開放量子系統下量子邏輯閘的最佳化控制

Optimal Control of Quantum Gate Operations in Open Quantum Systems

黃琮暐(Tsung-Wei Huang)

指導教授 ： 管希聖

國立臺灣大學/理學院/物理研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.03219

摘要

擁有操作時間遠快於去相干化(decoherence) 時間的通(universal set) 量子邏輯閘是實行量子電腦最重要的限制條件之一。除此之外， 符合錯誤限制條件的高度準確度量子邏輯閘(quantum gates)，對於發展可容錯的量子計算(fault-tolerant quantum computation)也是極於需要的。在這篇論文中，我們使用科羅托夫(Krotov)方法，在肯恩(Kane)的矽基底施子自旋量子電腦系統(silicon-based donor spin quantum computer ， 其中我們以予體電子自旋當做量子位元(qubit))中，找到接近最佳化時間的高準確度(high-fidelity) 量子邏輯閘的控制序列。首先，我們回顧肯恩的矽基底施子自旋量電腦系統，如何控制及構成量子邏輯閘，包括：阿達馬邏輯閘(Hadamard gate) 、受控制否邏輯閘(CNOT gate) 等等。其次，我們介紹科羅托夫最佳化方法，在電腦模擬中，這是一種最有效解決大維度向量空間最佳化控制問題的方法。之後，我們利用科羅托夫方法應用於肯恩的矽基底予體電子自旋量子，由此找出阿達馬邏輯閘的最佳化控制序列。在實現量子電腦的事件中，量子去相干化依舊是最主要的障礙。因此， 我們考慮去相干的模型， 利用主方程式(master equation) 導出量子位元的運動方程式， 進而構成量子邏輯閘在外加(熱庫)環境演化的運動方程式。最後， 我們利用科羅托夫方法找出阿達馬邏輯閘在外加環境影響下的最佳化控制序列。

關鍵字

最佳化控制 ； 量子邏輯閘 ； 開放量子系統

並列摘要

One of the important criteria for physical implementation of a practical quantum computer is to have a universal set of quantum gates with operation times much faster than the relevant decoherence time of the quantum computer. In addition, high-fidelity quantum gates to meet the error threshold are also desired for fault-tolerant quantum computation. So the main purpose of his thesis is to focus on finding control parameter sequence in near time-optimal way using an optimization approach, the Krotov method, for high-fidelity quantum gates in the Kane silicon-based donor spin quantum computer architecture where the donor electron
spins are defined as quantum bits (qubits). We first review the basics of silicon-based donor spin quantum computer proposed by Kane, and how to control the system and construct the quantum gates, including Hadamard gate, CNOT gate and so on, in canonical gate decomposition ways. We then introduce the Krotov optimization method which is one of the most effective and universal computation methods for
solving optimal control problems with a large dimension of state vectors. The Krotov method is then applied to find the optimal control sequence of a Hadamard gate in the Kane quantum donor electron spin computer. Quantum decoherece is still a major obstacle for the implementation of a pratical quantum computer. We then consider a decoherence model, derive a corresponding quantum master equation of the reduced density matrix of the qubits, and construct equations of motion for quantum gate evolution in the presence of external (thermal) environments. Finally, we apply the Krotov method to find optimal control sequence for Hadmard gate operation under the influence of external environments.

並列關鍵字

Optimal control ； Quantum gate ； Open quantum systems

參考文獻

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