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| Title: | 基於重要性採樣在量子電腦上的糾纏熵量測
Measuring entanglement entropy with importance sampling on quantum computers |
| Authors: | 林敬軒
Lin, Ching-Hsuan |
| Contributors: | 許琇娟
Hsu, Hsiu-Chuan
林敬軒
Lin, Ching-Hsuan |
| Keywords: | 量子計算
量子糾纏
機器學習
類神經網路
Metropolis 演算法
重要性採樣
純度估算
Randomized Measurement
Quantum computing
Quantum entanglement
Machine learning
Neural network
Metropolis sampling
Importance sampling
Purity estimation
Randomized measurement |
| Date: | 2023 |
| Issue Date: | 2023-09-01 16:28:20 (UTC+8) |
| Abstract: | 測量量子態的物理量在日漸進步的量子計算研究中扮演十分重要的
角色，當問題擴展至更複雜或龐大的量子系統時，對現行的量子電腦
的使用環境和硬體限制仍是一大挑戰。
本研究基於已被廣泛使用的 Randomized Measurement，設計一針
對純度估算之工具。其架構結合古典端方法和量子端的 Randomized
Measurement，追求純度估算時擁有低統計誤差。透過古典機器學習近
似高運算資源消耗的量子電路測量，並在估算量子子系統純度時引入
重要性採樣，其相對於均勻採樣的優勢讓系統可以顯著的減少對運算
資源和時間的需求。
本文將完整的介紹我們的系統架構，接著，從虛擬機和真實機上Product state、GHZ state 實驗開始，延伸至較複雜的 Bell state 之淬火動力學的純度估算結果。我們利用此工具實現精準且高效率的糾纏熵測量，展望在日後亦可被推廣至其他量子系統和物理量的計算。
Measuring the properties of a quantum state plays an important role in the rapidly developing field of quantum computing researches nowadays. When expanding the goal on large-scale or complex quantum systems, one may find it challenging to utilize quantum computers under current hardware conditions and environments.
In this research, we designed a toolbox for purity estimation based on the widely used randomized measurement protocol. A combination of classical machine learning and randomized measurements on the quantum states enables us to pursue low statistical error on purity estimation on both quantum simulators and real machines.
This toolbox improves the efficiency of measuring purity on quantum circuits via classical machine learning and importance sampling. It’s advantage over uniform sampling is the significant reduction on the demand of computational resources and time.
In this thesis, we provide a detailed introduction of the system’s structure. Starting from the product state and GHZ state, we further perform experiments on quench dynamics of Bell state, which exhibits longer range entanglement. Finally, we show that this toolbox realizes measurements of entanglement entropy with higher precision and efficiency. This study is expectedto be applied to other quantum systems and physical quantities in the future. |
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[4] John Preskill. Quantum Computing in the NISQ era and beyond. Quantum, 2:79, Aug 2018.
[5] The ibm quantum development roadmap, 2022. https://research.ibm.com/blog/ibm-quantum-roadmap-2025, accessed on 05/30/2023.
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[13] Aniket Rath, Rick van Bijnen, Andreas Elben, Peter Zoller, and Benoît Vermersch. Importance sampling of randomized measurements for probing entanglement. Phys. Rev. Lett., 127:200503, Nov 2021.
[14] Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, and Harald Weinfurter. Elementary gates for quantum computation. Physical Review A, 52(5):3457–3467, Nov 1995.
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[16] Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010.
[17] Po-Yao Chang. Topology and entanglement in quench dynamics. Physical Review B, 97(22), Jun 2018.
[18] Joseph Vovrosh and Johannes Knolle. Confinement and entanglement dynamics on a digital quantum computer. Scientific Reports, 11(1), Jun 2021.
[19] Francesco Mezzadri. How to generate random matrices from the classical compact groups, 2007. arXiv:math-ph/0609050 |
| Description: | 碩士
國立政治大學
應用物理研究所
110755003 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0110755003 |
| Data Type: | thesis |
| Appears in Collections: | [應用物理研究所 ] 學位論文
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