Instructor: Di Fang Syllabus
Please find the Course webpage on Canvas! This page is generated from Canvas and intended solely for maintaining a record of the teaching schedule and may not be consistently updated.
Please find the references (textbooks) for the course in the syllabus.
The chapters are:
Tentative Course Plan:
Slides for the first few lectures (basic QC Glossary): basicQC.pdf
Some handwritten notes may be posted (not guaranteed to be typofree); or References will be provided.
Week  Wednesday  Friday 
1  Course Policy; Philosophy/Motivation; History; Start of basic QC Glossary (braket notations) [Lecture Notes] 

2 
QC Glossary continued: Quantum States (qubits); Unitary operators (quantum gates); Nocloning theorem (simple version) 
common quantum gates; Universal gate sets; SolovayKitaev Theorem; Quantum Circuits (References on the proof of SolovayKitaev Theorem: [Childs Ch2.3], [NielsenChuang Appendix 3], and a mathematically rigor proof with all gaps filled.) 
3 
Measurements (measurement in different basis, partial measurement, observable); SWAP test; Relationship of Quantum Computing v.s. Classical Computing (reversible classical computing) 
Garbage and Uncompute; Exponential Quantum Advantage; Nocloning theorem (fullversion) 
4 
Hamiltonian Simulation and Trotterization; different error metrics (special case v.s. worst case); nofastforwarding theorem (Reference on nofastforwarding theorem: [Kothari's MS thesis] 
Analysis of Trotterization; Commutator Scaling; Examples 
5 
Watch a talk of your choice and/or think about what topic you'd like to work on for the course project. 
Phase kickback; Fourier transform on the Boolean cubic; DeutschJozsa Algorithm; BernsteinVazirani Algorithm 
6 
Hadamard test; Quantum Fourier transform; Quantum Phase Estimation 
Analysis of the textbook version QPE, and a brief review of literature on the stateoftheart QPE and QEEP results. 
7 
Remarks of QPE (A brief review of literature on the stateofthearts QPE & QEEP results; How to get $$\log(\delta^{1})$$ cost dependence); Further reading/watching of QPE & QEEP. 
Manybody Hamiltonian learning; QLSP (Quantum Linear System Problem) and HHL (the Harrowâ€“Hassidimâ€“Lloyd algorithm) [Lecture Notes] 
8 
More on Controlled Rotation; Classical arithmetic circuit; 
Grover search Analysis of upper bound (Perspective 2&3); Amplitude Amplification. 
9 
Lower bound of Grover; Amplitude Estimation 
Blockencoding, definition and understandings; Properties; linear combination of unitaries (LCU)  simple case 
10 
Happy Spring Break! 

11 
linear combination of unitaries (LCU)  general case; nearoptimal Hamiltonian simulation by truncated Taylor series; Motivation for OAA 
Oblivious Amplitude Amplification (OAA); QSP (Quantum Signal Processing) and QSVT (quantum singular value tranformation); Optimal Hamiltonian Simulation by QSVT 
12 
Other QSLAs  talk recording by Robin Kothari (using LCU + Chebyshev polynomial or Fourier approach for QLSA; Optional) 
Improved QLSA (Quantum Linear System Algorithm by QSVT; A dive into the idea of qubitization. 
13 
Prep for course project 
Prep for course project 
14 
Quantum (linear) Differential Equation Solvers  QLSAbased; timemarching and LCHS based (postQLSA algorithms) 
Project presentation (subject to change) 
15 
Project presentation 
Project presentation 