2022 Faculty Courses School of Science Department of Physics Graduate major in Physics
Special Topics in Physics VIII
- Academic unit or major
- Graduate major in Physics
- Instructor(s)
- Masayuki Ohzeki
- Class Format
- Lecture (Livestream)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Intensive
- Class
- -
- Course Code
- PHY.P558
- Number of credits
- 100
- Course offered
- 2022
- Offered quarter
- 2Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
As theoretical and experimental research on quantum computers matures, interest in the field is growing.
One unexpected connection is statistical mechanics.
Quantum annealing solves combinatorial optimization problems, and the amount of computation required to solve them is related to the quantum phase transition of the system under study.
Quantum error correction codes are related to frustration and gauge transformations of the spin-glass model.
Measuring quantum computation uses the distribution function of a classical spin system to investigate its properties.
The typical performance of quantum random circuits is known to correspond to the classical spin-glass model.
In studying such quantum computers, the correspondence with statistical mechanics cannot be avoided.
In this lecture, we will introduce such various points of contact and learn the knowledge of statistical mechanics necessary to understand quantum computers.
Course description and aims
To be able to understand quantum computers from the aspect of statistical mechanics.
Keywords
Quantum computers, quantum annealing, statistical mechanics, classical spin systems, spin glass
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 | Review of Quantum Mechanics and Statistical Mechanics | Check various calculations |
| Class 2 | Duality and phase transition | Check various calculations |
| Class 3 | Spin glass and gauge transformation | Check various calculations |
| Class 4 | Quantum error-correcting code and spin glass | Check various calculations |
| Class 5 | Measurement-based quantum computation and partition function | Check various calculations |
| Class 6 | Random quantum circuit and replica method | Check various calculations |
| Class 7 | Some progress | Check various calculations |
Study advice (preparation and review)
Textbook(s)
Spin glass and information processing by Hidetoshi Nishimori
Quantum Computation with Topological Codes: from qubit to topological fault-tolerance by Keisuke Fujii
https://arxiv.org/abs/1504.01444
Reference books, course materials, etc.
Distributed as appropriate.
Evaluation methods and criteria
Mainly by homework
Related courses
- PHY.S301 ： Statistical Mechanics
- PHY.S312 ： Statistical Mechanics II
- PHY.S440 ： Statistical Mechanics III
- PHY.Q207 ： Introduction to Quantum Mechanics(Lecture)
- PHY.Q208 ： Quantum Mechanics II(Lecture)
- PHY.Q311 ： Quantum Mechanics III(Lecture)
Prerequisites
Understanding of the basics of statistical mechanics.