Dancing with Qubits

How quantum computing works and how it can change the world

Robert S. Sutor 지음

Packt(GCO Science) 2019년 11월 28일 출간

작품소개

책소개

▶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.

목차

▶TABLE of CONTENTS
1. Why Quantum Computing?
？ PART I ？ Foundations
2. They're Not Old, They're Classics
3. More Numbers than You Can Imagine
4. Planes and Circles and Spheres, Oh My
5. Dimensions
6. What Do You Mean "Probably"?
？ PART II ？ Quantum Computing
7. One Qubit
8. Two Cubits, Three
9. Wiring Up the Circuits
10. From Circuits to Algorithms
11. Getting Physical
12. Questions about the Future

책 속으로

▶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...

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▶ Preface
When most people think about computers, they think about laptops or maybe even the bigger machines like the servers that power the web, the Internet, and the cloud. If you look around, though, you may start seeing computers in other places. Modern cars, for example, have anywhere from around 20 computers to more than 100 to control all the systems that allow you to move, brake, monitor the air conditioning, and control the entertainment system.

The smartphone is the computer many people use more than anything else in a typical day. A modern phone has a 64-bit processor in it, whatever a “64-bit processor” is. The amount of memory used for running all those apps might be 3Gb, which means 3 gigabytes. What’s a “giga” and what is a byte?

All these computers are called classical computers and the original ideas for them go back to the 1940s. Sounding more scientific, we say these computers have a von Neumann architecture, named after the mathematician and physicist John von Neumann.

It’s not the 1940s anymore, obviously, but more than seventy years later we still have the modern versions of these machines in so many parts of our lives. Through the years, the “thinking” components, the processors, have gotten faster and faster. The amount of memory has also gotten larger so we can run more―and bigger―apps that do some pretty sophisticated things. The improvements in graphics processors have given us better and better games. The amount of storage has skyrocketed in the last couple of decades, so we can have more and more apps and games and photos and videos on devices we carry around with us. When it comes to these classical computers and the way they have developed, “more is better.”

We can say similar things about the computer servers that run businesses and the Internet around the world. Do you store your photos in the cloud? Where is that exactly? How many photos can you keep there and how much does it cost? How quickly can your photos and all the other data you need move back and forth to that nebulous place?

It’s remarkable, all this computer power. It seems like every generation of computers will continue to get faster and faster and be able to do more and more for us. There’s no end in sight for how powerful these small and large machines will get to entertain us, connect us to our friends and family, and solve the important problems in the world.

Except . . . that’s false.

While there will continue to be some improvements, we will not see anything like the doubling in processor power every two years that happened starting in the mid-1960s. This doubling went by the name of Moore’s Law and went something like “every two years processors will get twice as fast, half as large, and use half as much energy.”

These proportions like “double” and “half” are approximate, but physicists and engineers really did make extraordinary progress for many years. That’s why you can have a computer in a watch on your wrist that is more powerful than a system that took up an entire room forty years ago.

A key problem is the part where I said processors will get half as large. We can’t keep making transistors and circuits smaller and smaller indefinitely. We’ll start to get so small that we approach the atomic level. The electronics will get so crowded that when we try to tell part of a processor to do something a nearby component will also get affected.

There’s another deeper and more fundamental question. Just because we created an architecture over seventy years ago and have vastly improved it, does that mean all kinds of problems can eventually be successfully tackled by computers using that design? Put another way, why do we think the kinds of computers we have now might eventually be suitable for solving every possible problem? Will “more is better” run out of steam if we keep to the same kind of computer technology? Is there something wrong or limiting about...

작가정보

저자(글) Robert S. Sutor

Robert S. Sutor has been a technical leader and executive in the IT industry for over 30 years. More than two decades of that have been spent in IBM Research in New York. During his time there, he worked on or led efforts in symbolic mathematical computation, optimization, AI, blockchain, and quantum computing. He is the co-author of several research papers and the book, Axiom: The Scientific Computation System with the late Richard D. Jenks.He also was an executive on the software side of the business in areas including emerging industry standards, software on Linux, mobile, and open source. He's a theoretical mathematician by training, has a Ph.D. from Princeton University, and an undergraduate degree from Harvard College. He started coding when he was 15 and has used most of the programming languages that have come along.