A great addition to the essential reading list for those interested in quantum computing

Book Review

“Dancing with Qubits - How Quantum Computing Works and How it can Change the World” By Robert Sutor (IBM)

Robert (“Bob”) Sutor’s "Dancing with Qubits" is a useful and timely contribution to the rapidly expanding list of books that have been published recently that position themselves as “introductions” to Quantum Computing.

In a publishing sector where such text-books typically end up being pale derivative versions of Nielsen and Chuang’s classic, “Quantum Computing and Quantum Information”, or which are so general as to be of little practical use, Sutor has delivered a work that is both accessible without being patronising, and that does not compromise on the serious (and significant) mathematical facility that is required to do anything more than develop an intuition for a complex subject that spans computer science, maths and quantum mechanics.

The title of the book is clearly inspired by Zeilinger’s “Dance of Photons” which was published almost a decade ago, and which has become a classic of its kind, and is indispensable in any initial reading list about quantum computing. Like Zeilinger, Sutor brings a hands-on “quantum native” approach to a subject that very quickly becomes intractable for the vast majority of computer scientists or mathematicians who are predominantly classically trained. To be perfectly frank, many recent “introduction to quantum computing” books have been authored by people who are not quantum-native. The difference between those works and books such as that by Sutor, or Zeilinger (or of course Nielsen and Chuang) becomes very clear very quickly – I talk a little more about that below.

Dancing with Qubits is very much an "Arm Wave Free Zone". As a text-book it benefits also from being bang upto date in terms of the advances in quantum computing that have been announced in the past year or so. The book, for example, includes a substantial section that provides a carefully structured exposition of how quantum computers actually work on the hardware side. It is noticeable that most, if not all, recent authors of introductions to quantum computing have been people who lack first hand working knowledge in this area. The section on T1 and T2 coherence measures, for example, lifts the veil on a topic that almost everyone will have heard about but have little more than a vague intuition for. Sutor succeeds in marrying the theory with reality in the space of just over 6 pages with fulsome diagrams and thorough (i.e. no short cuts) mathematical formalism that takes full advantage of the foundations laid in previous sections. Similarly the section “What does it take to be a qubit” is pretty much the best simple hardware linked explanation I have seen in any published format as part of a general introduction to quantum computing with not a single wave of an arm to be seen :)

A notable difference between “Dancing with Qubits” and many other introductory books, is the way that it has been organised. The sections on quantum computing don’t actually start until almost half-way through the book. This means that there are over 200 pages of mathematical instruction, covering everything from linear algebra, probability theory, trigonometry to basic number theory. These mathematical sections follow a precise and well written introduction to the foundations of computer science and an equally well presented opening chapter titled simply “Why Quantum Computing ? ” It is possible that certain readers might not need the full mathematical instruction on offer, but I would imagine that for most who fall into the ideal readership catchment area, the first half of the book will be a godsend. Anyone with a curious disposition, and decent high school maths under their belt will be able to follow the pedagogical style without much problem, and for those who don’t need the detail, they can plough on to the second half of the book. In this respect Sutor reminds me a little of Susskind and “Quantum Mechanics – The Theoretical Minimum”.

The other convention that will be useful to the very large number of people who will navigate and use the book as a traditional academic text-book based on topics rather than treating it as something to be read from start to finish like a novel or long form journalism, is the addition of an upfront summary of the chapter to be read that is situated at the start of each chapter, along with a mini table of contents covering that same chapter. This is a useful approach that is not often used, but which is extremely helpful. The introductory sections at the start of each chapter are supplemented with a more traditional closing summary at the end of the chapter. I can’t recall anything this thorough in other introductory text books. This shows a care and attention to detail that bears in mind his likely readership that I find refreshing. This is a complex subject and readers new to the topic need all the help they can get and Sutor tries his best to carry everyone along.

Additionally, and personally something I find to be very effective, Sutor has chosen to pull together publication and journal references on a chapter by chapter basis rather than having dozens and dozens of unwieldy pages hidden away at the end of the book. I suspect (sadly) that a lot of the material that is contained in these references will be locked away behind pay walls and thus not available to the general public, but a reasonable proportion of the older papers and articles have passed into the public domain.

The true heart of the book starts in Section II, with the chapter titled “One Qubit”. Sutor’s immense grasp and mastery of his subject comes to the fore as he changes stance from “Maths Lecturer” to “Deep thinking quantum computing specialist”, and someone who obviously understands the subtle but significant differences between “classical” and “quantum” approaches to the whole issue of information theory.

The section starts with a quote from Niels Bohr

“Anyone who is not shocked by quantum theory has not understood it”

Which stands in contrast with the regular choice of most authors of books about quantum computing who choose to run with a version of Feynman’s (alleged) oft misquoted remark “…if you think you understand quantum mechanics, you don’t understand quantum mechanics…” The choice of Bohr over Feynman reflects Sutor’s philosophical approach to quantum computing, which becomes very clear as he slowly but surely takes his reader by the hand and swims out of the shallows into the deeps.

Sutor believes that the most enduring mystery in science – quantum mechanics – is also capable of being used in order to solve some of humanity’s most compelling problems. I have had the privilege of meeting and getting to know Charlie Bennett and there is more than a little Bennett in Sutor’s tone and ‘voice’. This may not be so surprising since both work at IBM. In any event, I think this “ground” up approach that treats the subject with the deference and awe that it deserves is Sutor’s strength, and one of the reasons why I thoroughly enjoyed this second section so much. It is clearly the heart of the book.

