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Essential Mathematics for Quantum Computing

Essential Mathematics for Quantum Computing

By : Leonard S. Woody III
4.6 (19)
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Essential Mathematics for Quantum Computing

Essential Mathematics for Quantum Computing

4.6 (19)
By: Leonard S. Woody III

Overview of this book

Quantum computing is an exciting subject that offers hope to solve the world’s most complex problems at a quicker pace. It is being used quite widely in different spheres of technology, including cybersecurity, finance, and many more, but its concepts, such as superposition, are often misunderstood because engineers may not know the math to understand them. This book will teach the requisite math concepts in an intuitive way and connect them to principles in quantum computing. Starting with the most basic of concepts, 2D vectors that are just line segments in space, you'll move on to tackle matrix multiplication using an instinctive method. Linearity is the major theme throughout the book and since quantum mechanics is a linear theory, you'll see how they go hand in hand. As you advance, you'll understand intrinsically what a vector is and how to transform vectors with matrices and operators. You'll also see how complex numbers make their voices heard and understand the probability behind it all. It’s all here, in writing you can understand. This is not a stuffy math book with definitions, axioms, theorems, and so on. This book meets you where you’re at and guides you to where you need to be for quantum computing. Already know some of this stuff? No problem! The book is componentized, so you can learn just the parts you want. And with tons of exercises and their answers, you'll get all the practice you need.
Table of Contents (20 chapters)
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1
Section 1: Introduction
4
Section 2: Elementary Linear Algebra
8
Section 3: Adding Complexity
13
Section 4: Appendices
Appendix 1: Bra–ket Notation
Appendix 2: Sigma Notation
Appendix 5: References

Polar form

The polar form is based on polar coordinates, which you may or may not be used to. If not, the next section goes through these, otherwise, you can skip it. Also, the rest of the chapter is heavy on trigonometry and we use radians for all angles. If you require a quick refresher on these, please consult the Appendix.

Polar coordinates

Polar coordinates are another way of representing points in 2. We are very familiar with the Cartesian coordinate system and its points, such as (x,y). Now we will represent a point with two coordinates called r and θ. The following diagram is very helpful in terms of putting this all together:

Figure 6.6 – Polar coordinates on a graph

As you can see, r is the hypotenuse of a right triangle with the other two sides being the Cartesian coordinates x and y. Because of this, it is easy to derive the equation to find r given the Cartesian coordinates using the Pythagorean theorem:

...

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