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  • 學位論文

非馬可夫開放系統中量子邏輯閘的最佳化控制

Optimal Control of Quantum Gates for a Non-Markovian Open Quantum Qubit System

指導教授 : 管希聖
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摘要


量子邏輯閘 (Quantum Gate) 是在實際的物理上實現量子電腦最基本的元件。其中,固態的約瑟夫森量子元件 (Superconducting Josephson-Junction Qubit) 是實現量子邏輯閘最好的候選人之一。 而通常在面對建立量子邏輯閘的過程中,受環境影響的去相干化 (Decoherence) 和耗散 (Dissipation) 是最主要的課題。藉由克服此課題我們才有可能建造一個高準確度 (Fidelity) 且錯誤大約在10^-3~10^-4之間的量子邏輯閘。因此,找尋一個好的操作策略來降低影響與建造量子邏輯閘是非常重要的。最佳化控制方法 (Optimal Control Method) 是其中一個有效的工具,並且已經被用在減少與環境的作用和建造高準度的量子邏輯閘上。另外,最佳化控制方法亦已經被拿來使用在假設環境與系統是沒有記憶效應的馬可夫開放系統 (Markovian Open Qunatum System) 上。但是,在諸多實際的相關實驗上,非同時的記憶效應 (Non-Local Memory Effect) 對於量子系統的影響是需要被關切的。尤其是在固態的裝置上環境的記憶效應是不可忽略的。所以,將最佳化控制方法延伸到在非馬可夫開放系統 (Non-Markovian Open Quantum System) 建立量子邏輯閘的研究是值得且具有必要性的。在本論文裡,我們首先回顧一些基礎的量子超導電路 (Superconducting Quantum Circuit) 並且介紹量子計算元件 (Quantum Qubit Device) 。接著,被視為解決最佳化問題其中一個最有效且恆定的計算方法─科羅多夫的最佳化控制方法 (Krotov Optimization Method) 將被引入。我們跟著推導非馬可夫開放系統以及含時的非馬可夫量子模型,並且將科羅多夫最佳化控制方法應用在非馬卡夫的單一量子邏輯閘 (Z-Gate)上。 並且發現控制相關係數 (Control-Dissipation Correlation) 和記憶效應 (the memory effect) 在高準確度的量子邏輯閘建立上,扮演極重要的角色。

關鍵字

開放系統 量子 邏輯閘 最佳化 控制

並列摘要


One of the fundamental criteria for physical implementation of a practi- cal quantum computer is to design a reliable universal set of quantum gates. A promising class of candidates for realization of scalable quantum com- puters are solid-state quantum devices based on superconducting Josephson- junction qubits. Typically, a central challenge to overcome in this enterprise is decoherence and dissipation induced by the coupling to the its environ- ment. It is thus important to find strategies to alleviate the problems and to to build a high-fidelity quantum gates meeting the error threshold of about 10− 3 ∼ 10− 4 . Optimal control method is one of the powerful tools already applied to the problem of dynamical decoupling from the environment and to finding the control sequence for high-fidelity quantum gates. Furthermore, optimal control technique has recently been applied to Markovian open quan- tum systems in which the approximation of the bath correlation function be- ing delta-correlated in time is assumed. H owever, in some real experiments, we need to consider the non-local memory effects of the bath on the dynamics of the qubits. Especially, the bath memory effects are typically non-negligible in solid state devices. Thus it is desirable to apply optimal control technique to quantum gate operations in the non-Markovian open quantum systems. In this thesis, we first review some basic elements of superconducting quan- tum circuit and introduce the quantum qubit devices. We then introduce the Krotov optimization method which is one of the most effective and univer- sal computation methods for solving optimal control problems. Then the quantum master equation approach for non-Markovian open quantum sys- tems with time-dependent external control are presented. The Krotov based optimal method is then used to implement quantum logical gates for a single qubit in a non-Markovian environment. It is possible to achieve high-fidelity Z-gate with error less than 10^−5 for the non-Markovian open qubit system. The control-dissipation correlation and the memory effect of the bath are cru- cial in achieving the high-fidelity gates.

並列關鍵字

Optimal Control Quantum Gate Non-Markovian Markovian Open Quantum Qubit System

參考文獻


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