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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

Linearity

What makes a transform linear? This question gets to the heart of linear algebra. The concept of linearity ties together all the other concepts we have considered so far and the ones to come. Indeed, quantum mechanics is a linear theory. That's what makes linear algebra crucial to understanding quantum computing.

Before I define linearity, let's look at what it is not. Real-life examples of non-linearity abound. For example, exercising 1 hour a day for 24 days does not give the same result as exercising 24 hours in 1 day. Watering a plant is another good non-linear example. Giving a plant 1 gallon of water a day for 100 days will be much better than giving it 100 gallons in 1 day. These are both examples of non-linear relationships. How much you put in does not always translate to what you get out.

Linear relationships, on the other hand, are proportional. Speed is a good example. If you go 20 mph for 1 hour, you'll cover 20 miles. If you go 1 mph for...

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