An Invitation to Quantum Information and Quantum Computing,
November - December, 2021

Lecturer 1: Ray-Kuang Lee, National Tsinghua University. E-mail: rklee@ee.nthu.edu.tw. http://mx.nthu.edu.tw/~rklee/
Lecturer 2: Chi-Kwong Li, College of William & Mary. E-mail: qc1979.ckli@gmail.com, http://cklixx.people.wm.edu
Assistant: Anandu Kalleri Madhu, National Tsinghua University. E-mail: anandu.k.madhu@gmail.com

Meeting time, format, and registration.

• Wednesday and Friday (Taiwan Time) 9:00 -- 10:00 a.m. using Microsoft Team.
• Video links will be sent to you if you are not able to attend the meetings in time.
• A website will be set up for discussion during and after the meetings.
• If you are interested, please send your name, affiliation (department and institution), position (graduate student, professor, etc.) to Anandu (E-mail: anandu.k.madhu@gmail.com) so that an online meeting invitation will be sent to you.

Description of the lecture series.

Quantum information science and quantum computing are rapidly growing areas. The study concerns the use of quantum properties to store, transmit, and manipulate data. Recent study has connected the topic to other research areas such as image processing, machine learning, neural network, etc. The study requires knowledge from a wide spectrum of different disciplines including mathematics, physics, computer science, chemistry, engineering, material science, etc.

The goal of this lecture series is to use elementary matrix theory approach to introduce the subject to beginners, and also provide a platform for people from different background to exchange experiences and idea about quantum properties and how they can be use to solve problems in quantum information, quantum computing, and other topics.

We will not assume any quantum mechanics background from the audience, and require only basic courses in calculus and linear algebra. Background in group theory and differential equations will be useful, but not necessary. The discussion will focus on three components and their expected outcome are listed below.

• Weeks 1 - 3. Background of matrix theory and quantum mechanics.
  We will use the Hilbert space model for quantum mechanics to explain the counterintuitive behavior of quantum systems, and how to use mathematical theory to develop theory and design algorithms to solve problems in quantum information, quantum computing, and related areas.
  Expected outcome. After these lectures, audiences should have a basic idea of how quantum properties can be used to approaches practical problems.
  They may try to formulate problems of other areas in the quantum setting and ask whether they can be solved by quantum approaches.
• Weeks 4 - 6. Quantum Information.
  Selected topics will be presented to illustrate how one can use quantum properties to transmit information securely, how external (quantum) environments will affect the processing of quantum information, and how one can apply correction schemes to deal with such problems. In particular, we will discuss the implementation issues, and demonstrate how to use currently available quantum computers such as the IBM online quantum computer, linear optics, NMR, to carry out the quantum computing, and quantum error correction schemes.
  Expected outcome. After these lectures, audiences may try to implement quantum algorithms on the IBM online quantum computers, or other quantum computing platforms.
• Weeks 7 - 9. Quantum Computing.
  We will introduce some basic quantum algorithms such as the Duetsh-Jorza algorithms, Grover's search algorithm, and Shor's factorization algorithm.
  Expected outcome. After these lectures, audiences may try to implement existing or design new quantum algorithms.

Current research topics and Research group discussion.
We will present current research problems on the topics whenever possible. Participants are welcomed to suggest problems for discussion and investigations. Extra discussion and research group meetings may be arranged.

Reference books and lecture notes.

• Our discussion will be based on the first 12 chapters of the following book:
  M. Nakahara and T. Ohmi, Quantum computing: From Linear Algebra to Physical Realizations,
  CRC Press, Taylor and Francis Group, New York, 2008.
  http://www.amazon.com/Quantum-Computing-Algebra-Physical-Realizations/dp/0750309830
• Supplementary notes is posted in the "Classnote and Discussion Topics" section below, and audiences are welcomed to give comments on them.
• Additional references:
  • Nielsen and Chuang, Quantum Computation and Quantum Information Science, Cambridge.
  • Watrous, The Theory of Quantum Information, Cambridge.
  • Yanofsky and Mannucci, Quantum Computing for Computer Scientists, Cambridge.
  • The Functional Analysis of Quantum Information Theory a collection of notes based on lectures by Gilles Pisier, K. R. Parthasarathy, Vern Paulsen and Andreas Winter. https://arxiv.org/pdf/1410.7188.pdf
  • Learn Quantum Computation using Qiskit , IBM Qiskit online material.

• Supplementary notes for Week 1. (Try the open problems and exercises!)
  Class notes. [ Lecture on Nov. 03. ] [ Lecture on Nov. 05. ]
  Discussion topics for week 1.
  (1) What is your expectation of the course?
  (2) Do you have some specific topics in mind that you want to know?
  (3) Any suggestions for the lectures.
  (Submitted to qc1979.ckli@gmail.com)
  
• Supplementary notes for Week 2. (Try the open problems and exercises!)
  Class notes. [ Lecture on Nov. 10. ] [ Lecture on Nov. 12. ] Discussion topics for week 2.
  Any thoughts/comments about the counter-intuitive quantum properties?
  
• Supplementary notes for Week 3. (Try the open problems and exercises!)
  Class notes. [ Lecture on Nov. 17. ] [ Lecture on Nov. 19. ] Discussion topics for week 3.
  Please share any comments or experiences for quantum postulates, quantum states, measurements, etc. Also, if you know any interesting books, youtube clips, etc. please let me know. Furthermore, let me know if the lectures are unclear.
• Supplementary notes for Week 4. Class notes. [ Lecture on Nov. 24. ] Class notes. [ Lecture on Nov. 26. ]
• Supplementary notes for Week 5. Class notes. [ Lecture on Dec. 3. ] Links to the IBMQ notes on Dense coding and Teleportation
  [https://qiskit.org/textbook/ch-algorithms/superdense-coding.html] [https://qiskit.org/textbook/ch-algorithms/teleportation.html]
  Useful files prepared by Anandu:
  [http://cklixx.people.wm.edu/teaching/QC2021/tele1.jpg] [http://cklixx.people.wm.edu/teaching/QC2021/teleportation.ipynb]
  [http://cklixx.people.wm.edu/teaching/QC2021/superdense.jpg] [http://cklixx.people.wm.edu/teaching/QC2021/superdense-coding.ipynb]
• Week 6. No supplementary note. Please read Chapter 5 of the textbook.
  Class notes. [ Lecture on Dec. 8. ] [ Lecture on Dec. 10. ]
• Week 7. No supplementary note. Please read Chapters 6 and 7 of the textbook.
  Class notes. [ Lecture on Dec. 15 - 1.] [ Lecture on Dec. 15 - 2. ]
  Class notes. [ Lecture on Dec. 17 - 1.] [ Lecture on Dec. 17 - 2.]
• Week 8. No supplementary note. Please read Chapter 8 of the textbook.
  Class notes. [ Lecture on Dec. 21.]
  Class notes on Quantum state tomography. [ Lecture on Dec. 24.]
  
• Week 9. No supplementary note. See Chapter 10 of textbook for Quantum error correction, and Chapter 12 for some discussion on Tomography. Class notes on Qauntum operations with special properties. [ Lecture on Dec. 29.]
  Class notes on Quantum error correction. [ Lecture on Dec. 31.]