# Review of Quantum Computing for Everyone

The MIT Press, Cambridge, MA, 2019

216 pp., illus. 60 b/w. Trade, $24.95

ISBN: 9780262039253.

This book has a title that is very timely. Anyone interested in recent advances in computation cannot have failed to recognise the potential of the power of applying quantum mechanics to calculations. This is shortened to “Quantum Computing.” The additional phrase “for Everyone” implies that everyone can get to grips with it. This is only true if you can tolerate linear algebra and matrix multiplication together with the adoption of ket and bra notation from quantum mechanics. This is decidedly not everyone, or perhaps even most people, but let’s forgive a catchy title. It certainly helps that the book is written in a direct no-nonsense style with no frills.

The book opens with easy to understand concepts of spin and measurement, plus polarisation. In chapter 2 the mathematics starts, and the reader might be forgiven for thinking that this will soon be over and that the rest of the book is free from mathematics, but this is not the case. To be fair to Chris Bernhardt, he does emphasise how important understanding the basics of chapter 2 is, but to the non-mathematical reader, concepts come thick and fast and will seem relentless. So, it has to be assumed that you are willing to learn and get on board with the concepts introduced in chapter 2. Without them most of the rest of the book will not be well understood. For example, the concept of a qubit (chapter 3) can only be introduced using linear algebra. An alternative would be to use complex numbers, but the author avoids these––rightly so in my view though there are some minor drawbacks later.

The whole idea that nothing is settled until it is measured is well catered for by these linear algebra operations, as one assigns probabilities early on and the act of making the measurement is modelled by multiplying the quantum entities, represented by kets and bras. The author carefully distinguishes between classical physics whereby we are certain of the state, and that this does not change when measured, and quantum physics. In quantum physics a state has to be represented in such a way that all the possible states are somehow indicated and the right one emerges once a measurement is made. It is this measurement that is represented by all the linear algebra operations.

Later chapters introduce quantum entanglement and quantum teleportation. Entanglement implies, amongst other things, that the state of an object quite distant from another can be affected by measuring the state of just one of the objects: “spooky action at a distance” as Albert Einstein called it. It is counter-intuitive but is substantiated by experiment. It is proved using the mathematics of chapter 2, old fashioned linear algebra. Bell’s inequality has a chapter to itself, and it is in this chapter that the author explains the essential fact that no classical theory can ever reproduce entanglement. However, thanks to Artur Ekert, there seems to be a protocol to protect our internet security despite entanglement.

Teleportation sounds like science fiction, the “beam me up now, Scotty” beloved of Star Trek. However here it is only information content that is “beamed” and not all of Captain Kirk himself. Maybe the information content of Captain Kirk could be transported instantly from one body to a receiving one; however, this would be poor television, and such macroscopic events would still not be possible using current quantum scale physics. The energy required is the mass multiplied by the square of the speed of light, a huge quantity even for moderate masses.

Later in the book there is more mathematics in the form of Boolean algebra and the mathematics of gates (in particular the NAND gate) and then on to quantum gates and circuits. All of this material is well enough written and explained, but it is not a holiday read. If attention to detail flags through distraction from that hot sun, the rest of the book will not be well understood.

The last chapter of the book looks into the future and shows us that the author is convinced of the power of quantum computing in important areas such as cryptography and internet security. Various algorithms are described in words, but details are avoided as they would be too mathematical. The author is certainly convinced of a bright future for quantum computing, and this reviewer cannot but agree. So, if you are interested in learning more about quantum computing and are willing to put in a few hours of hard work learning, or preferably being re-acquainted with, linear algebra, then this book is highly recommended.