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| 題名: | 以數位量子電腦模擬價鍵態動力學
Simulating the dynamics of a valence bond state with digital quantum computers |
| 作者: | 黃靖泰
Huang, Ching-Tai |
| 貢獻者: | 林瑜琤
Lin, Yu-Cheng
黃靖泰
Huang, Ching-Tai |
| 關鍵詞: | 含噪聲中尺度量子計算
Hadamard 測試
隨機測量
經典影子
Rényi 糾纏熵
Loschmidt 回聲
Noisy Intermediate-Scale Quantum (NISQ) computation
Hadamard test
randomized measurement
classical shadow
Rényi entanglement entropy
Loschmidt echo |
| 日期: | 2025 |
| 上傳時間: | 2025-09-01 16:52:09 (UTC+8) |
| 摘要: | 本研究以 IBM Quantum 提供之量子電腦與模擬器，實作一維完全二聚化 XXZ 自旋-1/2反鐵磁鏈之量子淬火動力學，並透過「Hadamard 測試」(Hadamard test) 與「隨機測量」兩種方法計算隨時間演化之 Rényi 糾纏熵與 Loschmidt 回聲。我們以一價鍵固態為初始態，進行 XXZ 自旋鏈具各種非同向性參數之淬火實驗，比較兩種方法的效能及擴展性。
Hadamard 測試可直接估算由完全二聚化 XXZ 自旋鏈產生的任意時間點之量子態係數，能準確求得小系統於真實量子機器模擬之結果。然而當系統尺寸增加，因電路深度上升與係數絕對值遞減，在具噪聲的真實量子電腦上將導致顯著失真的結果，侷限其僅適用小系統模擬。為克服上述侷限，我們利用量子電路執行時間演化。因哈密頓量完全二聚化性質，我們得以在無 Trotter 誤差情形下以量子電路製備不同時間點之量子態，並進一步以隨機測量及其後處理法估算 Rényi 糾纏熵與 Loschmidt 回聲。在隨機測量選取量子閘方面，我們考慮兩種隨機基底轉換：Haar 隨機單量子閘以及隨機 Pauli 測量。隨機 Pauli 測量在真實量子硬體執行成本較低，可在現有資源下提供可靠的數據。在後處理部分，我們比較 Hamming 距離方法與經典影子 (classical shadow) 技術。我們實驗結果顯示，經典影子後處理法在高糾纏態下表現佳，具低誤差，而 Hamming 距離法在精確度上具整體穩定性。
綜合而言，Hadamard 測試適用於小系統高精確度交疊計算；而隨機測量法則更適用於含噪聲中尺度量子計算，具較高的實用性與擴展性。本研究展示兩類方法在不同情境下的優勢與限制，亦提供未來研究多體量子模擬與評估量子電腦效能之基礎。
This thesis investigates the quench dynamics of a one-dimensional fully dimerized spin-1/2 XXZ antiferromagnetic chain using IBM Quantum computers and simulators. Two approaches—the Hadamard test and randomized measurements—are employed to evaluate the time-evolved Rényi entanglement entropy and Loschmidt echo. We initiate the dynamics from a valence-bond solid and evolve it under the XXZ Hamiltonian with a range of anisotropy parameters, using this setting to benchmark the performance and scalability of these two methods.
The Hadamard test provides direct amplitude estimation of the time-evolved quantum state generated by the fully dimerized Hamiltonian, yielding high-precision results for small systems even on real quantum devices. However, as system size increases, deeper circuits and smaller amplitude magnitudes significantly reduce accuracy on noisy hardware, restricting its use to small-scale simulations. To overcome this limitation, we execute Trotter-error-free time-evolution circuits for the dimerized XXZ chain and apply randomized measurement techniques to estimate observables. We compare Haar-random single-qubit unitaries and random Pauli measurements, with the latter offering lower hardware overhead and reliable performance on current hardware. For post-processing, we assess both the Hamming distance method and the classical shadow technique. Our results show that classical shadows provide lower estimation errors in highly entangled regimes, while the Hamming distance method provides robust performance across parameter ranges.
In summary, the Hadamard test is well-suited for high-precision overlap estimation in small systems, whereas randomized measurement methods offer greater practicality and scalability for noisy intermediate-scale quantum (NISQ) computations. This study clarifies the strengths and limitations of both approaches under various scenarios and provides a foundation for future studies in many-body quantum simulation and quantum hardware benchmarking. |
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[20] S. Chen, W. Yu, P. Zeng, and S. T. Flammia. “Robust Shadow Estimation.” PRX Quantum 2 (2021), p. 030348.
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| 描述: | 碩士
國立政治大學
應用物理研究所
112755001 |
| 資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0112755001 |
| 資料類型: | thesis |
| 顯示於類別: | [應用物理研究所 ] 學位論文
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