Abstract
Prof. Chris Bernhardt's book "Quantum Computing for Everyone" on the fundamentals of quantum computing stands out among the many. By today, I had read all the pages of it and understood almost all of its content. I want to look back on it and use it to help me move forward in the future. I also wrote this article because it might be useful for other readers.
●What kind of book is it
This book is a rigorous explanation of what quantum computing is, rather than just general knowledge. It differs from many other books in that it does a great job of explaining the essence of quantum computing in high school mathematics. At the beginning, it says, "The goal is not to give some vague idea of these concepts but to make them crystal clear." Exactly so, until the very end, "crystal clarity" was true.
Although it is at a basic level, qubits, quantum superposition, quantum entanglement, and even "Bell's inequality", which became a hot topic at the 2022 Nobel Prize in Physics, are explained with a certain degree of rigor. He skillfully organizes a difficult system and makes it as simple as possible. And while maintaining the rigor of using mathematical formulas, it is described so that it can be understood at the high school mathematics level.
For example, Simon's algorithm at the end looks very difficult. But the concise explanation using the Kronecker Product of the Hadamard matrices is really nice and makes it understandable. Also, the generation (output) of the linear equations for the elements of the secret string includes control to amplify or cancel the probability amplitude, such as the interference of two waves. This is also a way to get in touch with the essence of quantum computing.
Moreover, the book is written from a very broad perspective. The author is also the author of the book "Turing's Vision - the birth of computer science -" and has a deep knowledge of computational science. In fact, this book is not just a technical book, but shows everywhere the viewpoint of basic theory of computation such as computational complexity and reversibility. It also appropriately explains the discussions of Einstein, Schrödinger, Bohr, Bell, and others, which are related to the fundamentals of quantum physics, to broaden the reader's background. From an educational point of view, the theory is always followed by a concrete example so that the reader can follow the calculations. It helps a lot in checking understanding.
So far, this book may give you a solid impression, but it also writes about the relationship with the daily life of society as follows, and it makes me feel bright. For example, the following episodes are written. (1) In the explanation of the polarization of light: he puts in his pocket polarizers given to him by a physicist friend of his and enjoys its wonder. (2) There is a street in Belfast named "Bell's Theorem" which can be found on Google maps. (3) We may not know whether the quantum measuring device is rotating or whether the moving qubit is rotating. It's like when I'm commuting to work, I don't know if my train has started or the train across from me has started. (4) In the qubit error correction section: when he was a student, he suffered from 33 popping sounds per minute when the vinyl record was scratched. However, the error correction function of the CD eliminated it.
●How did I read this book
Before I came across this book, I was learning quantum annealing and made some applications for combinatorial optimization problems. I also got fragmentary knowledge about gate-type quantum computing from information on the web. But this book is the first time I've systematically learned about quantum computing.
I spent several hours reading each day. It took about 2.5 months to finish reading all the pages. At this point, I was able to understand almost everything in this book. During this time, I understood the difficult parts by reading them twice, three times, or more. In the process, I asked him several questions about the book by e-mail, and he kindly answered them. In some ways, this has allowed me to move forward. I also stopped at key milestones and published them as blog posts to ensure my understanding. A list of such articles is included at the end of this article.
This book aims to provide a thorough understanding of theory. It does not use currently available quantum circuit simulators or quantum computers. I followed suit and avoided using quantum circuit simulators until I could understand them on paper and pencil. After fully understanding it, I confirmed it with a simulator. I felt that such a procedure would deepen my understanding. In other words, I thought that running the simulator from the beginning and looking at the results would prevent me from delving deeper into the algorithm itself. Quantum circuit simulators would not have existed in the days of pioneers such as Bell, Deutsch, Simon and Grover.
●closing
This book describes the amazing properties of quantum and the numerous quantum algorithms that make use of them. Among them, if I were to list three that impressed me the most, they would be (1) Bell's inequality, (2) quantum teleportation, and (3) Simon's algorithm. Now that I understand almost everything in this book, I'm on a higher tier. In the future, I will be able to tackle even more advanced quantum algorithms. In the final chapter, he also considers IBM and Google's quantum computer development status and its impact. I would like to end by quoting the author's words:
“Computation is really quantum computation. Classical computations are just special cases of quantum ones.”
“The greatest years for quantum computation are ahead of us.”
●Blog posts written to confirm understanding of the book (mostly in Japanese)
・Simon's Monumental Quantum Algorithm（2022-12-11）
・Qubit error correction using quantum teleportation（2022-12-04）
・Fredkin's Universal Logic Gate with Billiard Balls（2022-11-16）
・A street in Northern Ireland named "Bell's Theorem"（2022-10-24）
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