Preface

1. Part 1 One Qubit to Rule Them All: Working with One Qubit

2. Chapter 1 What Is (and What Is Not) a Quantum Computer FREE CHAPTER

• 1.1 Quantum computing: myths and realities
• 1.2 Superposition, entanglement, interference, and other mysterious quantum phenomena
• 1.3 The shape of things to come
• Summary

3. Chapter 2 Qubits, Gates, and Measurements

• 2.1 What is a qubit?
• 2.2 Extracting information from qubits
• 2.3 How to transform a qubit state
• Summary

4. Chapter 3 Applications and Protocols with One Qubit

• 3.1 Quantum money
• 3.2 Quantum key distribution with the BB84 protocol
• 3.3 Other protocols with individual qubits
• Summary

5. Chapter 4 Coding One-Qubit Protocols in Qiskit

• 4.1 Quantum software and the case for Qiskit
• 4.2 How to work with one qubit in Qiskit
• 4.3 Implementing the BB84 protocol
• Summary

6. Part 2 Qubit Meets Qubit: Two Qubits and Entanglement

7. Chapter 5 How to Work with Two Qubits

• 5.1 One plus one is more than two: two-qubit states
• 5.2 Measuring two-qubit systems
• 5.3 Two-qubit gates
• Summary

8. Chapter 6 Applications and Protocols with Two Qubits

• 6.1 Superdense coding
• 6.2 The CHSH game
• 6.3 Deutsch’s algorithm
• Summary

9. Chapter 7 Coding Two-Qubit Algorithms in Qiskit

• 7.1 Working with two qubits in Qiskit
• 7.2 Superdense coding
• 7.3 The CHSH game
• 7.4 Deutsch’s algorithm
• Summary

10. Part 3 Working with Many Qubits

11. Chapter 8 How to Work with Many Qubits

• 8.1 Multi-qubit states
• 8.2 Measuring many qubits
• 8.3 Multi-qubit gates and universality
• Summary

12. Chapter 9 The Full Power of Quantum Algorithms

• 9.1 Quantum teleportation
• 9.2 The Deutsch–Jozsa algorithm
• 9.3 The Bernstein–Vazirani algorithm
• Summary

13. Chapter 10 Coding with Many Qubits in Qiskit

• 10.1 Working with many qubits in Qiskit
• 10.2 Quantum teleportation
• 10.3 The Deutsch–Jozsa algorithm
• 10.4 The Bernstein–Vazirani algorithm
• Summary

14. Part 4 The Stars of the Show: Main Quantum Algorithms

15. Chapter 11 Finding the Period and Factoring Numbers

• 11.1 The prime importance of prime factors
• 11.2 Shor’s algorithm
• 11.3 Preparing a periodic sequence
• 11.4 Finding the period with the quantum Fourier transform
• 11.5 Quantum phase estimation
• Summary

16. Chapter 12 Searching and Counting with a Quantum Computer

• 12.1 Searching in an unsorted list
• 12.2 Grover’s algorithm
• 12.3 Counting with the quantum Fourier transform
• Summary

17. Chapter 13 Coding Shor and Grover’s Algorithms in Qiskit

• 13.1 The QFT in Qiskit
• 13.2 Shor’s algorithm
• 13.3 Grover’s algorithm
• Summary

18. Part 5 Ad Astra: The Road to Quantum Utility and Advantage

19. Chapter 14 Quantum Error Correction and Fault Tolerance

• 14.1 The need for error correction
• 14.2 Quantum error correction
• 14.3 Implementing the Shor code in Qiskit
• 14.4 Fault-tolerant quantum computing
• Summary

20. Chapter 15 Experiments for Quantum Advantage

• 15.1 The race for quantum advantage
• 15.2 Random circuit sampling
• 15.3 The best is yet to come
• Summary

21. Bibliography

22. Solutions

• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11
• Chapter 12
• Chapter 13
• Chapter 14

23. Index

Appendix A Mathematical Tools

• A.1 Complex numbers
• A.2 Linear algebra
• A.3 Inner products and adjoint operators
• A.4 A crash course in modular arithmetic

1. Appendix B The Bra-Ket Notation and Other Foundational Notions

• B.1 Ket’s evil sibling: bras
• B.2 The Bloch sphere

2. Appendix C Measuring the Complexity of Algorithms

3. Appendix D Installing the Tools

• D.1 Getting Python
• D.2 Installing the libraries
• D.3 Accessing IBM’s quantum computers

4. Appendix E Production Notes