Sign In Start Free Trial
Account

Add to playlist

Create a Playlist

Modal Close icon
You need to login to use this feature.
  • Book Overview & Buying Essential Mathematics for Quantum Computing
  • Table Of Contents Toc
  • Feedback & Rating feedback
Essential Mathematics for Quantum Computing

Essential Mathematics for Quantum Computing

By : Leonard S. Woody III
4.6 (19)
close
close
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)
close
close
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

Gram-Schmidt

The Gram-Schmidt process is an algorithm in which you input a basis set of vectors and it outputs a basis set that is orthogonal. We can then normalize that set of vectors, and suddenly, we have an orthonormal set of basis vectors! This is very helpful in quantum computing and other areas of applied math, as an orthonormal basis is usually the best basis for computations and representing vectors with coordinates.

Gram-Schmidt Is a Decomposition Tool

While we won't go into it in this book, the Gram-Schmidt process is used in certain decompositions, so it's good to know from that vantage point too.

Let's look at an example before getting into the nitty-gritty of the actual procedure (which can be dry and dull). Let's say I have a basis for ℂ2, such as the following:

These vectors are not orthogonal, since their inner product does not equal 0:

They are also not normalized. Now, I want...

Unlock full access

Continue reading for free

A Packt free trial gives you instant online access to our library of over 7000 practical eBooks and videos, constantly updated with the latest in tech

Create a Note

Modal Close icon
You need to login to use this feature.
notes
bookmark search playlist font-size

Change the font size

margin-width

Change margin width

day-mode

Change background colour

Close icon Search
Country selected

Close icon Your notes and bookmarks

Delete Bookmark

Modal Close icon
Are you sure you want to delete it?
Cancel
Yes, Delete

Delete Note

Modal Close icon
Are you sure you want to delete it?
Cancel
Yes, Delete

Edit Note

Modal Close icon
Write a note (max 255 characters)
Cancel
Update Note

Confirmation

Modal Close icon
claim successful

Buy this book with your credits?

Modal Close icon
Are you sure you want to buy this book with one of your credits?
Close
YES, BUY