10:20-11:50 and 14:20-15:50 on Tuesdays and Thursdays, from Apr 21 to May 14, 2026

Room 505, Cosmology Building, NTU 

Course Format

The class will have daily homework and no final and no mid-term exams

In-Person ONLY Class.

Objectives

The class introduces basic quantum algorithms for scientific computation, their mathematics, intuition behind quantum computing and quantum algorithms, and implementation to solve interesting problems. 

Prerequisites 

Graduate standing or upper-division standing and/or consent of the instructor. 

Knowledge, Skills, and Abilities Students Gain from this Course (Learning Outcomes)

The goal is to learn the basic concepts of geometric representation theory, assuming minimal prerequisites. To complete the textbook within the course timeframe, we will focus on core material and skip some early introductory sections. (Note: The instructor is also learning this subject.)

Knowledge, Skills, and Abilities Students Should Have Before Entering This Course

Familiar with Python. Good math background (complex numbers/arithmetic, linear algebra and LINEAR ALGEBRA, probability + statistics)

Topic

• Advanced linear algebra, Hilbert spaces (reading homework before the class starts)

• State postulate and simplified Born rule (Day 1)

• Quantum operation/gate postulate and quantum circuits (Day 1)

• Composite quantum system postulate, Quantum Entanglement, and composite quantum gates (Day 2)

• Measurement postulate: projective measurement, the Born rule, quantum circuits with observables and general projective measurements, general observables via Hermitian matrices (Day 2, pre-reading materials on spectral decomposition, Hermitian operators, and orthogonal projectors)

• Quantum Teleportation, No-cloning and no-deleting theorems (Day 3)

• Quantum entanglements and density matrices: the Schmidt Decomposition Theorem, quantum entanglement, density matrix, post-measurement mixed stages, partial trace operations (Day 3)

• Quantum postulates via density matrices (Day 4)

• Quantum Fourier Transform and Quantum Phase estimation (Day 4)

• Parametrization for quantum states and gates (Day 5)

• Variational Quantum eigensolver (Day 5)

• Variational Quantum Least Squares (Day 6)

• Quantum Natural Gradient (Day 6, Day 7)

• Variational Quantum Classifier (Day 7)

• Quantum neural networks (Day 8)

Credit

2

Design Assignments

All assignments involve:

• Theoretical questions regarding learned methods or algorithms

• Application of methods and/or algorithms to applications with implementation in Qiskit.

Computer

All programming exercises will be in Qiskit. Installing Qiskit: My suggestion is: First install Visual Studio Code. Then follow something like this https://www.youtube.com/watch?v=dZWz4Gs_BuI 

Scheme

Some homework problems will be assigned during the class. There will be no exam. The grades are assigned based on students’ in-class performance.

Text

• Typed Lecture Notes, and Whiteboard/blackboard lectures. 

• Quantum Supremacy: How the Quantum Computer Revolution Will Change Everything: Kaku, Michio: 9780385548366

This books talks about quantum supremacy over digital computing

• Quantum Computation and Quantum Information: 10th Anniversary Edition 

This is considered as the bible for quantum computing and quantum information.

Course Number/ ID

No.: NCTS 5062
ID: V41 U5110
(三校聯盟之學生於課程網選課適用)