reducing about 38%.參考文獻 [Chen et al., 2016] Chen, Z., Kelly, J., Quintana, C., Barends, R., Campbell, B., Chen, Y., Chiaro, B., Dunsworth, A., Fowler, A., Lucero, E., et al. (2016). Measuring and suppressing quantum state leakage in a superconducting qubit. Physical review letters, 116(2):020501.[Chow et al., 2010] Chow, J. M., DiCarlo, L., Gambetta, J. M., Motzoi, F., Frunzio, L., Girvin, S. M., and Schoelkopf, R. J. (2010). Optimized driving of superconducting artificial atoms for improved single-qubit gates. Physical Review A, 82(4):040305.[Gambetta et al., 2011] Gambetta, J. M., Motzoi, F., Merkel, S., and Wilhelm, F. K. (2011). Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator. Physical Review A, 83(1):012308.[Motzoi et al., 2009] Motzoi, F., Gambetta, J. M., Rebentrost, P., and Wilhelm, F. K. (2009). Simple pulses for elimination of leakage in weakly nonlinear qubits. Physical review letters,103(11):110501.[Rol et al., 2017] Rol, M., Bultink, C. C., O’Brien, T. E., De Jong, S., Theis, L. S., Fu, X., Luthi, F., Vermeulen, R. F., De Sterke, J., Bruno, A., et al. (2017). Restless tuneup of high-fidelity qubit gates. Physical Review Applied, 7(4):041001.[Schuster et al., 2005] Schuster, D., Wallraff, A., Blais, A., Frunzio, L., Huang, R.-S., Majer, J., Girvin, S., Schoelkopf, and RJ (2005). ac stark shift and dephasing of a superconductingqubit strongly coupled to a cavity field. Physical Review Letters, 94(12):123602. 描述 碩士
國立政治大學
應用物理研究所
110755011資料來源 http://thesis.lib.nccu.edu.tw/record/#G0110755011 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-Cheng en_US dc.contributor.author (Authors) 吳岱家 zh_TW dc.contributor.author (Authors) Wu, Dai-Jia en_US dc.creator (作者) 吳岱家 zh_TW dc.creator (作者) Wu, Dai-Jia en_US dc.date (日期) 2023 en_US dc.date.accessioned 1-Sep-2023 16:29:11 (UTC+8) - dc.date.available 1-Sep-2023 16:29:11 (UTC+8) - dc.date.issued (上傳時間) 1-Sep-2023 16:29:11 (UTC+8) - dc.identifier (Other Identifiers) G0110755011 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/147300 - 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) 110755011 zh_TW dc.description.abstract (摘要) 在 2019 年底 Google 藉由 49 個陣列量子位元（Qubit）實現了量子霸（QuantumSupremacy）一詞後世界各國爭相研究量子電腦這一門相當先進的技術。隨著時間緩慢推移研究技術逐漸成長，現在一部量子電腦中的量子位元最多已經來到了 433 個（IBM Osprey），在台灣也有許多研究機構正在努力研究中像是中央研究院、鴻海研究院等等。超導量子位元就像傳統 LC 電路，在進入超導態後因為約瑟芬接面（JosephsonJunction）的特性，使得此位元中不同能階的能量差不再是等間距，我們就可以利用此特性來操作位元在特定能階上躍遷。在操作時我們需要在極低溫且極短的時間內精準操控每一顆量子位元，也就是將一段微波脈衝輸進此位元的操作閘，藉由此脈衝提供位元量子態改變所需要的能量。目前大多數的研究提供了精準的微波控制方法「絕熱邏輯閘導數去除法」（Derivative Removal by Adiabatic Gate, DRAG），藉由在波形中增加了特定比例的正交部分與提供隨波型函數變化的頻率，使其能夠更精準操控位元。在本論文當中會先借一般高斯波形脈衝討論克里福操作誤差（Error per Clifford）與脈衝長度的關係，再以其與 DRAG 方法生成之脈衝所得結果進行比較。接著在控制脈衝長度下，使用 DRAG 方法以其不同的正交比例作為變因討論何種比例會生成最低克里福操作誤差之脈衝。經過了前述兩個實驗我們可以控制許多影響誤差的因素，我們將在這些實驗結果上以不同的脈衝波形做為實驗變因，討論哪種波形對控制位元躍遷的幫助最大，最後為此波型尋找其作為脈衝最適合的波寬。最後經由比對在相同脈衝長度為條件下優化後的 DRAG 脈衝與一般高斯波形脈衝，我們成功將克里福操作誤差由 0.01285 ± 0.0006 優化至 0.00798 ± 0.0001，降低約38％。 zh_TW dc.description.abstract (摘要) At the end of 2019, Google achieved quantum supremacy using 49-qubit arrays, sparking a global race among countries to study quantum computers, an advanced technology. As time flows, research in this field gradually grew, and now quantum computers can have up to 433 qubits (IBM Osprey). In Taiwan, many research institutions, such as Academia Sinica and Foxconn Research Institute, are actively engaged in quantum computing research.Superconducting qubits are similar to traditional LC circuits. When in a superconducting state, these qubits exhibit specific transition frequencies due to the characteristics of Josephson junctions. In operation, precise control over each qubit is required