Computing With Quantum Cats: From Colossus to Qubits - Rilegato

Gribbin, John

Rilegato

ISBN 10: 1616149213 ISBN 13: 9781616149215

Casa editrice: Prometheus Books, 2014

Riassunto

A mind-blowing glimpse into the near future, where quantum computing will have world-transforming effects.

The quantum computer is no longer the stuff of science fiction. Pioneering physicists are on the brink of unlocking a new quantum universe which provides a better representation of reality than our everyday experiences and common sense ever could. The birth of quantum computers - which, like Schrödinger's famous "dead and alive" cat, rely on entities like electrons, photons, or atoms existing in two states at the same time - is set to turn the computing world on its head.

In his fascinating study of this cutting-edge technology, John Gribbin updates his previous views on the nature of quantum reality, arguing for a universe of many parallel worlds where "everything is real." Looking back to Alan Turing's work on the Enigma machine and the first electronic computer, Gribbin explains how quantum theory developed to make quantum computers work in practice as well as in principle. He takes us beyond the arena of theoretical physics to explore their practical applications - from machines which learn through "intuition" and trial and error to unhackable laptops and smartphones. And he investigates the potential for this extraordinary science to create a world where communication occurs faster than light and teleportation is possible.

This is an exciting insider's look at the new frontier of computer science and its revolutionary implications.

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Informazioni sull?autore

John Gribbin gained a PhD from the Institute of Astronomy in Cambridge (then under the leadership of Fred Hoyle) before working as a science journalist for Nature and later New Scientist. He is the author of a number of bestselling popular science books, including In Search of Schrödinger's Cat, In Search of the Multiverse, Science: A History, and The Universe: A Biography. He is a Visiting Fellow at the University of Sussex and in 2000 was elected a Fellow of the Royal Society of Literature.

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COMPUTING with QUANTUM CATS

FROM COLOSSUS TO QUBITS

By JOHN GRIBBIN

Prometheus Books

Copyright © 2014 John Gribbin
All rights reserved.

ISBN: 978-1-61614-921-5

Contents

Acknowledgments, vii, 
Introduction: Computing with Quantum Cats, 1, 
PART ONE: COMPUTING, 
1 Turing and the Machine, 9, 
2 Von Neumann and the Machines, 53, 
First Interlude: Classical Limits, 90, 
PART TWO: QUANTA, 
3 Feynman and the Quantum, 99, 
4 Bell and the Tangled Web, 135, 
Second Interlude: Quantum Limits, 176, 
PART THREE: COMPUTING WITH QUANTA, 
5 Deutsch and the Multiverse, 183, 
6 Turing's Heirs and the Quantum Machines, 226, 
Coda: A Quantum of Discord, 267, 
Notes, 271, 
Sources and Further Reading, 279, 
Picture Acknowledgments, 283, 
Index, 285, 

CHAPTER 1

Turing and the Machine

If necessity is the mother of invention, the computer had twomothers—cryptography and the hydrogen bomb. But therewas only one father: Alan Mathison Turing.

A CHILD OF EMPIRE

Turing was conceived in India, where his father, Julius, was amember of the Indian Civil Service helping to administer thisjewel in the crown of the British Empire; but he was born,on June 23, 1912, in Maida Vale, London, when his parentswere on home leave. He already had a brother, John, born inIndia on September 1, 1908. When Julius returned to Indiatheir mother, Sara, stayed in England with the two boys, butonly until September 1913, when she rejoined her husbandand left the children in the care of a retired army colonel andhis wife, who lived at St. Leonards-on-Sea in Sussex. Therewas a nanny who looked after the two boys and the colonel'sfour daughters, together with another boy whose parents wereoverseas, and later three cousins of Alan and John. Theirmother returned for the summer of 1915, staying with theboys in rented rooms in St. Leonards, and both parents cameto England in the spring of 1916—the first time that Alanreally had an opportunity to get to know his father. At theend of this leave, in August, Julius Turing returned to Indiafor his next three years' tour of duty. John had already beensent away to school at Hazelhurst, in Kent; Alan, havingbeen just one of a motley group of children, now became ineffect the only child of a single parent, who took him almosteverywhere with her, including to the High Anglican churchshe attended (which he hated) and to art classes (she was anaccomplished watercolorist), where he was the darling of thefemale students.

Alan was remembered as a bright, untidy child with a predilectionfor inventing his own words, such as "quockling" todescribe the sound of seagulls and "greasicle" for a gutteringcandle. It was impossible to pull the wool over his eyes—whenhis nanny tried to let him win a game they were playing bymaking poor moves, he saw through the subterfuge and wasinfuriated; when his mother was reading him a story and left adull passage out, he yelled: "You spoil the whole thing." Norwas he ever in any doubt about the accuracy of his own worldview:he knew, for example, that the fruit which tempted Evein the Garden of Eden was a plum. But he never could tell leftfrom right, and marked his left thumb with a red spot so thathe would know which was which.

