# Overall Rating ★★★★☆

This book, Quantum Computing for Everyone" Chris Bernhardt, The MIT Press Cambridge, which has been meticulously compiled by extracting only the essential tools necessary for understanding quantum computers for beginners, can be considered a highly challenging read.

Of course, this book does not provide a systematic understanding of quantum mechanics; however, it effectively conveys the fascination of quantum phenomena. It succinctly and easily explains the mechanism of quantum computers utilizing these phenomena. The book is structured and curated with the aim of providing the shortest path to theoretically understanding how quantum computers are realized as conceptual devices. This makes it highly educational.

As a matter of personal preference, it might be beneficial to enhance the mathematical explanations for beginners to achieve a more balanced approach. Additionally, it's worth noting that this book serves as an introduction, and for those seeking a deeper understanding in terms of physical or logical implementation, further exploration into advanced literature may be necessary.

# Target Audience

The intended audience appears to be individuals who:

Have studied up to high school mathematics and are willing to make a little extra effort.

Seek an approachable understanding of quantum computers but also want to comprehend them from a mathematical perspective.

Typically, understanding quantum computers requires a grasp of quantum mechanics, a field that can be challenging to comprehend. Even attempting to gain a solid mathematical understanding of quantum mechanics involves a considerable amount of effort just to learn the mathematical framework. Furthermore, without a solid grasp of basic physics, reaching the understanding of quantum mechanics is a formidable task.

In other words, comprehending quantum computers is incredibly challenging! For those who perceive it as such, this book offers a refreshing and promising proposition. How does it fare in reality?

# Author

After obtaining a Ph.D. in Mathematics from the University of Warwick, the author became a Mathematics Professor at Fairfield University. Their primary focus in writing lies in computer theory, spanning various fields, including mathematics, physics, and computer science.

# Chapter 1: Spin

A classic approach to introducing quantum mechanics is to begin with an explanation of spin, particularly delving into the Stern-Gerlach experiment. The Stern-Gerlach experiment is a fascinating phenomenon, and its perplexity effectively conveys the intrigue of quantum mechanics (in fact, understanding this phenomenon is crucial for grasping the fundamental principles of quantum computers). The chapter also introduces experiments involving polarizing filters. Using diagrams to illustrate the concept that light passes through a polarizing filter due to its transverse wave nature might make the sense of wonder more accessible.

# Chapter 2: Linear Algebra

This chapter serves as a review of the basics of linear algebra, which may seem obvious to those who have studied it before. However, individuals unfamiliar with the subject may find some explanations lacking. In particular, the use of bracket notation in contrast to traditional linear algebra might pose a slight challenge for beginners (though they may choose to read on without worrying too much about the differences).

Nevertheless, I hope readers will be surprised and intrigued by the minimal mathematical framework presented. The absence of complex linear algebra, operators, Hamiltonians, observables, eigenvalues, and the lack of correspondence between the Schrödinger and Heisenberg pictures may seem unconventional. (Come to think of it, not even the uncertainty principle, which always appears in the introduction to quantum mechanics, is mentioned!) Yet, rest assured, it works!

# Chapter 3: Spin and Quantum bits

In Chapter 3, readers learn how to explain the mysterious experimental results seen in Chapter 1 using the language of linear algebra. While it may seem exceedingly basic, it helps one understand that quantum mechanics is a mechanics that is often challenging to explain in ordinary natural language. However, I suggest providing a slightly more straightforward explanation of the situation setting in the BB84 protocol. It was a great opportunity to delve into the theme of communication using quantum bits, which is in line with the book, and rushing through it seems a bit of a missed opportunity.

# Chapter 4: Quantum Entanglement

Instead of delving into the phenomenon of quantum entanglement from an observational perspective, Chapter 4 provides a concise explanation of the formalism of quantum entanglement through equations and interpretations. It introduces the possibilities of communication and touches on the understanding of the phenomenon. A deeper understanding is deferred to later chapters. This approach to explanation seems clear and suitable for beginners.

# Chapter 5: Bell's Inequality

Chapter 5 provides an understanding of Bell's Inequality by performing actual calculations with a simple system as an example. Basic concepts are discussed, such as the differing results obtained for the same phenomenon under classical and quantum interpretations, with experimental support favoring the quantum explanation. The chapter ultimately leads to the explanation of the Ekert protocol, where the existence of this inequality becomes the decisive factor in measuring whether communication using quantum bits is intercepted. If anything, a more in-depth explanation using equations for the Ekert protocol would have been appreciated.

# Chapter 6: Classical Theory, Gates, and Circuits

This chapter effectively summarizes the relationship between logic gates, the fundamental components of computers, and Boolean algebra in an easily understandable manner. Using the example of billiard ball computing, it succinctly illustrates how logical gates can be conceptually designed through small particle collisions and reflections, ultimately connecting to the principles of quantum computing. While briefly reviewing the basics of information theory, the presentation seems minimal yet clear, making it accessible even for beginners.

# Chapter 7: Quantum Gates and Circuits

In this chapter, quantum gates that realize CNOT are introduced in a somewhat ad hoc manner. It might be less stressful to read with the attitude that such conceptual devices exist rather than questioning how they are actually implemented. Once overcoming this hurdle, the discussion on phenomena with names like "super-dense coding" and "quantum teleportation" proceeds relatively smoothly. However, it would have been beneficial to have a bit more concrete explanation on how the implementation is achieved, especially towards the end of the chapter. While the final chapter provides an overview at the hardware (product level), some examples or illustrations on how quantum gates are implemented at the level of real experimental setups would have been appreciated.

# Chapter 8: Quantum Algorithms

This chapter serves as the climax of the book. Utilizing the input provided thus far, algorithms that use quantum phenomena to solve specific problems are introduced. Regardless of their utility, the chapter illustrates instances where these algorithms can solve certain problems exponentially faster compared to classical computer-implemented algorithms. Three algorithms—Deutsch's algorithm, Deutsch-Josza algorithm, and Simon's algorithm—are presented. While these algorithms explore the properties of a relatively simple unknown function, understanding the detailed procedures can be quite challenging and is where readers may need to put in extra effort. Although conceptual insights into how problems are solved in cases of extremely simple problem setups are provided, readers interested in more challenging applications may need to refer to advanced literature or research papers.

# Chapter 9: Impacts of Quantum Computing

Starting with the discussion that RSA, the currently prevalent encryption method, would be compromised if Shor's algorithm is realized, Chapter 9 introduces various cases where quantum computing could have significant applications. Particularly, the application of quantum computing to problems with immense computational requirements, such as computational simulations of chemical phenomena, based on the idea of "let quantum problems be solved by quantum means," is explored. The chapter also briefly touches on recent trends in commercial hardware related to quantum computing.

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