within extremely low temperatures and short time frames. It involves applying microwave pulses into the control gate, to induce an energy change in its quantum state. Most research has provided a precise microwave control method called ”Derivative Removal by Adiabatic Gate, DRAG,” which involves adding specific proportions of a quadrature component to the waveform and providing a frequency that varies with the waveform function to achieve more accurate qubit control.In this thesis, we first discuss a relationship between the error per Clifford and the pulse duration by a conventional Gaussian waveform control pulse. We compare the results obtained using DRAG-generated pulses with those obtained using conventional pulses. Next, under a controlled pulse duration, we vary the quadrature proportions of the DRAG method to determine which proportion generates the lowest error per Clifford. By controlling various factors that affect errors through these experiments, we will try to explore which pulse waveform contributes the most to controlling qubit transitions and finally find the most suitable pulse width for this waveform.Finally, by comparing the optimized DRAG pulse with the general Gaussian pulse under the same gate time condition, we successfully optimized the error per Clifford from 0.01285±0.0006 to 0.00798±0.0001, reducing about 38%. en_US dc.description.tableofcontents 第一章 引言 1第二章 物理模型 2第一節 超導量子位元-Transmon 2第二節 DRAG 10第三節 操作誤差檢驗方法：隨機標竿分析法 12第三章 實驗方法與架構 14第一節 量子位元 14第二節 量測裝置 16第三節 實驗方法與預期 20第四章 實驗數據與分析 30第一節 DRAG 方法中最佳正交比例 30第二節 躍遷脈衝的最佳脈衝長度 33第三節 躍遷脈衝的最佳波形 35第四節 躍遷脈衝中波寬與長度的關係 36第五章 結論 37參考文獻 38 zh_TW dc.format.extent 19953023 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0110755011 en_US dc.subject (關鍵詞) 超導量子位元 zh_TW dc.subject (關鍵詞) 約瑟芬接面 zh_TW dc.subject (關鍵詞) 絕熱邏輯閘導數去除法 zh_TW dc.subject (關鍵詞) 克里福操作誤差 zh_TW dc.subject (關鍵詞) Superconducting qubit en_US dc.subject (關鍵詞) Transmon en_US dc.subject (關鍵詞) Josephson junction en_US dc.subject (關鍵詞) Deviative Removal by Adiabatic Gate(DRAG) en_US dc.subject (關鍵詞) Error per Clifford en_US dc.title (題名) 超導量子位元控制脈衝之優化 zh_TW dc.title (題名) Optimizing control pulses for superconducting qubits en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [Chen et al., 2016] Chen, Z., Kelly, J., Quintana, C., Barends, R., Campbell, B., Chen, Y., Chiaro, B., Dunsworth, A., Fowler, A., Lucero, E., et al. (2016). Measuring and suppressing quantum state leakage in a superconducting qubit. Physical review letters, 116(2):020501.[Chow et al., 2010] Chow, J. M., DiCarlo, L., Gambetta, J. M., Motzoi, F., Frunzio, L., Girvin, S. M., and Schoelkopf, R. J. (2010). Optimized driving of superconducting artificial atoms for improved single-qubit gates. Physical Review A, 82(4):040305.[Gambetta et al., 2011] Gambetta, J. M., Motzoi, F., Merkel, S., and Wilhelm, F. K. (2011). Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator. Physical Review A, 83(1):012308.[Motzoi et al., 2009] Motzoi, F., Gambetta, J. M., Rebentrost, P., and Wilhelm, F. K. (2009). Simple pulses for elimination of leakage in weakly nonlinear qubits. Physical review letters,103(11):110501.[Rol et al., 2017] Rol, M., Bultink, C. C., O’Brien, T. E., De Jong, S., Theis, L. S., Fu, X., Luthi, F., Vermeulen, R. F., De Sterke, J., Bruno, A., et al. (2017). Restless tuneup of high-fidelity qubit gates. Physical Review Applied, 7(4):041001.[Schuster et al., 2005] Schuster, D., Wallraff, A., Blais, A., Frunzio, L., Huang, R.-S., Majer, J., Girvin, S., Schoelkopf, and RJ (2005). ac stark shift and dephasing of a superconductingqubit strongly coupled to a cavity field. Physical Review Letters, 94(12):123602. zh_TW
