Computing with Quantum Cats

Published 2014 by Prometheus Books

Computing with Quantum Cats: From Colossus to Qubits
. Copyright © 2014 by John Gribbin. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, digital, electronic, mechanical, photocopying, recording, or otherwise, or conveyed via the Internet or a website without prior written permission of the publisher, except in the case of brief quotations embodied in critical articles and reviews.

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Acknowledgments

Introduction: Computing with Quantum Cats

PART ONE: COMPUTING

1           Turing and the Machine

A Child of Empire
—
Sherborne
—
Cambridge…
and Princeton
—
Bletchley and the Bombe
—
The Flowering of Colossus
—
Anticlimax: After Bletchley

2           Von Neumann and the Machines

Jancsi
—
Johnny and the Institute
—
Johnny and the Bomb
—
The American Heritage
—
A German Diversion
—
The Second Strand
—
ENIAC
—
Von Neumann Picks Up the Ball
—
Self-Replicating Robots

First Interlude: Classical Limits

PART TWO: QUANTA

3           Feynman and the Quantum

MIT
—
From Princeton to Los Alamos
—
Schrödinger and His Equation
—
The Experiment with Two Holes
—
Integrating History
—
A PhD with a Principle
—
Cats Don't Collapse
—
The Gateway to Quantum Computation
—
Fredkin, Feynman and Friends

4           Bell and the Tangled Web

Dropping the Pilot
—
Von Neumann Gets It Wrong
—
Spooky Action at a Distance
—
Bohm Does the Impossible
—
From Belfast to Bohm, and Beyond
—
Von Neumann's Silly Mistake and Bell's Inequality
—
First Fruits
—
Closing the Loophole

Second Interlude: Quantum Limits

PART THREE: COMPUTING WITH QUANTA

5           Deutsch and the Multiverse

Everett Sets the Scene
—
Solving the Measurement Problem
—
The Worlds of Deutsch
—
A Measure of Universes
—
The Good: Cracking Codes Conveniently
—
The Bad: Limits of Quantum Computation
—
The Ugly: Making It Work

6           Turing's Heirs and the Quantum Machines

The Key Criteria
—
Josephson and the Junction
—
Leggett and the SQUID
—
Computing with SQUIDs
—
Corralling with Quantum Dots
—
The Nuclear Option
—
The Nuts and Bolts of NMR
—
Trapped Ions Take a Bow
—
The Teleportation Tango
—
Fun with Photons

Coda: A Quantum of Discord

Notes

Sources and Further Reading

Picture Acknowledgments

Index

This book grew out of conversations with the quantum computer group at Sussex University, in particular Winfried Hensinger, who opened my eyes to the dramatic progress now being made in the practical application of ideas that seemed esoteric even a few years ago. I already knew something about those esoteric ideas thanks to David Deutsch, of the University of Oxford, and Terry Rudolph, at London's Imperial College. Thanks also to the helpful people at Bletchley Park, Gonville and Caius College, Cambridge, and the David Bohm Archive at Birkbeck College, London; and to John Carl, Frank Carter, Terry Clark, David Darling, Artur Ekert, Lucien Hardy, Mark Hogarth, Betty Houghton, Tero Keski-Valkama, Tony Leggett, Lawrence Lerner, Irfan Siddiqi and Michelle Simmons.

Both experimental and theoretical physicists are currently excited by the prospect of developing computers operating on quantum principles. There is also a lively interest among the military—a source of a great deal of funding—and big business. Quantum computation is one of the hottest scientific topics of the second decade of the twenty-first century, and it all depends on manipulating quantum entities (electrons, photons or single atoms) that are in two states at the same time—exactly like Schrödinger's famous “dead and alive” cat. Hence my title.

This is a watershed time in computational science, because quantum computers do much more than operate faster than conventional computers—although they certainly do that. For example, they can be used to crack codes that are literally uncrackable by conventional computers, which is a major reason for the interest of the military and big business. This has been known in theory for decades (Richard Feynman
was one of the first people to speculate along these lines); but now working quantum computers are actually being used. Admittedly, as yet they involve very large pieces of expensive and temperamental equipment solving very simple problems, such as finding the factors of the number 15. But nobody who has seen the evolution of conventional computers from expensive, temperamental, laboratory-sized machines full of glowing “valves” to the PC and the iPad can doubt that within a decade the computer world will be turned upside down. More esoterically, such machines will enable physicists to come to grips with the nature of quantum reality, where communication can occur faster than the speed of light, teleportation is possible, and particles can be in two places at once. The implications are as yet unknowable, but it is fair to say that the quantum computer represents an advance as far beyond the conventional computer as the conventional computer is beyond the abacus.

