Advanced Math Techniques for Quantum Computing

This course covers the Math you need to begin learning about quantum algorithms and applications of quantum computing.

This is primarily a Math course. It doesn’t cover any quantum algorithms or applications. This course teaches you the Math you need to begin learning about quantum algorithms. Quantum algorithms will be covered in later courses.

Almost everything in this course is explained with rigorous proofs. After you complete this course, quantum physics will not seem so mysterious.

**PREREQUISITES**

To get the most from this course, you must be completely familiar with all the topics covered in the earlier prerequisite courses:

QC051 ,

QC101 ,

and QC151 .

**MATH TECHNIQUES COVERED IN THIS COURSE**

Orthonormality

Basis Vectors & Change of Basis

Bloch Sphere

Tensor Products

Multi-Qubit Tensor Algebra

Entanglement in terms of Degrees of Freedom

Partial Measurements

Cryptography with Entanglement

Deconstruction of Hermitian and Unitary Matrices into a Sum of Outer Products

**QUANTUM APPLICATIONS COVERED IN THIS COURSE**

Superdense Coding

Quantum Teleportation

Proof of No-Cloning Theorem

Bell’s Theorem (Statement and Proof)

**HOW TO GET THE MOST FROM THIS COURSE**

The material presented here is significantly more advanced than my previous courses on QC.

To get the most from this course, you might need to rewind and repeat each lesson 2-3 times.

It is a good idea to pause the lessons frequently and follow along with the Math.

Give yourself breaks between lessons. After you complete a lesson, wait a day, or at least an hour before moving on to the next lesson.

Enroll today and I will see you in class.

1

Welcome

2

Recap & Revision of Concepts

1

Probability of Measurement

2

Orthonormality

3

Orthonormality in Bracket Notation

4

Introduction to Basis Vectors

5

Basis Vectors for Spin

6

Introduction to Degrees of Freedom

7

Degrees of Freedom for a Single Qubit

8

Global & Relative Phase

9

Bloch Sphere

10

Tensor Products

11

Tensor Products of Matrices

12

Multi-Qubit Basis Vectors

13

Brackets of Tensor Terms

14

Multi-Qubit Tensor Algebra

15

Entanglement & Degrees of Freedom

16

Entanglement in Bracket Notation

17

Change of Basis

18

Multi-Qubit Measurements

19

Partial Measurement of Multiple Qubits

20

Square Matrices in Bracket Notation

21

Multi-Qubit Transformation Matrices

22

Cryptography with Entanglement

23

Expected Value of Measurables

24

Expected Value in Matrix Form

25

Deconstruction of Hermitians

26

Deconstruction of Unitary Matrices

1

Proof of No-Cloning Theorem

2

Superdense Coding

3

Quantum Teleportation

4

Bell's Theorem - 1 - Statement

5

Bell's Theorem - 2 - Lemma

6

Bell's Theorem - 3 - Proof

1

Conclusion

You can view and review the lecture materials indefinitely, like an on-demand channel.

Definitely! If you have an internet connection, courses on Udemy are available on any device at any time. If you don't have an internet connection, some instructors also let their students download course lectures. That's up to the instructor though, so make sure you get on their good side!

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