Having taught himself to read (from a book appropriatelycalled Reading without Tears), Alan first encountered formaleducation at the age of six, when his mother sent him to alocal day school to learn Latin. This failed to stir his interest,but highlighted his great difficulty with the physical processof writing, especially with the ink pens in use at the time. Hiswork was always a mess of scratchy scribbles, crossings-outand blots, reminiscent of nothing so much as the spoof handiworkof Nigel Molesworth in the stories by Geoffrey Willansand Ronald Searle.

Alan's next meeting with his father came in 1919, whenJulius's leave included a holiday in Scotland: here the seven-year-oldboy impressed his family on a picnic by tracking theflights of wild bees to their intersection to find honey. But inDecember both parents sailed for India, and Alan returnedto the colonel's house in St. Leonards while John went backto school in Hazelhurst. The next two years saw a changein Alan. When his mother next returned, in 1921, she foundthat the vivacious and friendly boy she had left in Englandhad become "unsociable and dreamy," while his educationhad been so neglected that at nearly nine he had not learnedhow to do long division. She took him away for a holiday inBrittany, and then to London, where she taught him long divisionherself. She later recalled that when he had been shownhow to find the square root of a number, he worked out forhimself how to find the cube root.

At the beginning of 1922, it was time for Alan to followhis brother John to Hazelhurst, a small school for thirty-sixboys aged from nine to thirteen, with just three teachersand a matron who looked after the boys. The brothers weretogether at Hazelhurst for only one term before John left atEaster for Marlborough College and the public-school educationfor which "prep" schools such as Hazelhurst werepreparing their boys. The same year, Alan was given a bookcalled Natural Wonders Every Child Should Know, by EdwinBrewster. This first encounter with science made a deepimpression on him, especially the way the author likened theworkings of the body, even the brain, to a machine. He wasless impressed by the sporting activities that young Englishgentlemen of the time were expected to enjoy (or at leastendure), and later claimed that he had learned to run fast(he became a very good long-distance runner as an adult)in order to keep away from the ball during hockey. He wasalso disturbed by the imprecision of some of his teachers, andwrote to John that one of them "gave a quite false impressionof what is meant by x." His concern was not for himself, butthat the other boys might be misled.

The summer of 1922 brought the return of Alan's fatheron leave once more, and another happy family holiday inScotland. But in September his parents left him back atHazelhurst, departing down the drive of the school with Sarabiting her lip as she watched her son running futilely afterthe taxi, trying to catch up with them. Bored by school, Alanachieved nothing spectacular in the way of marks, but lovedinventing things and developed a passion for chemistry—whichwas purely a hobby: God forbid that a prep schoollike Hazelhurst should have anything to do with science.Science was almost as conspicuous by its absence at mostpublic schools, so when in the autumn of 1925 Alan surprisedeveryone by doing well in the Common Entrance examinationthat was a prerequisite to the transition, his future presentedhis parents with something of a conundrum. Johnmade an impassioned plea to their parents not to send hisunusual younger brother to Marlborough, which "will crushthe life out of him," and Sara Turing worried that her sonmight "become a mere intellectual crank" if he failed to adaptto public school life. The puzzle of what to do with him wassolved by a friend of hers who was married to a science masterat Sherborne, a school in Dorset established back in 1550 andbrought into the modern public school system in 1869. Thefriend assured Sara that this would be a safe haven for her boy,and Alan started there in 1926.

SHERBORNE

He was due to arrive for the start of the summer term, onMay 3, from Brittany, where his parents were living to avoidpaying British income tax. On the ferry to Southampton,Alan learned that there would be no trains, because of thegeneral strike; totally unfazed, and still a month short of hisfourteenth birthday, he cycled the 60 miles to Sherborne,staying overnight at Blandford Forum. This initiative wassufficiently unusual to merit a comment in the WesternGazette on May 14. The same initiative and independencewere shown a little later when Alan worked out for himselfthe formula known as "Gregory's series" for the inversetangent, unaware that it had been discovered in 1668 by theScottish mathematician James Gregory (inventor of a kind oftelescope that also bears his name), and even earlier by theIndian mathematician Madhava.