Early on in Dancing with Qubits, Sutor informs his readers that analogies don’t work – or at least don’t work well enough in any serious way. This decision – to eschew analogy as a method to describe quantum principles – means that each of the actual examples are worked through in great detail. It is this challenge that is the foundational basis of the book as a whole, and ultimately is the reason why Sutor succeeds in his objective of delivering an introduction to quantum computing that works across for a wide variety of audiences. It is also here that Sutor most clearly establishes a baseline between himself and those who are not “quantum native”. I know from personal experience that it is very easy when explaining things to a non-specialist audience, to fall into the trap of using an easy analogy. I also know how dangerous these analogies can be – in fact classical analogies can be a hindrance to true understanding, and there is no substitute to working from the ground up and mastering (or at least understanding) the formalism of quantum physics at a basic level.

The section on binary addition using logic gates is an example of how Sutor’s approach to exposition works in practice – and works well. Most non-specialists will have a reasonably well-developed intuition in appreciating that binary code is the underlying language of all computer programming. Working from that intuition to understanding how arithmetic using qubits takes advantage of binary addition using logic gates in quantum computers to build circuits, once understood will be better than any classical analogy.

The iconic examples that everyone uses to explain how quantum computers might be provably better and more effective than classical computers are the Deutsch-Josza algorithm, Shors factoring algorithm, Grover’s search algorithm, and Quantum Teleportation. In many respects whether and how these examples are handled (explained) is a very good way of assessing so called ‘introductory’ books. It is here that Dancing with Qubits scores as highly as anything currently available.

Despite being an important tool for secure quantum communications, Quantum Teleportation (“QT”) very often suffers from the immediate association with the entirely science fiction construct by the creators of the Star Trek film and TV series when entire humans and groups of humans could magically be transported (“teleported”) from a space ship to the surface of a planet or even to other space ships. Nothing of that sort is anticipated or promised in Quantum teleportation, not the least of the reasons being that the no-cloning condition of quantum mechanics would make such an act virtually impractical.

QT was first developed formally by Charlie Bennett and Giles Brassard in the early 1990’s, although experimental proofs were not implemented until 1997. In very basic terms, QT allows two spatially separated parties to exchange messages in a secure manner by utilising the uniquely quantum mechanical property of entanglement. Entanglement, along with superposition and interference are the core quantum mechanical properties that are exploited by quantum computers and are the reason why quantum computing is often described as being "the way that nature computes”.

QT requires three qubits. In most examples, the ubiquitous “Alice and Bob” exchange a pair of entangled particles (A and B), with Alice then having an extra particle (X). Alice wants to tell Bob about the information contained in X (let’s say that if the particles were photons, then she wants to tell Bob about the polarity of X), and therefore performs the equivalent of a Bell measurement on particle X and particle A, and sends the result to Bob. The key here is to remember that Alice does not herself know the polarity of X. The result of the bell measurement has to be sent to Bob classically (meaning the information cannot travel faster than the speed of light). However, in contravention of every known classical rule, computational or otherwise, Bob, upon receiving the results of Alice’s Bell measurement of X and A will be able to decide which sort of measurement to perform on particle B, and that result will tell him something that not even Alice knew, i.e the exact state of X (the information in this case being the polarity of X).

As noted above, QT, via entanglement, exploits the essential (and still mysterious) quality of quantum computing that underpins so much of the computational power that can be derived from quantum processors. The protocols and original papers and experiments are utterly beautiful, and in fact the quantum circuits that implement QT are simple and straightforward (at least as simple and straightforward as any quantum circuit could be).

Sutor’s determination not to compromise in terms of detail whilst at the same time treating his readers with respect without patronising them, comes to the fore in this section. His decision to unpack equations so that each step is fully explained, and his ability to “signpost” how each line relates to previous sections is so good that on the strength of this section alone I have recommended the book to a number of friends who have struggled to understand Quantum Teleportation. None of them is a mathematician or scientist, all are professionals in their own field, and good examples of the ideal reader for a book such as this.

There are inevitably some areas of Dancing with Qubits that could be improved. The notational index at the end of the book refers the reader back to parts of the book where the symbols occur. There is in fact a section on mathematical symbols just a few pages prior in the appendix. I think both sections could usefully be combined and of course in doing so there would be no inconsistency in the notation covered in the appendix versus the index. I also thought that after an encouraging start to the section on “Questions about the Future” which kicks off with Turing’s wonderful quote “..we can only see a short distance ahead but we can see plenty that needs to be done”, Sutor fails to provide much more than a list of questions that, whilst challenging, are left slightly hanging and give the impression of an addition or afterthought that might have been suggested more by editors and publishers than being a core part of the author’s original chapter plan. In any event I have heard Sutor speak on the topic, and for the reason that I think he has a very clear minded philosophy about quantum computing, hearing his views on the near term would be interesting. I have added a link below to one of many of Sutor's talks in the recent past which shed some light on his opinions and views about the near term future of quantum computing.

All in all Dancing with Qubits is a very cool piece of work and one that I would recommend to my previously published short list of recommended reading for anyone wanting to get more deeply acquainted with a topic that we are all going to be hearing a great deal more about in 2020 and beyond.

 Ilyas Khan, Cambridge England December 8th 2019