利用單NQ串標記的量子位元高效編碼來模擬電子組態問題

Abstract

在使用量子處理器模擬電子結構問題時，將量子態對應到量子位元空間的編碼是必要的。在已被提出的編碼方法中，量子位元高效編碼透過僅將正確電子數的量子態編碼到量子位元空間，來減少量子位元的使用量。然而，在使用量子位元高效編碼時，因為對激發算符的直接展開，系統哈密頓量中的包立項數量增長得比其他編碼方法快得多。在量子位元高效編碼的結構下，一種新的標記方法在本論文中被提出，被稱為單NQ串標記。使用此標記的目的是通過結合激發算符表達式中的相同項來減少包立項的數量。我們使用單NQ串標記的量子位元高效編碼來模擬電子結構問題，並得到了優於使用預設標記的模擬結果。

A fermionic-to-qubit encoding is essential in simulating electronic structure problems with quantum processors. Among the proposed encoding schemes, the qubit-efficient encoding (QEE) reduces the qubit usage to O(m log n) by only encoding physical configurations to qubit space, compared to other common encoding schemes that need n qubit to simulate the system with n spin-orbitals and m electrons. However, the number of Pauli terms in the QEE Hamiltonian grows much faster than other encoding schemes because of the direct expansion on the excitation operators. Under the structure of QEE, a new labeling method, named single NQ-string labeling, is proposed in this thesis, which aims to reduce the number of Pauli terms by combining similar terms in the expression of excitation operators. Simulations for electronic structure problems using QEE with the single NQ-string labeling are made, and the results outperform those of QEE with default labeling and the parity encoding.