2023 Faculty Courses School of Computing Department of Mathematical and Computing Science Graduate major in Mathematical and Computing Science
Quantum Computation and Quantum Information
- Academic unit or major
- Graduate major in Mathematical and Computing Science
- Instructor(s)
- Ryuhei Mori
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- MCS.T413
- Number of credits
- 200
- Course offered
- 2023
- Offered quarter
- 4Q
- Syllabus updated
- Jul 8, 2025
- Language
- Japanese
Syllabus
Course overview and goals
With the progress of quantum information technology in recent years, learning the fundamentals of quantum information processing has become increasingly important. This course deals with the fundamentals of quantum mechanics based on linear algebra and information processing using quantum mechanics. Students learn the fundamentals of computation and communication based on quantum mechanics.
This is an intensive lecture held on Zoom. Please check the Japanese version of the syllabus for the schedule.
Course description and aims
The followings are student learning outcomes.
(1) Fundamentals of quantum mechanics based on linear algebra.
(2) Understanding of quantum mechanics based on nonlocality.
(3) Basic quantum information processing such as quantum teleportation.
(4) Fundamentals of quantum computation using quantum circuits.
(5) Basic quantum algorithms such as phase estimation, Shor's algorithm, Grover's algorithm etc.
Keywords
Quantum computation, quantum information
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Conducting face-to-face lectures. All documents used in the lectures are uploaded to GitHub. Assignments are given in each class.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Quantum theory: Quantum states and quantum measurements, Bell test | Exercises on formulation of quantum theory |
| Class 2 | Single qubit: Bloch sphere, unitary operators, universality of single qubit gate | Calculations of unitary operation on single qubit |
| Class 3 | Two and more qubits: Tensor product, entanglement, Schmidt decomposition | Calculations of unitary operation on two and more qubits |
| Class 4 | Spectral decomposition, purification and superdense coding | Exercises on spectral decomposition and purification |
| Class 5 | Quantum teleportation | Exercises on partial measurement of quantum state in joint system |
| Class 6 | Nonlocality: Bell's inequality, GHZ paradox, XOR games | Calculations of the winning probability of XOR games |
| Class 7 | Discrimination of quantum states: Holevo--Helstrom theorem, trace norm | Calculation of trace norm |
| Class 8 | Quantum cryptography: BB84 | Exercises on quantum cryptography |
| Class 9 | Quantum circuit: Deutch--Josza algorithm | Calculations of the output state of quantum circuits |
| Class 10 | Universality of quantum circuit 1 | Design of quantum circuits |
| Class 11 | Universality of quantum circuit 2 | Design of quantum circuits |
| Class 12 | Quantum phase estimation | Analysis of quantum phase estimation |
| Class 13 | Shor's algorithm | Derivation of eigenvector of unitary operators |
| Class 14 | Grover's algorithm and its optimality | Proofs on generalizations of Grover's algorithm |
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 required.
Reference books, course materials, etc.
Michael A. Nielsen and Isaac L. Chuang, "Quantum Computation and Quantum Information," 10th Anniversary edition, Cambridge University Press 2010.
Evaluation methods and criteria
Assignments: 100%
Related courses
- MCS.T203 ： Linear Algebra and Its Applications
Prerequisites
There is no condition for taking this class. But it requires sufficient understanding of linear algebra.