Taiwan Mathematics School: Introduction to Quantum Algorithms for Scientific Computation
Speaker: Prof. Tan Bui-Thanh (University of Texas at Austin)
Time: 2026/4/21 - 5/14 Every Tuesday and Thursday 10:20 - 11:50, 14:20 - 15:50
Venue: Rm. 505, 5th Floor, Cosmology Hall, NTU

Contact: Murphy Yu (murphyyu@ncts.tw)
請注意：
本課程為台大學分課程，三校聯盟可依課號選課 (NCTS5062)；
他校學生可申請台大成績證明，詳情請聯絡數學組游小姐 (murphyyu@ncts.tw)。

Organizers:
Weichung Wang (National Taiwan University)
Matthew M. Lin (National Cheng Kung University)
Hao-Chung Cheng (National Taiwan University)

1. Course 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.

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

3. 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)

4. Knowledge, Skills, and Abilities Students Gain from this Course (Learning Outcomes)
Students will understand the motivation, construction, theory, and implementation of many basic and state-of-the-art quantum algorithms for sciences and engineering problems. They will be able to apply these approaches to solve the similar problems and their extensions.
 
5. Topics
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)
 
6. Design Assignments
All assignments involve:
Theoretical questions regarding learned methods or algorithms
Application of methods and/or algorithms to applications with implementation in Qiskit.
 
7. 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 

8. 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.
 
9. Credit: 1
Course No.: NCTS5062
Course ID: V41 U5110

10. Registration
https://forms.gle/HwyQuSGQBBcqLiPH