An Invitation to Quantum Information and Quantum Computing,
November  December, 2021
A lecture series delivered at the National Tsinghua University.
Lecturer 1: RayKuang Lee,
National Tsinghua University. Email: rklee@ee.nthu.edu.tw.
http://mx.nthu.edu.tw/~rklee/
Lecturer 2: ChiKwong Li,
College of William & Mary. Email: qc1979.ckli@gmail.com,
http://cklixx.people.wm.edu
Assistant: Anandu Kalleri Madhu,
National Tsinghua University. Email: 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 (Email: 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 DuetshJorza 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/QuantumComputingAlgebraPhysicalRealizations/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.
Classnotes and discussion topics.