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A Practical Guide to Quantum Machine Learning and Quantum Optimization

You're reading from   A Practical Guide to Quantum Machine Learning and Quantum Optimization Hands-on Approach to Modern Quantum Algorithms

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Product type Paperback
Published in Mar 2023
Publisher Packt
ISBN-13 9781804613832
Length 680 pages
Edition 1st Edition
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Authors (2):
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Elías F. Combarro Fernández-Combarro Álvarez Elías F. Combarro Fernández-Combarro Álvarez
Author Profile Icon Elías F. Combarro Fernández-Combarro Álvarez
Elías F. Combarro Fernández-Combarro Álvarez
Samuel González Castillo Samuel González Castillo
Author Profile Icon Samuel González Castillo
Samuel González Castillo
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Table of Contents (27) Chapters Close

Preface 1. Part I: I, for One, Welcome our New Quantum Overlords
2. Chapter 1: Foundations of Quantum Computing FREE CHAPTER 3. Chapter 2: The Tools of the Trade in Quantum Computing 4. Part II: When Time is Gold: Tools for Quantum Optimization
5. Chapter 3: Working with Quadratic Unconstrained Binary Optimization Problems 6. Chapter 4: Adiabatic Quantum Computing and Quantum Annealing 7. Chapter 5: QAOA: Quantum Approximate Optimization Algorithm 8. Chapter 6: GAS: Grover Adaptive Search 9. Chapter 7: VQE: Variational Quantum Eigensolver 10. Part III: A Match Made in Heaven: Quantum Machine Learning
11. Chapter 8: What Is Quantum Machine Learning? 12. Chapter 9: Quantum Support Vector Machines 13. Chapter 10: Quantum Neural Networks 14. Chapter 11: The Best of Both Worlds: Hybrid Architectures 15. Chapter 12: Quantum Generative Adversarial Networks 16. Part IV: Afterword and Appendices
17. Chapter 13: Afterword: The Future of Quantum Computing
18. Assessments 19. Bibliography
20. Index
21. Other Books You May Enjoy Appendix A: Complex Numbers
1. Appendix B: Basic Linear Algebra 2. Appendix C: Computational Complexity 3. Appendix D: Installing the Tools 4. Appendix E: Production Notes

1.5 Working with multiple qubits and universality

Now that we have mastered working with two-qubit systems, it will be fairly straightforward to generalize all the notions that we have been studying to the case in which the number of qubits in our circuits is arbitrarily big. You know the drill: we will start by defining, mathematically, what a multi-qubit system is, we will then learn how to measure it and, finally, we will introduce quantum gates that act on many qubits at the same time.

1.5.1 Multi-qubit systems

With all that we have learned so far, it will now be very easy to understand how to work with multi-qubit systems.

As you may have already deduced, if we have qubits, the states that constitute the computational basis are

We usually omit the symbol to write

or

\left| {00\cdots 0} \right\rangle,\left| {00\cdots 1} \right\rangle,\ldots,\left| {11\cdots 1} \right\rangle

or simply

\left| 0 \right\rangle,\left| 1 \right\rangle,\ldots,\left| {2^{n} - 1} \right\rangle.

Important note

When using the notation for basis states, the total number of qubits must be clear from context. Otherwise, a state like, for example, might mean either , , , or any string with...

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A Practical Guide to Quantum Machine Learning and Quantum Optimization
Published in: Mar 2023
Publisher: Packt
ISBN-13: 9781804613832
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