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Essential Mathematics for Quantum Computing

You're reading from   Essential Mathematics for Quantum Computing A beginner's guide to just the math you need without needless complexities

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Product type Paperback
Published in Apr 2022
Publisher Packt
ISBN-13 9781801073141
Length 252 pages
Edition 1st Edition
Languages
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Author (1):
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Leonard S. Woody III Leonard S. Woody III
Author Profile Icon Leonard S. Woody III
Leonard S. Woody III
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Table of Contents (20) Chapters Close

Preface 1. Section 1: Introduction
2. Chapter 1: Superposition with Euclid FREE CHAPTER 3. Chapter 2: The Matrix 4. Section 2: Elementary Linear Algebra
5. Chapter 3: Foundations 6. Chapter 4: Vector Spaces 7. Chapter 5: Using Matrices to Transform Space 8. Section 3: Adding Complexity
9. Chapter 6: Complex Numbers 10. Chapter 7: EigenStuff 11. Chapter 8: Our Space in the Universe 12. Chapter 9: Advanced Concepts 13. Section 4: Appendices
14. Other Books You May Enjoy Appendix 1: Bra–ket Notation 1. Appendix 2: Sigma Notation 2. Appendix 3: Trigonometry 3. Appendix 4: Probability 4. Appendix 5: References

Chapter 6: Complex Numbers

"What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Ψ is surely fundamentally a real function."

– Letter from Schrödinger to Lorentz. June 6, 1926.

Even the great physicist Erwin Schrödinger was perplexed by the occurrence of complex numbers in quantum mechanics. Yet, complex numbers have been found to be inherent to quantum mechanics and, hence, quantum computing. Up until now, we have concentrated on the real numbers to make concepts easier to get across. It is time now to cross the Rubicon and make our way into the complex plane. You have probably come across complex numbers before, but we will go into great depths about them in this chapter. I think it is unfortunate that René Descartes named i an imaginary number, as it makes it seem that this topic should be otherworldly. But so was the number 0 when it was introduced, and the same with negative numbers. No one gives...

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