QC051: Math Prerequisites for QC - Content moved to QC101

Name: QC051: Math Prerequisites for QC - Content moved to QC101
Rating: 4.4 (897 reviews)

THE CONTENTS OF THIS COURSE HAVE BEEN ADDED TO QC101. Purchase this course if you want only the math lessons

Created byKumaresan Ramanathan

Last updated 10/2022

English

What you'll learn

Math prerequisites for Quantum Computing and Quantum Physics

Course content

6 sections • 114 lectures • 4h 13m total length

Introduction4:40
Boolean Algebra4:43
Boolean Variables & Operators7:09
Reviewing Your Experience0:21
Truth Tables3:17
Logic Gates1:22
Identify how boolean values map to signals, with true as 1 and on, false as 0 and off, and how gates such as and, or, and not form computing basis.
Logic Circuits0:52
AND Gate0:58
OR Gate0:51
NOT Gate1:03
Multiple Input Gates1:35
Equivalent Circuits 11:59
Equivalent Circuits 20:59
Universal Gate: NAND2:56
Exclusive-OR2:17
Explore the exclusive-or gate and its XOR truth table. Learn how to perform A = A XOR B as an atomic operation, updating A by XORing B in quantum architectures.
XOR for Assignment2:03
Use the xor gate to perform variable assignment in quantum computing by initializing A to 0 and xor B onto A, yielding A = B.
XOR of Bit Sequences 12:40
Learn to xor bit sequences to produce a consistent-length output by processing inputs element by element. Review the xor truth table and see how paired bits generate the output sequence.
XOR of Bit Sequences 24:21

Introduction to Probability5:08
Probability of a Boolean Expression1:42
Mutually Exclusive Events3:01
Independent Events1:16
Define independent events as occurrences with no influence on each other. Illustrate with two dice throws, two coin tosses, and unrelated choices like Alice and Bob's car colors.
Manipulating Probabilities with Algebra2:24
P( Mutually Exclusive Events )0:53
P( Independent Events )1:17
Complete Set of Mutually Exclusive Events2:00
P( A OR B )1:35
Examples0:51
Examples7:53
P( Bit Values )3:56
Analysis with Venn Diagrams1:27
Venn Diagram P( A AND B )0:53
Venn Diagram P( A OR B )1:09
Explore the probability of A or B as the union of A and B in a Venn diagram, with the red region representing P(A or B).
Venn Diagram P( NOT A )0:34
Examples2:42
Examples2:35
Conditional Probability2:06
Examples1:28

Introduction to Statistics1:21
Random Variables1:33
Explore random variables as uncertain outcomes mapped to numbers, using dice and coin toss examples. Analyze aggregate behavior and compute the average value, illustrating +1 and -1 mappings.
Mapping Random Variables4:20
Mean, Average, Expected Value ...1:49
Example2:23
Example1:37
Beyond Mean1:46
Standard Deviation3:50
Examples4:15
Combinations of Random Variables2:53
Correlation2:35
Analysis of Correlation6:19
Test to Determine if Real-World Random Variables are Correlated1:20

Introduction to Complex Numbers5:07
Position complex numbers as intermediate quantities that simplify quantum state transformations through linear operations, highlighting their algebraic completeness and usefulness in modeling quantum systems.
Imaginary i4:55
Addition1:54
Subtraction1:08
Multiplication by a Real0:55
Division by a Real0:41
Complex Multiplication2:30
Examples1:26
Complex Conjugates1:37
Squared Magnitude2:12
Complex Division3:01
Examples1:12
Divide complex numbers by conjugates to obtain real denominators, multiply numerator and denominator by the conjugate, and simplify to final answers such as -11/85 - (58/85)i and -2 + 5i.
Euler's Formula2:15
Polar Form2:44
Examples2:43
Fractional Powers3:24
Complex Cube Roots of 11:30
Square Root of i1:29
2D Coordinates3:00

Matrices1:38
Matrix Dimensions2:13
Matrix Addition1:42
Subtraction1:12
Scalar Multiplication1:12
Matrix Multiplication7:40
Matrix multiplication, essential for quantum computing, multiplies a row of the first matrix by a column of the second and sums the products to form each result element.
Examples0:59
Examples0:41
3x3 Example0:59
Exercises0:33
Pause the video to work through exercises, verify your computations against the provided answers, and tackle additional problems to reinforce math prerequisites for QC.
More Multiplications0:57
When is Multiplication Possible?2:06
Learn when matrix multiplication is possible: the number of columns of the first matrix must equal the number of rows in the second, as shown by matching dimensions.
Example1:23
Not Commutative1:52
Associative & Distributive1:25
Dimension of Result2:22
Odd Shaped Matrices1:03
Examples1:01
Outer Product1:47
Compute the outer product by multiplying a column matrix with a row matrix to form a table of all pairwise products, illustrated by animation.
Exercise0:21
Inner Product1:43
Exercises0:41
Identity Matrix2:16
Matrix Inverse2:46
Transpose1:21
Transpose Examples1:00
Transpose of Product1:16
Complex Conjugate of Matrices1:19
Adjoint1:07
Unitary1:45
Hermitian1:08
Hermitian & Unitary1:37
Why Hermitian or Unitary?0:57
Vectors & Transformations4:50
Define vectors as column matrices and show how a square matrix maps a column vector via x2 = Ax1 + By1, y2 = Cx1 + Dy1, and eigenvectors.
Rotation in 2D1:51
Special Directions3:59
Eigen Vectors & Eigen Values4:35
More Eigen Vectors2:58
Conclusion0:51

Requirements

Students must have completed 12th grade Math and Physics in high school

Description

THE CONTENTS OF THIS COURSE HAVE BEEN ADDED TO QC101.

Purchase this course if you want only the math lessons without the rest of QC101.

The contents of this course have been added to the section on Math Foundation in QC101.

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This is a refresher course in Mathematics for students who studied Math and Physics through 12th grade high school, but have now forgotten many of the details. In less than 4 hours I review the Math you will need to understand quantum computing concepts.

The focus is on getting you up to speed as quickly as possible. I cover what you need to know: Probability, Statistics, Boolean Logic, Complex Numbers, and Linear Algebra. You will not waste time on topics you do not need for quantum computing.

To get the most out of this course, you need to have already studied Math at a 12th grade level in high-school. This is merely a review course to help you refresh your memory. If you have not studied these topics in high school, then this 4 hour course cannot substitute for 2 years of high school Math classes.

This course reviews basic high-school Math. It doesn't go into any details about quantum physics or quantum computing. Those topics will be discussed in subsequent courses of this series.

Who this course is for:

Students who studied Math & Physics in 12th grade high school many years ago and now need a refresher course in basic Math

QC051: Math Prerequisites for QC - Content moved to QC101

What you'll learn

Explore related topics

Course content

Boolean Algebra18 lectures • 44min

Cryptography5 lectures • 14min

Probability20 lectures • 45min

Statistics13 lectures • 36min

Complex Numbers19 lectures • 44min

Linear Algebra & Matrices39 lectures • 1hr 11min

Requirements

Description

Who this course is for: