臺灣博碩士論文加值系統

在量子化學計算領域中，解決大分子的電子結構問題是個重要的研究課題。量子電腦的出現提供了我們解決古典量子化學難解問題的可能性。在本論文中，我們在不同的擬設下使用稱為變分量子特徵解法的量子—古典混合演算法去模擬一些簡單的分子並比較與討論其結果。最後，我們闡明了可以在不影響能量準確度的情形下減少基於么正耦合簇單激發與雙激發方法擬設的變數數量，進而減少此擬設在量子電腦上的邏輯閘使用量。

Solving electronic structure problems for large molecules is an important research topic in quantum computational chemistry. Quantum computers provide a possibility for solving these quantum chemistry problems that are intractable classically. In this thesis, we use the hybrid-quantum classical algorithm — variational quantum eigensolver (VQE) to simulate the molecular energies of some simple molecules based on two different kinds of ansatzes and discuss their results. In particular, we illustrate the number of parameters of unitary coupled-cluster with single- and double-excitation (UCCSD) ansatz can be educed without the loss of accuracy in energy difference.

摘要 I
Abstract II
List of Figures V
List of Tables VII
1 Introduction 1
2 Quantum Computation on Quantum Chemistry 2
2.1 Quantum Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Electronic Structure Problem . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Mapping Fermions to Qubits . . . . . . . . . . . . . . . . . . . . . . . 6
2.3.1 Jordan-Wigner Transformation . . . . . . . . . . . . . . . . . 7
2.3.2 Parity Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.3 Bravyi-Kitaev Encoding . . . . . . . . . . . . . . . . . . . . . 8
2.4 Reduction of Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Variational Quantum Eigensolver for Quantum Chemistry 12
3.1 Parameterized state preparation . . . . . . . . . . . . . . . . . . . . . 13
3.1.1 Chemistry-inspired ansatz . . . . . . . . . . . . . . . . . . . . 13
3.1.2 Hardware heuristic ansatz . . . . . . . . . . . . . . . . . . . . 16
3.2 Energy measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Optimization and classical feedback . . . . . . . . . . . . . . . . . . 18
4 Results and Discussions 20
4.1 Ansatz Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.1.1 UCCSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.1.2 Heuristic ansatz . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2 Measurement and Optimization . . . . . . . . . . . . . . . . . . . . . 28
4.3 Comparison with Classical and Experimental results . . . . . . . . . . 31
4.4 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . 32
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