Calculation of Quantum Entanglement Entropy Using the Holographic Principle and Artificial Intelligence = 홀로그래피 원리와 인공지능을 이용한 양자 얽힘 엔트로피 계산

다국어 초록 (Multilingual Abstract)

Efforts to unify quantum field theory (QFT) and gravity through supersymmetry have faced significant challenges, with no experimental evidence of supersymmetry at the energy scales probed by the Large Hadron Collider (LHC). However, the discovery of the AdS/CFT correspondence, or holography, has provided a new framework to bridge these fields. This duality links supergravity in Anti-de-Sitter (AdS) spacetime, a negatively curved spacetime with at least one time-like space dimension, to strongly correlated QFTs on its boundary. Visualized spatially excluding the time axis, these spacetimes exhibit a sphere, where supergravity governs the interior, while the boundary hosts a gravity-free QFT characterized by strong many-body interactions.

Holography has emerged as a powerful tool for addressing complex many-body problems, such as strongly entangled matters including chemistry and biology and quantum computing systems that require robust error correction through strong correlations. By mapping these problems onto analytically tractable black hole physics, the framework overcomes the limitations of conventional perturbation methods.

Deriving corresponding supergravity solutions from QFT remains challenging due to the increasing dimensional complexity, even though the AdS-to-QFT direction is well-established. Neural network-based AI models offer a promising approach to this problem by learning patterns from known AdS supergravity–QFT pairs and generalizing them to infer supergravity configurations for given QFTs.

This project incorporates modifications to enhance model flexibility and performance to prior studies using the Linear-Axion and Gubser-Rocha models. By integrating these improvements with AI-driven methods, the project advances the reverse-mapping process, contributing to both theoretical physics and practical applications in strongly correlated systems and quantum technologies.

국문 초록 (Abstract)

초대칭성에 기반해 양자장론과 중력이론을 통합하려는 시도는 초대칭성의 실험상 미발견으로 실패라는 것이 중론이다. 그러나 시공간의 관점에서 음의 곡률에 적어도 한 공간차원은 시간적인 반안좌성 (Anti-de-Sitter) 시공간에 대한 블랙홀의 초중력 이론이 시공간에 충분한 경계조건이 있어 공간차원만 시각화시 구형이라면, 구의 표면에서 평 범한 공간의 양자장론이 대응하는, 홀로그래피로 불리는 성질이 발견됐다. 이는 물리, 화학, 생물학 분야 응집물질의 강한 양자얽힘이나 더 많고 서로 강하게 얽혀야 계산능 력과 에러수정에 유리한 양자컴퓨터 등 양자적 강상관계 문제를 불안정한 섭동전개가 아닌 단일 블랙홀 물리로 바꿔 더 정확한 결과를 해석적으로 얻는 수단을 제공한다.

역으로 양자장론으로부터 대응하는 초중력 블랙홀을 찾기는 차원의 추가와 다른 변 수들의추가로쉽지않으나,신경의특성을모방한인공신경망학습모델에증명의정방향 초중력 블랙홀-양자장론 쌍을 학습시키고 증명의 역방향 추론을 하는 데 대하여, 본 연 구는 기존 연구에 기반하되 선형 엑시온과 굽스터-로차 모델을 학습시킴에 있어 성능과 학습데이터에 개선 가능한 부분을 반영하고자 한다.

목차 (Table of Contents)

• Abstract (English) i
• Abstract (Korean) iii
• List of Contents v
• List of Tables vii
• List of Figures viii
• 1 Introduction 1
• 1.1 Introduction 1
• 2 The Backgrounds and The Methodology 3
• 2.1 The Curvatures in Geometry in Physics 3
• 2.1.1 The Curvature, from Mathematics to Physics 3
• 2.1.2 Curvature in General Relativity 7
• 2.2 Types of Curved Spacetime: What is Anti-de-Sitter Spacetime 8
• 2.2.1 The Euclidean Spacetime 9
• 2.2.2 The de-Sitter Spacetime 11
• 2.2.3 The Anti-de-Sitter Spacetime 13
• 2.2.4 Spacetimes in General Views 15
• 2.3 The Correspondence of Theories between AdS and flat Spacetime 17
• 2.3.1 The AdS/CFT Correspondence 18
• 2.3.2 The Limits, and a Novel Approach with Neural Networks 30
• 2.4 The Entanglement Entropy 32
• 2.4.1 The Basic Concept of the Quantum Entanglement Entropy 32
• 2.4.2 Switching from QFT to AdS Spacetime 34
• 2.4.3 The Action Models of Gravity 36
• 2.5 The Methodology of Approaching 42
• 2.5.1 The Details of Model to Demonstrate 42
• 3 Results 46
• 3.1 Computational Level Modifications 46
• 3.1.1 Additional Structure to Neural Nodes 49
• 3.2 Equation Level Modifications 53
• 3.2.1 The Linear-Axion Model 53
• 3.2.2 The Gubster-Rocha Model 55
• 4 Discussion 57
• Summary 61
• References 64
• A Fragments of the Unuseds 70
• A.1 About the Penrose junction condition 70
• A.2 About 2.3.1 71
• A.2.1 The Supercurrent 71
• A.2.2 The supersymmetry comparison by the sectors 72
• A.3 About 2.4.3 72
• A.3.1 The Beginning of Derivatization of the Gubser-Rocha Model 72
• B Summary in Mind map forms 73
• C Codes 76
• C.1 main 76
• C.2 Libraries 78
• C.2.1 tensormultiprocessings.py 78
• C.2.2 phyparameters.py 107
• C.2.3 perfparameters.py 108
• C.2.4 timegen.py 108
• C.2.5 refdata.py 110
• C.2.6 model.py 116
• C.2.7 teaching.py 126
• C.2.8 dataiod.py 133
• D Abbreviations 147
• Acknowledgements 148