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
|Intercultural skills||Communication skills||✔ Specialist skills||Critical thinking skills||✔ Practical and/or problem-solving skills|
Lectures are given by using class materials such as slides. Assignments are given every time.
|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|
Michael A. Nielsen and Isaac L. Chuang, "Quantum Computation and Quantum Information," 10th Anniversary edition, Cambridge University Press 2010.
Final exam: 30%
There is no condition for taking this class. But, it requires sufficient understanding of linear algebra.