課程大綱

課程資訊

課程名稱

量子資訊與計算
Quantum Information and Computation

開課學期

112-2

授課對象

電機資訊學院電機工程學研究所

授課教師

鄭皓中

課號

CommE5061

課程識別碼

942 U0750

班次

學分

3.0

全/半年

半年

必/選修

選修

上課時間

星期一2,3,4(9:10~12:10)

上課地點

備註

上課地點:電二143
總人數上限：100人

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課程概述

This course is scheduled as three parts: the mathematical formalism of quantum information, its application in computing tasks, and its application in information-processing and more advanced topics.

Part I - Closed Quantum Systems
1. Foundations and Postulates for Closed Quantum Systems: Quantum States, Evolution, and Projective Measurements.
2. The Quantum No-Go Theorem: No-Cloning Theorem, No-Signaling Theorem, and No-Perfect Discrimination.
3. Basic Quantum Protocols: Teleportation, Dense Coding, Quantum Key Distribution.
4. Quantum Computation I: Quantum Circuit Model and Algorithms.
5. Quantum Computation II: Algorithms Based on Amplitude Amplification.
6. Quantum Computation III: Algorithms Based on Phase Estimation.
7. Quantum Computation IV: Integer Factorization Algorithm.
8. Quantum Non-Local Games.

Part II - Open Quantum Systems
9. Foundations and Postulates for Open Quantum Systems: Density Operators, Quantum Channels, and Quantum Measurements.
10. Distance Measures: Quantum Fidelity, Trace Distance, and Quantum Entropies.
11. Quantum Shannon Theory I: Quantum Compression.
12. Quantum Shannon Theory II: Hypothesis Testing and Classical Communication over Quantum Channels.
13. Quantum Shannon Theory III: Quantum Communication over Quantum Channels.
14. Quantum Error Correction.
15. Advanced Topics: Quantum Machine Learning (as time permits).

課程目標

1. Introduce fundamental concepts and mathematical framework of quantum information (the so-called quantum bits)---how to model it, process it, and measure it.

2. Present core quantum computing topics including quantum circuit models and basic quantum algorithms, and how to harness quantum computing power to speed-up classical computational tasks.

3. Learn compressing quantum information and communicating classical/quantum information through a quantum channel, and various quantum information-processing protocols.

4. Develop necessary abilities for students to independently study advanced topics in quantum information sciences and to innovate applications in quantum information technology.

5. Perform a term project on studying advanced topics of the latest research, experiment development, technologies of quantum information processing.

6. Equip students with sufficient backgrounds to self-study academic papers and self-learn in this field after taking this course.

課程要求

The course is intended for graduate students (undergraduate students are very welcome) who have previously taken courses of linear algebra and basic probability theory. No previous background in quantum mechanics is required.
The grading criterion is based on homework (45%), mid-term exam (15%), and final project (30%).

預期每週課後學習時數

Eluid Kipchoge: "No human is limited."
The sky's the limit.
You are encouraged to explore relevant books, materials, and papers. It is up to you to determine how much time you want to devote to this course.
From previous students, the minimum time is expected to be 10 hours per week.

Office Hours

每週一 12:10~13:10 備註： The office hour is every week after the course. Otherwise, please make appointment by email.

指定閱讀

Course Slides and References

參考書目

[1] Michael Nielsen and Issac Chuang. Quantum Computation and Quantum Information, Cambridge University Press, 2009.
[2] P. Kaye, R. Laflamme, M. Mosca. An Introduction to Quantum Computing, Oxford University Press, 2007.
[3] Benjamin Schumacher and Michael Westmoreland. Quantum Processes systems, and Information, Cambridge Press, 2010.
[4] Joseph M. Renes. Quantum Information Theory: Concepts and Methods, de Gruyter, 2022.
[5] Mark M. Wilde. Quantum Information Theory, Cambridge University Press, 2018.
[6] John Watrous. The Theory of Quantum Information, Cambridge University Press, 2018.
[7] Mario Ziman and Teiko Heinosaari. The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement, Cambridge University Press, 2011.

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	Homeworks	45%	HW1 (15%), HW2 (15%), HW3 (15%)
2.	Mid-term exam	25%	Only a double-sized A4 note is allowed in exam.
3.	Final project	30%

課程進度

週次	日期	單元主題
第0週	2/12	Recap on Linear Algebra (HW 0 released)
第1週	2/19	Logistics & Overview of Quantum Information and Computation
第2週	2/26	Postulates for Closed Quantum Systems
第3週	3/4	The No-Go Theorems (HW 1 released)
第4週	3/11	Basic Quantum Protocols
第5週	3/18	Quantum Computing I: Quantum Circuits and The Oracle models
第6週	3/25	Quantum Computing II: The Amplitude Amplification Algorithm (HW 2 released)
第7週	4/1	Quantum Computing III: The Phase Estimation Algorithm
第8週	4/8	Quantum Computing IV: The Integer Factorization Algorithm
第9週	4/15	Non-Local Games
第10週	4/22	Mid-term exam (physical)
第11週	4/29	Open Quantum Systems & Quantum Operations (HW 3 released)
第12週	5/6	Quantum Information Theory I: Quantum Compression
第13週	5/13	Quantum Information Theory II: Classical Communication over Quantum Channels
第14週	5/20	Quantum Information Theory III: Quantum Communication over Quantum Channels
第15週	5/27	Quantum Error Correction
第16週	6/3	Final Project Presentation