超導量子位元控制脈衝之優化

Abstract

在 2019 年底 Google 藉由 49 個陣列量子位元（Qubit）實現了量子霸（Quantum\nSupremacy）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。\n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（Josephson\nJunction）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。\n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。\n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.\nSuperconducting 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.\nIn 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.\nFinally, 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%.