Quantum Computing since Democritus 1st Edition

If you're a computational complexity theorist, then everything looks like .. well, a problem in computational complexity. Scott Aaronson is astonishingly bright, on top of his subject and genuinely droll: this book gives you a fly-on-the-wall view of how he engaged with his students at the University of Waterloo.

We start with a tour of prerequisites. Chapter 2 covers axiomatic set theory (ZF); chapter 3 Gödel's Completeness and Incompleteness Theorems, and Turing Machines. In chapter 4 we apply some of these ideas to artificial intelligence, discuss Turing's Imitation Game and the state of the art in chatbots, and also Searle's Chinese Room puzzle. Aaronson invariably provides a fresh perspective on these familiar topics although already we see the `lecture note' character of this book, where details are hand-waved over (because the students already know this stuff, or they can go away and look it up).

Chapters 5 and 6 introduce us to the elementary computation complexity classes and explain the famous P not = NP conjecture. This is not a first introduction - you are assumed to already understand formal logic and concepts such as clauses, validity and unsatisfiability. Chapters 7 and 8 introduce, by way of a discussion on randomness and probabilistic computation, a slew of new complexity classes and the hypothesised relations between them, applying some of these ideas to cryptanalysis.

Chapter 9 brings us to quantum theory. Six pages in we're talking about qubits, norms and unitary matrices so a first course on quantum mechanics under your belt would help here. The author's computer science take on all this does bring in some refreshing new insights. We're now equipped, in chapter 10, to talk about quantum computing. Typically this is not architecture or engineering discussion; Aaronson is a theorist, and for his community, quantum computing means a new set of complexity classes with conjectural relationships to those of classical computation.

We now go off at a tangent as the author critiques Sir Roger Penrose's views on consciousness as a quantum gravity phenomenon. I think it's fair to say that no-one in AI takes this idea seriously, but the author has the intellectual resources to engage Penrose on his own ground here.

In chapter 12 we crank up the technical level to talk about decoherence and hidden variable theories. This is one of the most interesting chapters but is too discursive - really important concepts are touched on and then abandoned; for example the discussion of decoherence and the 2nd Law of Thermodynamics is set against a model of the multiverse, but it's never quite clear whether Aaronson is assuming the reality of the Everett Interpretation or whether he has some other, more purely mathematical model in mind.

Chapter 12 reminds us that a computational complexity theorist's idea of proof is a long way from that of a logician. We plunge into stochastic proofs, zero-knowledge proofs and probabilistically checkable proofs, all framed by a complexity analysis.

The next few chapters cover a series of topics in similar vein: quantum proofs (and their complexity classes), rebuttals of sceptical arguments against quantum computing (interesting and convincing), some technically demanding material on learning algorithms, and concepts of interactive proof.

The final few chapters are more philosophical: Aaronson applies his toolkit to topics such as the Anthropic Principle (via Bayesian reasoning); free will (he's in favour but has a highly-idiosyncratic view of what free will is); time travel (how closed timelike curves impact on classical and quantum computation); and cosmology (black holes, the information paradox, with firewalls bringing us up-to-date).

I have to say that I did finish this book - it didn't just sit on my coffee table, abandoned after the first few chapters, as the author rather fears in his preface. However, it has to be said that despite the author's undeniable enthusiasm, complexity theory remains a minority taste. There are plenty of insights and novel observations even for those of us less enthralled but I hope it's clear what kind of background the reader needs to get anything out of this volume.

To be fair, the book is already 362 pages long and to make the material less a write-up of post-graduate lecture notes and more a self-contained and smoothly-developed presentation of Aaronson's many original insights would seem to require an inordinate amount of time and effort, without substantially increasing the likely readership. I enjoyed it, but not without a degree of frustration.

To start with, I must say I'm an absolute layman when it comes to the subjects Aaronson is writing about here -- I'm a writer and software engineer, and my knowledge of physics and computer science comes from popularisations only.

That said, this is an absolutely marvelous introduction to what Aaronson refers to as quantitative epistemology. Aaronson here provides a basic overview of some of the most important concepts in the areas where mathematics, computation and physics meet, in an easy, comprehensible style. If you're interested in quantum mechanics, Turing machines, Godel's incompleteness theorem, or the P vs NP question, you'll find the best explanations I've seen in here.

The lectures on which this is based are all available on Aaronson's website for free, and I have read them many times over the years, but the book goes into more depth and holds together better, while keeping the humour of the originals.

This is not an easy-going book -- it requires work from the reader to follow, and you won't get all of it the first time. But nor is it an academic textbook -- there is some mathematics in it, but anyone who remembers fairly basic things like matrix multiplication should be fine following it.

In the title of this review I call it the Feynman Lectures for QC, and while it's nowhere near as thorough as that great work, it manages the rare feat of being both as clear and entertaining and as scientifically rigorous.

If you have any doubt as to whether this is the book for you or not, the lecture notes are still available to read for free on Aaronson's website. But I guarantee that if you have any interest at all in the most basic building blocks of our knowledge -- what we really know, deep down, about the way things work on the most fundamental level, you will not be disappointed in this book.

I found this book disappointing because it could have been a truly great book. What it's got going for it: Aaronson is very smart and reasonably eloquent. The table of contents is fantastic. He understands the material backwards and forwards.

What it's got against it: Scott makes two terrible mistakes. First, he tries overhard to be conversational. Some of this is just offputting, like the many appearances of profanity in the book. (What possible purpose could this serve?) But in many cases, he simply fails to take advantage of print as a medium. You can explain things multiple times in multiple ways. More formal and less formal. Basic idea and then development. This is never done. Everything is said basically once, at some almost completely unpredictable level of detail and formality.

The second problem is that Aaronson makes no distinction -- and I mean *no* distinction -- between what he actually knows and what he only thinks about. In some cases, he's speculating on things that other people know well, but he just goes on as if his opinion were gospel. A case in point is where he supports the view -- still not mainstream, I don't think -- that something "weird" happens when you cross the event horizon of a black hole not for any physical reason, but because he simply felt that "it should be that way." I'm sorry. If I want to adopt someone's vague intuition on this as physically accurate, I'll ask a physicist.

In other cases, he's speculating on things that no one knows about. But he still presents his speculations as if they were fact.

It's really a pity. I would have been pretty happy reading those speculations if they had only been clearly identified as such.

To see how a book like this can be done, check out Tegmark's "Our Mathematical Universe." That book is considerably less technical than this one (and the subject matter is very different), but does a wonderful job of avoiding the pitfalls into which Aaronson has fallen.