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.
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.
Quantum computation, quantum information
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||✔ Practical and/or problem-solving skills|
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|
|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|
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.
Michael A. Nielsen and Isaac L. Chuang, "Quantum Computation and Quantum Information," 10th Anniversary edition, Cambridge University Press 2010.
Assignments: 40%, Online final exam: 60%
There is no condition for taking this class. But, it requires sufficient understanding of linear algebra.