授業の目的 【英語】
Goals of the Course [ENG] | | 【Standardized across all programs】 In a global and interconnected society, mathematics play a central role. They are at the root of all communications tools, and serve as a universal language for natural and social sciences. All current technological developments are based on them. Mathematics can also be learned, enjoyed, and shared by everybody. Studying mathematics is also learning humility, tolerance, and diversity.
The aim of these Special Mathematics Lectures is to provide a solid knowledge on various mathematical topics. Concomitantly, students will develop a rigorous argumentation and a critical thinking. Each semester, a new subject is proposed, and these lectures are accessible to all students of Nagoya University, independently of their major and of their academic age. These special lectures also offer a unique opportunity to study in an international, transdisciplinary, and friendly environment. |
|
|
授業の達成目標 【英語】
Objectives of the Course [ENG] | | | The course will introduce the basics of quantum computation and information from a mathematical perspective. The objective is to acquire knowledge of the mathematical framework describing quantum bits (qubits), their properties and how they can be used to construct quantum computational circuits. Students will also obtain a basic understanding of quantum mechanical systems and their connection concepts in linear algebra. |
|
|
授業の内容や構成
Course Content or Plan | | Planned content (tentative):
- Introduction and linear algebra review
- Basic postulates of quantum mechanics
- Quantum states, evolution and measurement
- Entanglement
- Quantum circuits, algorithms and computation
- Introduction to quantum operations and information theory
- Further applications
この科目は英語で行います．
授業は量子情報・量子計算に用いられる数学の基礎の入門です．線形代数を枠組みとして量子力学の原則を学び，量子ビット（qubit）という量子情報の最小単位を導入します．数学的な性質，物理学や量子計算への応用も考察し，量子ビットでの情報通信の仕方は古典の情報通信との違いやメリットを理解する目標です． |
|
|
履修条件・関連する科目
Course Prerequisites and Related Courses | | A working knowledge of linear algebra (such as that obtained from the Linear Algebra I and II courses) will be expected.
Some familiarity with complex numbers and quantum mechanics will also be helpful, but is not required.
Motivated 1st year students can also attend without these prerequisites but after a discussion with the instructor.
線形代数の知識を期待しますが，やる気であれば，誰でも受講する可能です．複素数と量子力学を勉強したことがあるのは役立ちますが，必要ではありません．1年生も担当者と相談後，履修は可能です． |
|
|
成績評価の方法と基準
Course Evaluation Method and Criteria | | The grade will be determined by exercises and homework questions submitted by students throughout the semester.
Students who wish to withdraw from the topic are asked to inform the instructor. |
|
|
教科書
Textbook | | M. A. Nielsen & I. L. Chuang: Quantum Computation and Quantum Information. Cambridge University Press, 2010.
It is not necessary to purchase this textbook.
Lecture summary notes and other references will also be distriubuted. |
|
|
参考書
Reference Book | | W. Scherer. Mathematics of Quantum Computing. Springer, 2019.
Lecture notes by Scott Aaronson: https://www.scottaaronson.com/qclec.pdf |
|
|
課外学修等
Study Load (Self-directed Learning Outside Course Hours) | | | Exercises and homework questions will be given to students. Students are expected to read their notes, and to be familiar with the content of the previous lectures before each new lecture. |
|
|
注意事項
Notice for Students | | | It is expected that the students will show a certain maturity in studying independently and in choosing some exercises and problems to solve. Study sessions might be organized on a semi-regular basis. |
|
|
本授業に関するWebページ
Reference website for this Course | | |
|
担当教員からのメッセージ
Message from the Instructor | | "The course is a great opportunity to learn mathematics in an international environment.
日本人が含まれる一般プログラムの学生へ:
授業の参加・受講は大歓迎です！NU-EMIプロジェクトのおかげで，留学生のチューターによるサポートが無料で提供されています．" |
|
|
実務経験のある教員等による授業科目（大学等における修学の支援に関する法律施行規則に基づくもの）
Courses taught by Instructors with practical experience | | |
|
授業開講形態等
Lecture format, etc | | B-3）Face-to-face course （both simultaneous interactive and on-demand methods will be provided when necessary)
* Classrooms for face-to-face classes can be found in Timetable B on the ILAS website. |
|
|