鑽石中氮原子空缺中心量子邏輯閘的最佳化控制

Abstract

量子邏輯閘（Quantum Gate）能驅使一系列完備的量子態基底作期望的轉換，並且是實現量子計算在真實物理上的基本 元件之一。 許多量子裝置被考慮用來實現量子計算的執行。，其中有鑽石中氮原子空缺中心（Nitrogen-Vacancy Center）的自旋（Spin），其相干性（Coherence）是很長的時間，即使在室溫下也可完成量子操作。所以，它成為可信賴在實際上執行量子計算的候選之一。然而與環境耦合所造成的去相干性（Decoherence）妨礙實現高精確度（Fidelity）的量子邏輯閘,故如何去克服其去相干性是現今主要的課題之一。最佳化控制方法（Optimal Control Method）是其中一個有效地抑止去相干性的工具，並且完成高精準度的量子邏輯閘。在本論文中，我們先介紹科羅多夫的最佳化控制方法（ Krotov Optimization Method）,它是一個最有效率且恆定的計算方法用於求解最佳化控制問題。再來，我們會呈現含時變外加控制的非馬可夫開放系統(Non-Markovian Open Quantum System)的主運動方程（Quantum Master Equation）。接著利用科羅多夫的最佳化控制方法來實行鑽石中氮原子空缺中心量子邏輯閘，我們得到的控制脈衝可實現高精準度X-gate，Z-gate以及CNOT-gate,其誤差約為10^{-4}。

The ability to steer a complete set of basis quantum states towards a desired transformation, often referred to as a quantum gate, is one of the essentiality for physical implementation of quantum computing. Many quantum devices are considered and implemented to realize quantum gates. The spin of a nitrogen-vacancy (NV) center in diamond has long coherence times and reliability of quantum operations even at room temperature. Therefore, it becomes a promising candidate for a practical implementation of quantum computing. One of the key challenges now is to overcome the decoherence induced by the uncontrolled couplings to the surrounding environment, preventing high-fidelity gate performance. Optimal control method is one of the effective strategy to dynamically suppress decoherence and to achieve the high-fidelity quantum gates. In this thesis, we first introduce the Krotov optimization method which is one of the most effective and universal computation methods for solving optimal control problems. Then we present the quantum master equation approach for non-Markovian open quantum systems with time-dependent external control. The Krotov based optimal method is then used to implement quantum logical gates for spins of a NV center in diamond, interacting with nearby noise qubits and a Non-Markovian bath. We find the control pulses to achieve high-fidelity X,Z and CNOT gates with errors about 10^{-4} for the NV center.