▶Book Description
Quantum computing is making us change the way we think about computers. Quantum bits, a.k.a. qubits, can make it possible to solve problems that would otherwise be intractable with current computing technology.
Dancing with Qubits is a quantum computing textbook that starts with an overview of why quantum computing is so different from classical computing and describes several industry use cases where it can have a major impact. From there it moves on to a fuller description of classical computing and the mathematical underpinnings necessary to understand such concepts as superposition, entanglement, and interference. Next up is circuits and algorithms, both basic and more sophisticated. It then nicely moves on to provide a survey of the physics and engineering ideas behind how quantum computing hardware is built. Finally, the book looks to the future and gives you guidance on understanding how further developments will affect you.
Really understanding quantum computing requires a lot of math, and this book doesn't shy away from the necessary math concepts you'll need. Each topic is introduced and explained thoroughly, in clear English with helpful examples.
▶What You Will Learn
- See how quantum computing works, delve into the math behind it, what makes it different, and - - why it is so powerful with this quantum computing textbook
- Discover the complex, mind-bending mechanics that underpin quantum systems
- Understand the necessary concepts behind classical and quantum computing
- Refresh and extend your grasp of essential mathematics, computing, and quantum theory
- Explore the main applications of quantum computing to the fields of scientific computing, AI, and elsewhere
- Examine a detailed overview of qubits, quantum circuits, and quantum algorithm
▶Key Features
- Discover how quantum computing works and delve into the math behind it with this quantum computing textbook
- Learn how it may become the most important new computer technology of the century
- Explore the inner workings of quantum computing technology to quickly process complex cloud data and solve problems
▶Who This Book Is For
Dancing with Qubits is a quantum computing textbook for those who want to deeply explore the inner workings of quantum computing. This entails some sophisticated mathematical exposition and is therefore best suited for those with a healthy interest in mathematics, physics, engineering, and computer science.
▶What does this book cover?
Before we jump into understanding how quantum computing works from the ground up, we need to take a little time to see how things are done classically. In fact, this is not only for the sake of comparison. The future, I believe, will be a hybrid of classical and quantum computers. The best way to learn about something is start with basic principles and then work your way up. That way you know how to reason about it and don’t rely on rote memorization or faulty analogies.
- Chapter 1 – Why Quantum Computing?
In the first chapter we ask the most basic question that applies to this book: why quantum computing? Why do we care? In what ways will our lives change? What are the use cases to which we hope to apply quantum computing and see a significant improvement? What do we even mean by “significant improvement”?
‣ PART I – Foundations
The first full part covers the mathematics you need to understand the concepts of quantum computing. While we will ultimately be operating in very large dimensions and using complex numbers, there’s a lot of insight you can gain from what happens in traditional 2D and 3D.
- Chapter 2 – They’re Not Old, They’re Classics
Classical computers are pervasive but relatively few people know what’s inside them and how they work. To contrast them later with quantum computers, we look at the basics along with the reasons why they have problems doing some kinds of calculations. I introduce the simple notion of a bit, a single 0 or 1, but show that working with many bits can eventually give you all the software you use today.
- Chapter 3 – More Numbers than You Can Imagine
The numbers people use every day are called real numbers. Included in these are integers, rational numbers, and irrational numbers. There are other kinds of numbers, though, and structures that have many of the same algebraic properties. We look at these to lay the groundwork to understand the “compute” part of what a quantum computer does.
- Chapter 4 – Planes and Circles and Spheres, Oh My
From algebra we move to geometry and relate the two. What is a circle, really, and what does it have in common with a sphere when we move from two to three dimensions? Trigonometry becomes more obvious, though that is not a legally binding statement. What you thought of as a plane becomes the basis for understanding complex numbers, which are key to the definition of quantum bits, usually known as qubits.
- Chapter 5 – Dimensions
After laying the algebraic and geometric groundwork, we move beyond the familiar twoand three-dimensional world. Vector spaces generalize to many dimensions and are essential for understanding the exponential power that quantum computers can harness. What can you do when you are working in many dimensions and how should you think about such operations? This extra elbow room comes into play when we consider how quantum computing might augment AI.
- Chapter 6 – What Do You Mean “Probably”?
“God does not play dice with the universe,” said Albert Einstein. This was not a religious statement but rather an expression of his lack of comfort with the idea that randomness and probability play a role in how nature operates. Well, he didn’t get that quite right. Quantum mechanics, the deep and often mysterious part of physics on which quantum computing is based, very much has probability at its core. Therefore, we cover the fundamentals of probability to aid your understanding of quantum processes and behavior.
‣ PART II – Quantum Computing
The next part is the core of how quantum computing really works. We look at quantum bits—qubits—singly and together, and then create circuits that implement algorithms. Much of this is the ideal case when we have perfect fault-tolerant qubits. When we really create quantum computers, we must deal with the physical realities of noise and the need to reduce errors.
- Chapter 7 – One Qubit
At this point we are finally able to talk about qubits in a nontrivial manner. We look at both the vector and Bloch sphere representations of the quantum states of qubits. We define superposition, which explains the common cliché about a qubit being “zero and one at the same time.”
- Chapter 8 – Two Qubits, Three
With two qubits we need more math, and so we introduce the notion of the tensor product, which allows us to explain entanglement. Entanglement, which Einstein called “spooky action at a distance,” tightly correlates two qubits so that they no longer act independently. With superposition, entanglement gives rise to the very large spaces in which quantum computations can operate.
- Chapter 9 – Wiring Up the Circuits
Given a set of qubits, howdo you manipulate them to solve problems or performcalculations? The answer is you build circuits for them out of gates that correspond to reversible operations. For now, think about the classical term “circuit board.” I use the quantum analog of circuits to implement algorithms, the recipes computers use for accomplishing tasks.
- Chapter 10 – From Circuits to Algorithms
With several simple algorithms discussed and understood, we next turn to more complicated ones that fit together to give us Peter Shor’s 1995 fast integer factoring algorithm. The math is more extensive in this chapter, but we have everything we need from previous discussions.
- Chapter 11 – Getting Physical
When you build a physical qubit, it doesn’t behave exactly like the math and textbooks say it should. There are errors, and they may come from noise in the environment of the quantum system. I don’t mean someone yelling or playing loud music, I mean fluctuating temperatures, radiation, vibration, and so on. We look at several factors you must consider when you build a quantum computer, introduce Quantum Volume as a whole-system metric of the performance of your system, and conclude with a discussion of the most famous quantum feline. This book concludes with a chapter that moves beyond today.
- Chapter 12 – Questions about the Future
If I were to say, “in ten years I think quantum computing will be able to do . . . ,” I would also need to describe the three or four major scientific breakthroughs that need to happen before then. I break down the different areas in which we’re trying to innovate in the science and engineering of quantum computing and explain why. I also give you some guiding principles to distinguish hype from reality. All this is expressed in terms of motivating questions.
