Math 790: Mathematical Foundations of Quantum Algorithms and Applications (Spring 2025)

Instructor: Di Fang

This is a topic minicourse (with only 9 lectures) offered by Duke Math. To make it accessible to students without prior exposure to quantum mechanics, we will begin with the fundamentals. For a more comprehensive semester-long course on quantum algorithms, see Math 690: Quantum Scientific Computing (Spring 2024), which may be offered again in future years.

Time: TuTh 10:05AM - 11:20AM
Classroom: Gross Hall 304B

 

Tenative Lecture Plan (subject to change):

• Lec1 History, Motivation, Basics (states, gates)
• Lec2 No cloning theorem (simple ver), Gate examples (Paulis, Cliffords, etc), Solovay-Kitaev Theorem
• Lec3 Measurements. SWAP Test and Algorithm Analysis
• Lec4 Relationship between quantum computing v.s. classical computing; Garbage, Uncompute, No cloning theorem (general ver)
• Lec5 EQA; Hamiltonian Simulation via Trotterization
• Lec6 QFT on boolean cubes, Phase kickback, Deutsch-Jozsa Algorithm, Bernstein-Vazirani Algorithm
• Lec7 Block-encoding (definition and its properties), LCU
• Lec8 QSVT, Optimal Hamiltonian Simulation via QSVT
• Lec9 Quantum Linear System Algorithm via QSVT