You're reading from A Practical Guide to Quantum Machine Learning and Quantum Optimization

Product type Book

Published in Mar 2023

Publisher Packt

ISBN-13 9781804613832

Pages 680 pages

Edition 1st Edition

Languages

Concepts

Quantum Computing

Authors (2):

Elías F. Combarro

Samuel González-Castillo

View More author details

Table of Contents (27) Chapters

Preface

Part I: I, for One, Welcome our New Quantum Overlords

Chapter 1: Foundations of Quantum Computing

Chapter 2: The Tools of the Trade in Quantum Computing

Part II: When Time is Gold: Tools for Quantum Optimization

Chapter 3: Working with Quadratic Unconstrained Binary Optimization Problems

Chapter 4: Adiabatic Quantum Computing and Quantum Annealing

Chapter 5: QAOA: Quantum Approximate Optimization Algorithm

Chapter 6: GAS: Grover Adaptive Search

Chapter 7: VQE: Variational Quantum Eigensolver

Part III: A Match Made in Heaven: Quantum Machine Learning

Chapter 8: What Is Quantum Machine Learning?

Chapter 9: Quantum Support Vector Machines

Chapter 10: Quantum Neural Networks

Chapter 11: The Best of Both Worlds: Hybrid Architectures

Chapter 12: Quantum Generative Adversarial Networks

Part IV: Afterword and Appendices

Chapter 13: Afterword: The Future of Quantum Computing

Assessments

Bibliography

Index

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Appendix A: Complex Numbers

Appendix B: Basic Linear Algebra

Appendix C: Computational Complexity

Appendix D: Installing the Tools

Appendix E: Production Notes

Assessments

Chapter 1, Foundations of Quantum Computing

(1.1) The probability of measuring if the state of a qubit is is exactly

$\left. \left| \sqrt{\left. 1\slash 2 \right.} \right|^{2} = 1\slash 2. \right.$

In the same way, the probability of measuring is also . If the state of the qubit is , the probability of measuring is $\left. \left| \sqrt{\left. 1\slash 3 \right.} \right|^{2} = 1\slash 3 \right.$ and the probability of measuring is $\left. \left| \sqrt{\left. 2\slash 3 \right.} \right|^{2} = 2\slash 3. \right.$

Finally, if the qubit state is , the probability of measuring is $\left. \left| \sqrt{\left. 1\slash 2 \right.} \right|^{2} = 1\slash 2 \right.$ and the probability of measuring is $\left. \left| {- \sqrt{\left. 1\slash 2 \right.}} \right|^{2} = 1\slash 2. \right.$

(1.2) The inner product of and is $\sqrt{\left. 1\slash 2 \right.}\sqrt{\left. 1\slash 3 \right.} + \sqrt{\left. 1\slash 2 \right.}\sqrt{\left. 2\slash 3 \right.} = \sqrt{\left. 1\slash 6 \right.} + \sqrt{\left. 1\slash 3 \right.}.$

The inner product of and is $\sqrt{\left. 1\slash 2 \right.}\sqrt{\left. 1\slash 2 \right.} - \sqrt{\left. 1\slash 2 \right.}\sqrt{\left. 1\slash 2 \right.} = 0.$

(1.3) The adjoint of is itself and it holds that . Hence, is unitary and its inverse is itself. The operation takes to .

(1.4) The adjoint of is itself and it holds that . Hence, is unitary and its inverse is itself. The operation takes to and to . Finally, it holds that and that .