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Scott Aaronson

Quantum Computing Since Democritus 1st Edition

by Scott Aaronson (Author)

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Written by noted quantum computing theorist Scott Aaronson, this book takes readers on a tour through some of the deepest ideas of maths, computer science and physics. Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

ISBN-10

9780521199568
ISBN-13

978-0521199568
Edition

1st
Publisher

Cambridge University Press
Publication date

April 29, 2013
Language

English
Dimensions

5.98 x 1.01 x 8.98 inches
Print length

398 pages
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Editorial Reviews

Review

"Scott Aaronson has written a beautiful and highly original synthesis of what we know about some of the most fundamental questions in science: what is information? What does it mean to compute? What is the nature of mind and of free will? Highly recommended."
Michael Nielsen, author of Reinventing Discovery

"I laughed, I cried, I fell off my chair - and that was just reading the chapter on computational complexity. Aaronson is a tornado of intellectual activity: he rips our brains from their intellectual foundations; twists them through a tour of physics, mathematics, computer science, and philosophy; stuffs them full of facts and theorems; tickles them until they cry 'Uncle'; and then drops them, quivering, back into our skulls. Aaronson raises deep questions of how the physical universe is put together and why it is put together the way it is. While we read his lucid explanations we can believe - at least while we hold the book in our hands - that we understand the answers, too."
Seth Lloyd, Massachusetts Institute of Technology, author of Programming the Universe

"Not since Richard Feynman's Lectures on Physics has there been a set of lecture notes as brilliant and as entertaining. Aaronson leads the reader on a wild romp through the most important intellectual achievements in computing and physics, weaving these seemingly disparate fields into a captivating narrative for our modern age of information. Aaronson wildly runs through the fields of physics and computers, showing us how they are connected, how to understand our computational universe, and what questions exist on the borders of these fields that we still don't understand. This book is a poem disguised as a set of lecture notes. The lectures are on computing and physics, complexity theory and mathematical logic and quantum physics. The poem is made up of proofs, jokes, stories, and revelations, synthesizing the two towering fields of computer science and physics into a coherent tapestry of sheer intellectual awesomeness."
Dave Bacon, Google

"… how can I adequately convey the scope, erudition, virtuosity, panache, hilarity, the unabashed nerdiness, pugnacity, the overwhelming exuberance, the relentless good humor, the biting sarcasm, the coolness and, yes, the intellectual depth of this book?"
Frederic Green, SIGACT News

"It is the very definition of a Big Ideas Book … It's targeted to readers with a reasonably strong grounding in physics, so it's not exactly a light read … But for those with sufficient background, or the patience to stick with the discussion, the rewards will be great."
Sean Carroll and Jennifer Ouellette, Cocktail Party Physics, Scientific American blog

"The range of subjects covered is immense: set theory, Turing machines, the P versus NP problem, randomness, quantum computing, the hidden variables theory, the anthropic principle, free will, and time travel and complexity. For every one of these diverse topics, the author has something insightful and thought provoking to say. Naturally, this is not a book that can be read quickly, and it is definitely worth repeated reading. The work will make readers think about a lot of subjects and enjoy thinking about them. It definitely belongs in all libraries, especially those serving general readers or students and practitioners of computer science or philosophy. Highly recommended."
R. Bharath, Choice

"… lively, casual, and clearly informed by the author's own important work … stimulating … It should prove valuable to anyone interested in computational complexity, quantum mechanics, and the theory of quantum computing."
Francis Sullivan, Physics Today

"… a wonderful, personal exploration of topics in theory of computation, complexity theory, physics, and philosophy. His witty, informal writing style makes the material approachable as he weaves together threads of complexity theory, computing theory, mathematical logic, and the math and physics of quantum mechanics (QM) and quantum computing to show how these topics interrelate to each other, what that says about the universe, and something about us … this book is a treat."
G. R. Mayforth, Computing Reviews

Book Description

Takes students and researchers on a tour through some of the deepest ideas of maths, computer science and physics.

Product details

ASIN ‏ : ‎ 0521199565
Publisher ‏ : ‎ Cambridge University Press; 1st edition (April 29, 2013)
Language ‏ : ‎ English
Paperback ‏ : ‎ 398 pages
ISBN-10 ‏ : ‎ 9780521199568
ISBN-13 ‏ : ‎ 978-0521199568
Item Weight ‏ : ‎ 1.21 pounds
Dimensions ‏ : ‎ 5.98 x 1.01 x 8.98 inches

Best Sellers Rank: #305,583 in Books (See Top 100 in Books)
- #254 in Quantum Theory (Books)
- #966 in Computer Science (Books)
- #1,635 in Science & Mathematics

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196 ratings

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4.4 out of 5

196 global ratings

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VL

A very approachable, engaging, and ambitious book

Reviewed in the United States 🇺🇸 on March 31, 2013

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I agree with other reviewers that Quantum Computing Since Democritus is written in the spirit of the likes of Richard Feynman, Carl Sagan, and Douglas Hofstadter. It's funny, engaging, easy to get into, but also quite deep: Not so easy any longer if you intend to follow everything in detail. Why there is a painting of Che Guevara in a toga on the cover of the book however remains a mystery. ;)

