張量網路時間演化演算法在量子電路上之實踐

Abstract

操作和測量量子系統方面在過去幾年取得了顯著進展，這使得量子計算成為一個充滿潛力的研究領域，其中涵蓋了多體物理等多個主題。張量網絡（TNs）顯示出強大的數值技術，可以有效捕捉量子糾纏和相關性，其中，矩陣積態（MPS）是最常用的框架。MPS可以轉換為參數化的量子電路，並與時間演化算符結合，從而構建基於MPS的混合量子經典演算法。本論文對這種方法進行了深入探討，並展示了使用IBM噪音模型的模擬數據。然而，由於缺乏大規模量子錯誤更正，這種變分量子時間演化算法難以在真實量子處理器上實施。因此，我們提出了一種方法，直接對初始態施加時間演化算符。在減少量子閘數量後，我們在IBM量子計算機上實現了這些量子電路，並結合了全域去極化錯誤緩解方式。我們成功捕捉了易辛模型（TFIM）磁化強度的主要頻率，這也是本論文的最後部分。

Over the past few years, we have seen remarkable progress in our ability to manipulate and measure quantum systems, which makes quantum computing an exciting area of research on various themes including many-body physics. Tensor networks (TNs) have recently shown powerful numerical techniques that capture quantum entanglement and correlations. Among all the TN methods, matrix product state (MPS) is the most widely used framework and it also ensures the use of TNs is a parameterized wavefunctions. MPS can be transformed into parameterized quantum circuit, and combined with time evolution operator, hybrid quantum-classical algorithm base on MPS can be constructed. This thesis provides a more in-depth exploration of this method. And the data of simulations using the noise model of IBM real device were also exhibited in this thesis. Nevertheless, this variational quantum time evolution algorithm can barely be implemented on real quantum processors due to the lack of large-scale quantum error correction. Thus, we propose a time evolution method by directly impose time evolution operator on initial state. After reducing the number of quantum gates, we implement the quantum circuits on IBM quantum computers. Combined with error mitigation technique of global depolarizing errors, the dominant frequency of the transverse field Ising model (TFIM) can be captured and this is the last part of this thesis.