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2019　Quantum Computation and Quantum Information

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Academic unit or major
Graduate major in Mathematical and Computing Science
Instructor(s)
Mori Ryuhei 
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
Tue5-6(W834)  Fri5-6(W834)  
Group
-
Course number
MCS.T413
Credits
2
Academic year
2019
Offered quarter
4Q
Syllabus updated
2019/9/30
Lecture notes updated
2019/12/2
Language used
English
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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

Lectures are given by using class materials such as slides. Assignments are given every time.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Quantum mechanics: Quantum states and quantum measurements, Bell test Calculations of probability distribution of outcomes for given state and measurement
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, quantum teleportation Calculations of unitary operation on two and more qubits
Class 4 Nonlocality: Bell's inequality, GHZ paradox, XOR games Calculations of the winning probability of XOR games
Class 5 Quantum circuit: Deutch--Josza algorithm Calculations of the output state of quantum circuits
Class 6 Universality of quantum circuit Design of quantum circuits
Class 7 Solovay--Kitaev algorithm Improvements of Solovay--Kitaev algorithm
Class 8 Quantum phase estimation Analysis of quantum phase estimation
Class 9 Shor's algorithm Derivation of eigenvector of unitary operators
Class 10 Grover's algorithm and its optimality Proofs on generalizations of Grover's algorithm
Class 11 Quantum complexity theory: Complexity classes Proofs on complexity classes
Class 12 Quantum information theory: Discrimination of quantum states, matrix norm Calculation of matrix norm and the maximum probability for discriminating quantum states.
Class 13 Stabilizer states: Pauli group, Clifford group Calculations of operations from Clifford group to stabilizer states
Class 14 Quantum error-correcting codes Proofs on quantum error-correcting codes
Class 15 Quantum communication complexity Proofs on quantum communication complexity

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

Final exam: 30%
Assignments: 70%

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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