TOKYO INSTITUTE OF TECHNOLOGY

Course description and aims

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.

Student learning outcomes

- Understand the characteristic mathematics that appears in quantum information physics
- 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 that will be developed

Class flow

Mainly in the format of lectures.

Course schedule/Required learning

Out-of-Class Study Time (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）

Assessment criteria and methods

Graded based on assignments.

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 (i.e., required knowledge, skills, courses, etc.)

Audiences are assumed to be familiar with undergraduate level quantum and statistical mechanics.