2021 Quantum Computation and Quantum Information

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Academic unit or major
Graduate major in Mathematical and Computing Science
Instructor(s)
Mori Ryuhei 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Tue5-6()  Fri5-6()  
Group
-
Course number
MCS.T413
Credits
2
Academic year
2021
Offered quarter
3Q
Syllabus updated
2021/9/21
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

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.

Student learning outcomes

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 that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Lecture Videos are uploaded to YouTube. All documents used in the lectures are uploaded to GitHub. Students can communicate with lecturer on Slack. Assignments are given in each class.

Course schedule/Required learning

  Course schedule Required learning
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, bit commitment 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

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 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.

Assessment criteria and methods

Assignments: 40%, Online final exam: 60%

Related courses

  • MCS.T203 : Linear Algebra and Its Applications

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

There is no condition for taking this class. But, it requires sufficient understanding of linear algebra.

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