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TG4.1: High-performance computation and machine learning

I. Coordinator:
Pochung Chen 陳柏中 (NTHU)
pcchen [at] phys.nthu.edu.tw

II. Core Members:
Center Scientists
Pochung Chen 陳柏中 (NTHU)
Chia-Min Chung 鍾佳民 (NSYSU)
Yi-Ping Huang 黃一平 (NTHU)

Core members
1. Pochung Chen 陳柏中 (NTHU)  
2. Yi-Ping Huang 黃一平 (NTHU)   
3. Chia-Min Chung 鍾佳民 (NSYSU)  
4. Ming-Chiang Chung 張明強 (NCHU)  
5. Yu-Cheng Lin 林瑜琤 (NCCU)  
6. Hsiu-Chuan Hsu 許琇娟 (NCCU)  
7. Ching-Yu Huang 黃靜瑜 (THU)  

Postdocs
1. Amrita Ghosh (NCTS-HQ)  
2. Jozef Genzor (NCTS-HQ)  
3. Debasmita Maiti (Joint position with Pochung Chen)   

III. Research Themes:

• Entanglement structure in interacting topological and disordered systems

Entanglement is the feature that distinguishes the quantum many-body system from the classical system. Entanglement provides insights into the classification and physical properties of quantum phases of matter. In addition, the study of entanglement for many-body systems sits at the interface between condensed matter physics, high-energy physics, and quantum information.

We propose to study these subjects:
• Wavelet transformation and topological order.
• Entanglement structures in disordered system with strong interaction. 
• Entanglement structures in many-body localization.
• Topology and entanglement in non-equilibrium systems

Quantum phases of matter beyond equilibrium are an open research frontier. The interpretation and characterization of the spatiotemporal quantum order's physical properties require theoretical insights and advanced numerical techniques. We would like to develop numerical tools from different physical perspectives to tackle the challenge beyond equilibrium settings.

We propose to study these subjects:
• Topology and entanglement in quench and driven dynamics.
• Entanglement in non-equilibrium CFT.
• Integrable methods on non-equilibrium phases.
• Machine learning and Physics

The recent advances in machine learning shed new light on the study of many-body systems. The amazing efficiency in capturing essential physics in both classical and quantum complex systems suggests the possible connection with fundamental statistical mechanics. How to bridge and interpret the insights from machine learning to a theoretical physics framework is an intriguing problem.

We propose to explore these research directions:
• Use techniques from machine learning to tackle quantum many-body problems.
• Explore the possible connections between deep learning, the renormalization group, and tensor networks/MERA.
• Application of reinforcement learning in quantum control and error corrections.

IV. Activities

V. Expected achievements:
The TG group aims to develop advanced numerical techniques to simulate quantum systems, including but not limited to many-body quantum phases and phase transitions, non-equilibrium dynamics, and finite-temperature systems. 

Our group members have strong experience in simulating correlated electrons and frustrated spins. We will continue to publish works addressing the field's critical questions. We expect to achieve the following goals and join the forerunners in the research field.

• Developing advanced numerical techniques for quantum quench systems: We are developing new numerical techniques for quantum quench systems, and we expect that our techniques will be the standard tools in studying these systems. 
• Disorder-free localization phenomena: We are at the initial phase of exploring the disorder-free localization phenomenon. Our numerical techniques allow us to explore the fundamental mechanism behind the novel phenomena. We expect our work to give important insight into this new field and connect to the possible applications in quantum technologies.  
• We will also develop numerical methods to study the entanglement behavior of phases and phase transitions, hybridizing the subject with non-Hermitian dynamics and using a strong disorder renormalization group approach to study the related phenomenon. In addition, we would also like to bridge the artificial intelligence (AI) based approaches and suitable realizations in quantum computers to increase the synergy between different rapidly developing research frontiers with the study of quantum many-body dynamics. 
• We propose to initiate more collaborations within/outside the National Center of Theoretical Science along these lines. By organizing workshops and hosting visitors, we expect to have more and tighter international collaborations with the best groups, including Simon’s foundation in the US, Max Plank Institute in Germany, and Niels Bohr Institute in Denmark, and attract more young people to join the field.