《Quantum Computing since Democritus》 Scott Aaronson.pdf

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Contents

Preface

A Critical Review of Scott Aaronson’s quantum computing since democritus

Now for the actual preface

What’s new

Acknowledgments

1 Atoms and the void

2 Sets

Rules of first-order logic

Peano axioms for the nonnegative integers

Axioms of set theory

3 Gödel, Turing, and friends

Turing machines

Bonus addendum

Exercise

Further reading

4 Minds and machines

Puzzles

Answers to exercise from last chapter

5 Paleocomplexity

Further reading

Puzzle 1 from last chapter

Puzzle 2 from last chapter

6 P, NP, and friends

Petting zoo

Problem set

7 Randomness

Puzzles

8 Crypto

Answers to puzzles from Chapter 7

Crypto

Pseudorandom generators

One-way functions

Public-key cryptography

9 Quantum

A less than 0% chance?

Mixed states

The squaring rule

Real versus complex numbers

Linearity

Further reading

10 Quantum computing

Uncomputing

Relation to classical complexity classes

Quantum computing and NP-complete problems

Quantum computing and many-worlds

Further reading

11 Penrose

Opening the black box

At risk of stating the obvious

All aboard the holistic quantum gravy train

12 Decoherence and hidden variables

Into the abyss

Story 1. Decoherence

Decoherence and the Second Law

Story 2. Hidden variables

No-go theorems galore

Examples of hidden-variable theories

The flow theory

The Schrödinger theory

Bohmian mechanics

13 Proofs

What is a proof?

Probabilistic proofs

Zero-knowledge proofs

PCP

Complexity of simulating hidden-variable theories

14 How big are quantum states?

15 Skepticism of quantum computing

16 Learning

Puzzle

17 Interactive proofs, circuit lower bounds, and more

Interactive proofs

New developments

Quantum interactive proofs

18 Fun with the Anthropic Principle

19 Free will

Newcomb's Paradox

20 Time travel

21 Cosmology and complexity

22 Ask me anything

Index

more information - www.cambridge.org/9780521199568

http://youtu.be/f477FnTe1M0http://youtu.be/4qAIPC7vG3Y

Quantum Computing since Democritus Written by noted quantum computing theorist Scott Aaronson, this book takes readers on a tour through some of the deepest ideas of math, 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. scott aaronson is an Associate Professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology. Considered one of the top quantum complexity theorists in the world, he is well known both for his research in quantum computing and computational complexity theory, and for his widely read blog Shtetl-Optimized. Professor Aaronson also created Complexity Zoo, an online encyclopedia of computational complexity theory, and has written popular articles for Scientific American and The New York Times. His research and popular writing have earned him numerous awards, including the United States Presidential Early Career Award for Scientists and Engineers and the Alan T. Waterman Award. http://youtu.be/f477FnTe1M0http://youtu.be/4qAIPC7vG3Y

http://youtu.be/f477FnTe1M0http://youtu.be/4qAIPC7vG3Y

Quantum Computing since Democritus scott aaronson Massachusetts Institute of Technology http://youtu.be/f477FnTe1M0http://youtu.be/4qAIPC7vG3Y

cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S˜ao Paulo, Delhi, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521199568 C S. Aaronson 2013 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2013 Printed and bound in the United Kingdom by the MPG Books Group A catalog record for this publication is available from the British Library Library of Congress Cataloging in Publication data Aaronson, Scott. Quantum computing since Democritus / Scott Aaronson. pages cm Includes bibliographical references and index. ISBN 978-0-521-19956-8 (pbk.) 1. Quantum theory – Mathematics. 2. Quantum computers. QC174.17.M35A27 2013 621.391 – dc23 2012036798 I. Title. ISBN 978-0-521-19956-8 Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. http://youtu.be/f477FnTe1M0http://youtu.be/4qAIPC7vG3Y

To my parents http://youtu.be/f477FnTe1M0http://youtu.be/4qAIPC7vG3Y

http://youtu.be/f477FnTe1M0http://youtu.be/4qAIPC7vG3Y

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