Special Mathematics Lecture (Mathematics of quantum information theory)

Goals of the Course

【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.

Objectives of the Course

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.

Course Contents or Plan

Lecture summary notes

• 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

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.

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.

Study Load (Self-directed Learning Outside Course Hours)

Problem Sheet

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.

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.

Text Book

• 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 distributed.

Reference Book

• W. Scherer. Mathematics of Quantum Computing. Springer, 2019.
• Lecture notes by Scott Aaronson: https://www.scottaaronson.com/qclec.pdf

Additional information

Reference Website

This lecture is provided under Creative Commons Attribution-Non Commercial-ShareAlike 4.0 International.

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