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A Practical Guide to Quantum Computing

Name: A Practical Guide to Quantum Computing
ISBN: 9781835885949

by Elías F. Combarro, Samuel González-Castillo

July 2025

Beginner to intermediate

512 pages

11h 48m

English

Packt Publishing

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Preface
Part 1 One Qubit to Rule Them All: Working with One Qubit
Chapter 1 What Is (and What Is Not) a Quantum Computer
1.1 Quantum computing: myths and realities1.2 Superposition, entanglement, interference, and other mysterious quantum phenomena1.2.1 Superposition1.2.2 Entanglement1.2.3 Interference1.2.4 The uncertainty principle and the no-cloning theorem1.2.5 Simulating quantum computers with classical computers1.3 The shape of things to comeSummary
Chapter 2 Qubits, Gates, and Measurements
2.1 What is a qubit?2.1.1 Qubits and their states2.1.2 The bra-ket notation2.2 Extracting information from qubits2.3 How to transform a qubit state2.3.1 Quantum gates2.3.2 Quantum circuits2.3.3 Global and relative phasesSummary
Chapter 3 Applications and Protocols with One Qubit
3.1 Quantum money3.1.1 Creating the banknote3.1.2 Checking the banknote3.1.3 Detecting illegitimate quantum money3.2 Quantum key distribution with the BB84 protocol3.2.1 Alice, Bob, Eve, and the one-time pad3.2.2 BB84: the protocol3.2.3 Security of BB843.3 Other protocols with individual qubits3.3.1 Alternative QKD protocols3.3.2 The Elitzur–Vaidman bomb testerSummary
Chapter 4 Coding One-Qubit Protocols in Qiskit
4.1 Quantum software and the case for Qiskit4.2 How to work with one qubit in Qiskit4.2.1 Simulating the evolution of a state4.2.2 Getting samples from a simulator4.2.3 Getting results from real quantum hardware4.3 Implementing the BB84 protocolSummary
Part 2 Qubit Meets Qubit: Two Qubits and Entanglement
Chapter 5 How to Work with Two Qubits
5.1 One plus one is more than two: two-qubit states5.2 Measuring two-qubit systems5.3 Two-qubit gates5.3.1 Tensor products of gates5.3.2 The CNOT gate5.3.3 Entanglement5.3.4 The no-cloning theoremSummary
Chapter 6 Applications and Protocols with Two Qubits
6.1 Superdense coding6.2 The CHSH game6.3 Deutsch’s algorithm6.3.1 Deutsch’s oracle6.3.2 The inner workings of Deutsch’s algorithmSummary
Chapter 7 Coding Two-Qubit Algorithms in Qiskit
7.1 Working with two qubits in Qiskit7.2 Superdense coding7.3 The CHSH game7.4 Deutsch’s algorithmSummary

Part 3 Working with Many Qubits
Chapter 8 How to Work with Many Qubits
8.1 Multi-qubit states8.2 Measuring many qubits8.3 Multi-qubit gates and universality8.3.1 Tensor product gates8.3.2 The Toffoli gate8.3.3 Gate universalitySummary
Chapter 9 The Full Power of Quantum Algorithms
9.1 Quantum teleportation9.1.1 The details of quantum teleportation9.1.2 An overview of quantum teleportation9.2 The Deutsch–Jozsa algorithm9.2.1 Oracles, in all their glory9.2.2 The magic behind Deutsch–Jozsa9.2.3 The truth about quantum parallelism9.3 The Bernstein–Vazirani algorithmSummary
Chapter 10 Coding with Many Qubits in Qiskit
10.1 Working with many qubits in Qiskit10.1.1 Using registers10.1.2 How to verify the equivalence of circuits10.2 Quantum teleportation10.3 The Deutsch–Jozsa algorithm10.3.1 Let’s build some oracles10.3.2 Implementing the Deutsch–Jozsa algorithm10.4 The Bernstein–Vazirani algorithmSummary
Part 4 The Stars of the Show: Main Quantum Algorithms
Chapter 11 Finding the Period and Factoring Numbers
11.1 The prime importance of prime factors11.2 Shor’s algorithm11.2.1 Analysis of the method11.2.2 A simple example11.3 Preparing a periodic sequence11.3.1 Introducing a very periodic state11.3.2 Quantum circuit to obtain the periodic sequence11.4 Finding the period with the quantum Fourier transform11.4.1 QFT FTW!11.4.2 The QFT applied to periodic sequences11.4.3 Implementing the quantum Fourier transform11.5 Quantum phase estimationSummary
Chapter 12 Searching and Counting with a Quantum Computer
12.1 Searching in an unsorted list12.2 Grover’s algorithm12.2.1 Oracles, with a twist12.2.2 The initial setup12.2.3 Amplitude amplification12.2.4 Let’s play with the odds12.2.5 Not one, but many12.3 Counting with the quantum Fourier transformSummary
Chapter 13 Coding Shor and Grover’s Algorithms in Qiskit
13.1 The QFT in Qiskit13.2 Shor’s algorithm13.3 Grover’s algorithmSummary
Part 5 Ad Astra: The Road to Quantum Utility and Advantage
Chapter 14 Quantum Error Correction and Fault Tolerance
14.1 The need for error correction14.1.1 Our first error correction code14.2 Quantum error correction14.2.1 Bit flips14.2.2 Phase flips14.2.3 The Shor code14.3 Implementing the Shor code in Qiskit14.4 Fault-tolerant quantum computingSummary
Chapter 15 Experiments for Quantum Advantage
15.1 The race for quantum advantage15.2 Random circuit sampling15.2.1 Defining random circuit sampling15.2.2 Probability distributions with random unitaries15.2.3 The cross-entropy benchmark fidelity15.2.4 XEB and random circuit sampling15.3 The best is yet to comeSummary
Appendix A Mathematical Tools
A.1 Complex numbersA.2 Linear algebraA.2.1 Vector spacesA.2.2 Bases and coordinatesA.2.3 Linear maps and eigenstuffA.3 Inner products and adjoint operatorsA.4 A crash course in modular arithmetic
Appendix B The Bra-Ket Notation and Other Foundational Notions
B.1 Ket’s evil sibling: brasB.2 The Bloch sphere
Appendix C Measuring the Complexity of Algorithms
Appendix D Installing the Tools
D.1 Getting PythonD.2 Installing the librariesD.3 Accessing IBM’s quantum computers
Appendix E Production Notes
Bibliography
Solutions
Chapter 1Chapter 2Chapter 3Chapter 4Chapter 5Chapter 6Chapter 7Chapter 8Chapter 9Chapter 10Chapter 11Chapter 12Chapter 13Chapter 14
Index

Content preview from A Practical Guide to Quantum Computing

Chapter 7 Coding Two-Qubit Algorithms in Qiskit

Two heads are better than one, not because either is infallible, but because they are unlikely to go wrong in the same direction. — C.S. Lewis

In the last couple of chapters, we have studied quite a number of algorithms and protocols that work on two-qubit systems. It is thus time for us to learn how to use Qiskit to construct and run circuits that act on two qubits.

We will start with some simple examples that will illustrate how to work with two qubits in Qiskit. As you will soon see, adding a new qubit to the mix won’t change things that much. The only difference will be our having to keep track of which qubit we are applying gates to, and the introduction of two-qubit gates such as the CNOT ...

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A Practical Guide to Quantum Computing

by Elías F. Combarro, Samuel González-Castillo

Chapter 7 Coding Two-Qubit Algorithms in Qiskit

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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