Quantum Computing Algorithms : Discover How a Little Math Goes a Long Way / Barry Burd.

Format:

Book

Author/Creator:

Burd, Barry, author.

Language:

English

Subjects (All):

Quantum computing--Mathematics.

Quantum computing.

Computer algorithms.

Physical Description:

1 online resource (342 pages)

Edition:

First edition.

Place of Publication:

Birmingham, England : Packt Publishing Ltd., [2023]

Summary:

Explore essential quantum computing algorithms and master concepts intuitively with minimal math expertise required Key Features Learn the fundamentals with an introduction to matrix arithmetic Write quantum computing programs in Qiskit--IBM's publicly available quantum computing website Email your questions directly to the author--no question is too elementary Purchase of the print or Kindle book includes a free PDF eBook Book Description Navigate the quantum computing spectrum with this book, bridging the gap between abstract, math-heavy texts and math-avoidant beginner guides. Unlike intermediate-level books that often leave gaps in comprehension, this all-encompassing guide offers the missing links you need to truly understand the subject. Balancing intuition and rigor, this book empowers you to become a master of quantum algorithms. No longer confined to canned examples, you'll acquire the skills necessary to craft your own quantum code. Quantum Computing Algorithms is organized into four sections to build your expertise progressively. The first section lays the foundation with essential quantum concepts, ensuring that you grasp qubits, their representation, and their transformations. Moving to quantum algorithms, the second section focuses on pivotal algorithms -- specifically, quantum key distribution and teleportation. The third section demonstrates the transformative power of algorithms that outpace classical computation and makes way for the fourth section, helping you to expand your horizons by exploring alternative quantum computing models. By the end of this book, quantum algorithms will cease to be mystifying as you make this knowledge your asset and enter a new era of computation, where you have the power to shape the code of reality. What you will learn Define quantum circuits Harness superposition and entanglement to solve classical problems Gain insights into the implementation of quantum teleportation Explore the impact of quantum computing on cryptography Translate theoretical knowledge into practical skills by writing and executing code on real quantum hardware Expand your understanding of this domain by uncovering alternative quantum computing models Who this book is for This book is for individuals familiar with algebra and computer programming, eager to delve into modern physics concepts. Whether you've dabbled in introductory quantum computing material or are seeking deeper insights, this quantum computing book is your gateway to in-depth exploration.

Contents:

Cover

Title Page

Copyright and Credits

Contributors

Table of Contents

Preface

Introduction to Quantum Computing

Part 1: Nuts and Bolts

Chapter 1: New Ways to Think about Bits

Technical requirements

Bits and logic gates

Binary representation

Working with matrices

Vectors

Matrix multiplication

The tensor product

Combining gates and bits

Matrix representation of bits and gates

Matrix operations and computer logic

Jupyter notebooks

Creating and displaying values

Which values are (or are not) defined?

Stopping a run of the code

Saving your work

Copying this book's example code

Matrices in Python

Summary

Questions

Chapter 2: What Is a Qubit?

A qubit's values between 0 and 1

Are qubits useful?

How to make a qubit

What does "between |0⟩ and |1⟩" mean?

Qubits and Qiskit

Creating and running a quantum circuit

Understanding the Qiskit code

Variations of this chapter's code

Chapter 3: Math for Qubits and Quantum Gates

Matrices for qubit states and operations

Qubits on the Bloch sphere

More points on the Bloch sphere

The X gate

The Hadamard rotation

Combining gates along a single wire

Reversible operations

Reversing a matrix operation

Unitary matrices

Rotating the Bloch sphere around an axis

Experimenting with rotations

What is a radian?

A taste of trigonometry

Chapter 4: Qubit Conspiracy Theories

Multi-qubit gates

CNOT and flipped CNOT gates

SWAP gate

Toffoli gate

Magic tricks with multi-qubit gates

Introducing entanglement

Entanglement with matrices

Working with Qiskit

The four Bell states

Role of entanglement in quantum computing

Qubits don't plan ahead

What quantum theory predicts.

What would happen if there were hidden variables?

Bell's experiment in Qiskit

Combining probabilities

Addition (either this event or that event)

Subtraction (not this event)

Multiplication (this event and that event)

Division (this event assuming that event)

Further readings

Part 2: Making Qubits Work for You

Chapter 5: A Fanciful Tale about Cryptography

Sharing secrets

Adding Hadamard gates

Introducing randomness

Adding more randomness

Alice and Bob compare some of their bits

Some remaining bits form the secret key

Is the BB84 algorithm useful?

You can't copy a qubit

Qiskit code for the BB84 algorithm

Creating the circuits

Running the quantum circuits

Displaying the outcome

Getting more information about a circuit

Chapter 6: Quantum Networking and Teleportation

Transmitting bits and qubits

Classical networks

Quantum networks

Teleporting a qubit

Quantum operations for teleportation

Teleportation versus cloning

Coding the teleportation circuitry

Creating registers

Adding gates to the registers

Running the quantum circuit

Further reading

Part 3: Quantum Computing Algorithms

Chapter 7: Deutsch's Algorithm

Describing Deutsch's problem

Algorithms

Functions

Constant and balanced functions

Deutsch's problem

Solving Deutsch's problem

Phase kickback

Detecting a CNOT gate

Embedding a function in quantum circuitry

Creating oracles

Putting it all together

Deutsch's algorithm F.A.Q.

Coding Deutsch's algorithm

Chapter 8: Grover's Algorithm

How long does it take to find what you need?

The idea behind Grover's algorithm

The oracle.

The diffuser

Searching among eight items

Searching among any number of items

The optimal number of Grover iterate applications

Matrices for Grover's algorithm

A matrix for the oracle

A matrix for the diffuser

Coding Grover's algorithm with matrices

When to use Grover's algorithm

Encrypting passwords

Finding better approximations

Satisfying Boolean expressions

Coding Grover's algorithm with high-level functions

Gates and circuits for Grover's algorithm

Gates for the oracle

Gates for the diffuser

Coding Grover's algorithm with quantum gates

Epilogue - what does have to do with Grover's algorithm?

Chapter 9: Shor's Algorithm

A popular encryption scheme

An example of RSA encryption

How Shor's algorithm works

The role of a period in factoring a number

Repeated squaring

Complex numbers

Complex number basics

The connection between complex numbers and circles

Finding a sequence's period

The QFT matrix

Shoring up your knowledge

Illustrating Shor's algorithm with Qiskit code

Testing the QFT

Another implementation of Shor's algorithm

Part 4: Beyond Gate-Based Quantum Computing

Chapter 10: Some Other Directions for Quantum Computing

What is reducibility?

Quantum simulation

Quantum annealing

Quantum neural nets

Solving unsolvable problems

References

Assessments

Chapter 1, New Ways to Think about Bits

Chapter 2, What Is a Qubit?

Chapter 3, Math for Qubits and Quantum Gates

Chapter 4, Qubit Conspiracy Theories

Chapter 5, A Fanciful Tale about Cryptography

Chapter 6, Quantum Networking and Teleportation

Chapter 7, Deutsch's Algorithm

Chapter 8, Grover's Algorithm

Chapter 9, Shor's Algorithm.

Index

Other Books You May Enjoy.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781804610565

1804610569

OCLC:

1397312764