Conventional computers—often referred to as “classical” computers—store and manipulate information consisting of binary digits, or bits. These are like ordinary switches that can be in one of two positions, on or off, up or down. The state of a switch is represented by the numbers 0 and 1, and all the activity of a computer involves changing the settings on those switches in the appropriate way. My own computer is, while I am writing these sentences using a word processing program, also playing music, and has an e-mail program running in the background that will alert me if a new message comes in. All of this, and all the other things computers can do, is happening because strings of 0s and 1s are being moved and manipulated inside the “brain” of the computer.
¹

Eight bits like this make a byte, and because we are
counting in base two rather than base ten the natural steps up the ladder of multiplication do not go 10, 100, 1,000 and so on but 2, 4, 8, 16 and so on. It happens that 2
¹⁰
is 1,024, which is close to 1,000, and we are used to using base 10, so 1,024 bytes is called a kilobyte. Similarly, 1,024 kilobytes make a megabyte, and 1,024 megabytes make a gigabyte. The hard drive of my laptop computer can store 160 gigabytes of information, and the “brain”—the processor—can manipulate up to 2 gigabytes at a time, all in the form of strings of 0s and 1s (this is now a rather old machine; “this year's model” can do even better).

But a quantum computer is something else. In the quantum world, entities such as electrons can be in a superposition of states. This means that quantum switches can be in both states, on and off at the same time, like Schrödinger's “dead and alive” cat. Electrons themselves, for example, have a property called spin, which is not quite the same as what we mean by spin in our everyday world, but can be thought of as meaning that the electron is pointing either up or down. If we say that “up” corresponds to 0 and “down” corresponds to 1, we have a binary quantum switch. Under the right circumstances, this switch can exist in a situation where it is pointing both up and down at the same time. Or it can be pointing either up or down, giving three possibilities!

A single quantum switch that is in a superposition of states can “store” the numbers 0 and 1 simultaneously. By extension from the language of classical computers, such a quantum switch is called a qubit, short for “quantum bit” and pronounced “cubit,” like the biblical unit of length. The qubits are the “quantum cats” of my title. The existence of qubits has mind-blowing implications. Two classical bits, for example,
can represent any of the four numbers from 0 to 3, because they can exist in any of four combinations: 00, 01, 10 and 11. To represent all four of the numbers (0, 1, 2 and 3) simultaneously, you would need four pairs of numbers—in effect, one byte. But just two qubits can represent all four of these numbers simultaneously. A set of bits (or qubits) operating as a number store in this way is called a register. A register made up of eight qubits (a single qubyte) can represent not four but 2
⁸
numbers simultaneously. That's 256 numbers stored in a single qubyte. Or, as Oxford physicist David Deutsch would put it, it represents 256 different universes in the Multiverse, sharing the information in some way.

In a functioning quantum computer, any manipulation involving an operation on each of those 256 numbers represented by that qubyte of information is carried out simultaneously in all 256 universes, as if we had 256 separate classical computers each working on one aspect of the problem in our universe, or one computer that had to be run 256 times, once for each value of the number. Looking further into the future, a quantum computer based on a 30-qubit processor would have the equivalent computing power of a conventional machine running at 10 teraflops (trillions of floating-point operations per second)—ten thousand times faster than conventional desktop computers today, which run at speeds measured in gigaflops (billions of floating-point operations per second). These numbers hint at the prodigious power of a quantum computer; but the trick is to find a way of getting useful information out at the end of the calculation—getting the different universes to interfere with one another in the right way to produce an “answer” that
we can understand, without destroying the useful information along the way. This trick is now being achieved by several groups around the world, including a research team at my home base, Sussex University. This book will tell you how, in principle, to build a quantum computer. But to set this in context, I want to go all the way back to the beginning of machine computation as we know it—all the way back to the 1930s, less than a long human lifetime ago, and the work of the man who started the ball rolling.