||Scheme for Designing Quantum Logic Gate via Integrated Optimal Control and Genetic Algorithm
||Department of Engineering Science
In this thesis, we focus on diatomic molecular system (C^12 O^16) whether through laser pulse shaping simulation experiment to achieve quantum computation and the feasibility of quantum logic gate operations. The simulation often used two algorithms to control the electric field. One is optimal algorithm which can seek the laser pulse electric field used by the permutations between the frequency location and electric field amplitude through the greatest flexibility in the time domain, but it’s often doubt whether this electric field can be modulated in the actual experiment. Two is genetic algorithm which is a heuristic search method, the main task is search laser electric field within appropriate range of laser pulse waveform in the discrete frequency domain, due to the quantum bit (qubit) gradually raise up will cause search result divergence which led to non-convergence. Therefore, this project will be a combination of two methods which is the integrated optimal control and genetic algorithm to overcome these problems. At first, use the optimal control theory to obtain the initial electric field of the quantum logic gates and select the important frequency position to make reservations, then use by chromosomes form to encoding electric field and adjusting experimental parameter. Let it be initial electric field in genetic algorithm, and after evolving to achieve optimal feasibility pulsed laser electric field. Finally, this thesis has successfully simulated one qubit Hadamard and NOT gates, two qubit CNOT gate and three qubit Toffoli gate.
第一章 緒論 1
1-1 研究背景 1
1-2 文獻回顧 4
1-3 研究動機 7
1-4 本文架構 8
第二章 量子控制與資訊理論 9
2-5希爾伯特空間(Hilbert Space) 20
2-6約化李維空間(Liouville Space) 22
第三章 量子最佳化控制與飛秒雷射脈衝 31
3-1 CO分子轉動-振動能階模型 31
3-4-1 4-f脈衝整形裝置 47
3-4-2 LC-SLM的色散補償原理 49
第四章 整合最佳化控制及基因演算法 53
第五章 模擬結果與分析 73
5-1 一個量子位元邏輯閘之模擬 73
5-1-1 NOT量子邏輯閘 73
5-1-2 Hadamard量子邏輯閘 78
5-2 二個量子位元CNOT量子邏輯閘之模擬 84
第六章 結論與未來展望 99
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