2021 Faculty Courses School of Science Department of Physics Graduate major in Physics
Advanced Special Lectures in Physics XXXIX
- Academic unit or major
- Graduate major in Physics
- Instructor(s)
- Hiroaki Matsueda
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- PHY.P679
- Number of credits
- 100
- Course offered
- 2021
- Offered quarter
- 3Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
Information-theoretical approaches to various fields of physics have become extremely important in recent years. This is because the approaches are effective phenomenological ones that understand core heart of renormalization group and so on. Based on the concept of quantum entanglement, we discuss the structural theory of the quantum wave function. We also discuss the deep relationship between its structure and space-time physics. Furthermore, we examine the basic mathematics of the approaches such as singular value decomposition, wavelet, and information geometry, and we know their rich physical meanings. We will become familiar with the trends and thinking methods of interdisciplinary research in recent years, and we aim for a comprehensive understanding of the mathematical structure behind quantum information physics.
Course description and aims
- Understand the characteristic mathematics that appears in quantum information
- Understand entanglement as an index for understanding quantum many-body states
- Understand the scaling formula of entanglement entropy
- Understand the mathematical structure of wavefunctions according to the criticality of the system
- Understand the geometry of quantum states and the gauge/gravity correspondence
Keywords
Quantum spin systems, matrix product, quantum/classical correspondence, singular value decomposition (SVD), renormalization group, entanglement, entanglement entropy, matrix product state (MPS), tensor network, entanglement renormalization, multiscale entanglement renormalization ansatz (MERA), Bethe ansatz, conformal field theory (CFT), wavelet hyperbolic geometry, black hole, holography principle (bulk/edge correspondence, gauge/gravity correspondence), information geometry
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Mainly in the format of lectures
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Quantum spin systems | |
| Class 2 | Singular value decomposition | |
| Class 3 | Entanglement | |
| Class 4 | Tensor-network variational method and Bethe ansatz | |
| Class 5 | Close relationship between information and geometry | |
| Class 6 | From tensor network to spacetime | |
| Class 7 | Information-theoretical view for the analysis of gauge/gravity correspondence | |
| Class 8 | Analysis of many-body states by singular-value decomposition of correlation function matrix | Seminar |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None
Reference books, course materials, etc.
・松枝宏明著 量子系のエンタングルメントと幾何学－ホログラフィー原理に基づく異分野横断の数理－（森北出版）
・高柳匡著 ホログラフィー原理と量子エンタングルメント 臨時別冊・数理科学 ＳＧＣライブラリ１０６（サイエンス社）
・堀田昌寛著 量子情報と時空の物理 －量子情報物理学入門－ 臨時別冊・数理科学 ＳＧＣライブラリ１０３（サイエンス社）
Evaluation methods and criteria
Graded based on assignment.
Related courses
- PHY.Q207 ： Introduction to Quantum Mechanics(Lecture)
- PHY.Q208 ： Quantum Mechanics II(Lecture)
- PHY.S301 ： Statistical Mechanics(Lecture)
- PHY.S312 ： Statistical Mechanics II(Lecture)
Prerequisites
Audiences are assumed to be familiar with undergraduate level quantum and statistical mechanics.