This ambitious book weaves together many strands of inquiry: computation, science, mathematics, and philosophy. The conventional view of quantum mechanics, one that dates back to the first half of the 20th century yet is still often repeated in the media, is the notion that quantum theory is a mysterious "brute fact"; one that we have to accept without deeper understanding just because it works. Scott takes a refreshing and radical view. In his own words from the book:

"Quantum mechanics is a beautiful generalization of the laws of probability: A generalization based on the 2-norm rather than on the 1-norm, and on complex numbers rather than on nonnegative real numbers. It can be studied completely separately from its application to physics (and indeed doing so provides a good starting point for learning the physical application later). This generalized probability theory leads naturally to a new model of computation - the quantum computing model - that challenges notions of computation once considered a priori, and that theoretical scientists might have been driven to invent for their own purposes even if there were no relation to physics. In short, while quantum mechanics was invented a century ago to solve technical problems in physics, today it can be fruitfully explained from an extremely different perspective: as part of the history of ideas, math, logic, computation, and philosophy, about the limits of the knowable."

The wonderful thing about this book is that one can read it on a number of different levels. You can choose get a bird's eye view of many important ideas, or you can delve more deeply into the math. I consider this book's greatest achievement to be the way in which it makes the material approachable, builds the reader's intuition, and connects thing together in ways that may not be obvious. First of all it makes the reader *curious* about the technical details, which otherwise might seem pointless or boring to non-specialists; next it makes it a lot easier to know how to begin drilling into the more formal, mathematical aspects of the book.

I think Scott brings to this material a remarkable unifying vision. I feel like there's almost a complete education in math, physics, and comp sci concealed within this book. Scott takes us on a thrilling journey through many fields and ideas, often to unexpected places, like the information content of a black hole and the fundamental limits of computing based on things such as the schwarzschild radius.

13 people found this helpful

Helpful

Chris Larkin

Hanging out in the Complexity Zoo

Reviewed in the United States 🇺🇸 on July 23, 2014

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A more accurate title would be "Hanging out in the Complexity Zoo: Lecture Notes". While there is discussion on quantum mechanics especially in the view of it being 2-norm vectors being used in a probability like system, the main focus is on complexity. For example, there's a decent amount of focus on the Merlin-Arthur class of decision problems that can be solved where Merlin, an untrusted entity with unbounded computational resources, can send a polynomial-sized proof of a solution of the problem to Arthur, a Probabilistic polynomial-time (i.e. computational limited with randomness) verifier. Arthur then will verify the proof as correct at least 2/3s of the time. Near the end there is some discussion of topics like time travel, time, and free will. Typically by coming up with new types of problems such P(CTC) which is all problems solvable by a polynomial machine with closed timelike curves i.e. time travel.

The big problem with the book is that it's almost flat out not written for a causal reader. As admitted by the author, it's a collection of lecture notes from a class in 2006 that doesn't know what its audience is. It doesn't have enough handholding to be for general audiences, nor enough focus to be a textbook. There's a lot to learn and more importantly think about, but it's hard reading if you're not prepared.

The key things you need for the book is a solid understanding of matrices while a familiarity to computational nomenclature is greatly helpful. I will admit I let my matrices skills lapses which made this a hard book to read (I often had to stop and look up stuff on wikipedia) and I feel like I missed at least a decent chuck of the insights in the book. The author's wiki, the Complexity Zoo helped. The authorial tone is flippant and he's tries to exceptionally witty some of the time especially when he brings up Stephen Wolfram.

Unlike the author, I think the book could be general audience reachable with a chapter on matrices and another on basic terminology. It'll still be a hard read and never mass-markable, but it'll be more accessible to those with the inclination to read it.

Ultimately, I suggest the book if you found the above discussion of the Merlin-Arthur problems interesting and your matrices are up to snuff. If they're not, you'll want to skip it or get back to it once you do. I may reread it at some point, but ultimately I'll most likely use it as a reference from time to time (with a tab open to wikipedia).

14 people found this helpful

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Top reviews from other countries

Adam Carlton

Witty and erudite - but still lecture notes

Reviewed in the United Kingdom 🇬🇧 on October 17, 2013

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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.

16 people found this helpful

Edina Monsoon

Impressed

Reviewed in the United Kingdom 🇬🇧 on August 16, 2013

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I must admit I'm impressed. With a PhD in Astrophysics and Masters degrees in Maths, Physics and Software Engineering, it's rare indeed that I encounter a book which leaves me feeling thoroughly and irredeemably thick. Even Penrose's Road To Reality didn't leave me floundering quite as often. This is not a exactly a critique of Aaronson's book, but take it rather as a warning; despite its breezy style, this is not a book for the casual reader or dilettante. It will, however, reward the careful reader with a great deal more than the title promises. Aaronson has thought more deeply and more clearly than most about the nature of quantum physics and the fundamental limits of knowledge, and it is worth the reader's effort to at least attempt to follow the subtleties of his exposition.

6 people found this helpful

Vicki A. Bates

Efficient purchase

Reviewed in the United Kingdom 🇬🇧 on January 23, 2019

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Arrived quickly and as described. No idea about the content as bought it as a gift

David Wright

and fun, and laughter

Reviewed in the United Kingdom 🇬🇧 on February 17, 2015

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Wit, and physics, and fun, and laughter! What's not to like?

3 people found this helpful

Arthur Doohan

Five Stars

Reviewed in the United Kingdom 🇬🇧 on January 21, 2018

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Good quality, would repeat

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