Alan soon settled into his old habit of largely ignoringlessons that he found boring, then doing well in examinations,while continuing his private chemistry experiments andamusing himself with advanced mathematics. At Sherborne,grades depended on a combination of continuous assessmentand examinations, each marked separately but with afinal combined mark. On one occasion, Alan came twenty-secondout of twenty-three for his term's work, first in theexaminations, and third overall. His headmaster did notapprove of such behavior, and wrote to Alan's father: "Ihope he will not fall between two stools. If he is to stay ata Public School, he must aim at becoming educated. If he isto be solely a Scientific Specialist, he is wasting his time at aPublic School." But Alan escaped expulsion, and was rathergrudgingly allowed to take the School Certificate examination,which had to be passed before he could move on to the sixthform at the beginning of 1929. His immediate future afterschool, however, was decided as much by love as by logic.

As in all public schools, filled with teenage boys withno other outlet for their burgeoning sexuality, there wereinevitably liaisons between older and younger pupils, nomatter how much such relationships might be officiallyfrowned upon. It was in this environment that Alan realizedthat he was homosexual, although there is no recordof his having any physical relationships with other boysat school. He did, though, develop something more than acrush on a boy a year ahead of him at school, ChristopherMorcom.

The attraction was as much mental as physical (indeed,from Morcom's side it was all mental). Morcom was anothermathematician, with whom Alan could discuss science,including Einstein's general theory of relativity, astronomy,and quantum mechanics. He was a star pupil who workedhard at school and achieved high grades in examinations,giving Alan, used to taking it easy and relying on brillianceto get him through, something to strive to emulate. Theexamination they were both working for, the Higher SchoolCertificate (or just "Higher"), was a prerequisite to moving onto university. In the mathematics paper they sat, Alan scoreda respectable 1,033 marks; but Morcom, the elder by a year,scored 1,436.

In 1929, Morcom was to take the examination for a scholarshipat Trinity College, Cambridge. He was eighteen, andexpected to pass. Alan was desperate not to see his friend goon to Cambridge without him. He decided to take the scholarshipexamination at the same time, even though he wasstill only seventeen and Trinity was the top college in Britain(arguably, in the world) for the study of math and science,with a correspondingly high admission standard. The examinationswere held over a week in Cambridge, giving the twoShirburnians a chance to live the life of undergraduates, andto meet new people, including Maurice Pryce, another candidate,whom Alan would meet again when their paths crossedin Princeton a few years later.

The outcome was as Alan had feared. Morcom passed,gaining a scholarship to Trinity that gave him sufficient incometo live on as an undergraduate. Alan did not, and faced a separationof at least a year from his first love. But the separationbecame permanent when Morcom died, of tuberculosis, onFebruary 13, 1930. Alan wrote to his own mother: "I feel thatI shall meet Morcom again somewhere and that there will besome work for us to do together.... Now that I am left to doit alone I must not let him down." And in the spirit of doingthe work that they might have done together, or that Morcommight have done alone, and "not letting him down," Alantried once again for Cambridge in 1930. Once again, he failedto obtain a Trinity scholarship; but this time he was offered ascholarship worth £80 a year at his second choice of college,King's. He started there in 1931, when he was nineteen.

CAMBRIDGE ...

Turing managed the unusual feat of joining in both the sportinglife (as a runner and rower) and the academic life in Cambridge,while never quite fitting in anywhere socially. He also enjoyedat least one homosexual relationship, with another mathstudent, James Atkins. But it is his mathematical work that isimportant here. Turing's parting gift from Sherborne, in theform of a prize for his work, had been the book MathematicalFoundations of Quantum Mechanics, by the Hungarian-bornmathematician John von Neumann, who would soon playa personal part in Turing's story. In an echo of his earlydays at Sherborne, not long after he arrived in CambridgeTuring independently came up with a theorem previously(unbeknown to him) proven by the Polish mathematicianWaclaw Sierpinski; when Sierpinski's priority was pointed outto him, he was delighted to find that his proof was simplerthan that of the Pole. Polish mathematicians would also soonloom large in Turing's life.

In the early 1930s, the structure of the mathematics coursein Cambridge was changing. Everybody who entered in 1931(eighty-five students in all) took two key examinations, Part Iat the end of the first year and Part II at the end of the thirdyear. So-called "Schedule A" students left it at that, which wassufficient to gain them their degrees. But "Schedule B" students,including Turing, took a further, more advanced, examination,also at the end of their third year. For the intake whichfollowed Turing's year, the extra examination was taken aftera further (fourth) year of study, as it has been ever since: itbecame known as Part III, and is now roughly equivalent to aMaster's degree from other universities.

This peculiarity of the Cambridge system partly explainswhy Turing never worked for a PhD in Cambridge. Havingpassed his examinations with flying colors, he was offereda studentship worth £200 which enabled him to stay on atCambridge for a year to write a dissertation with which hehoped to impress the authorities sufficiently to be awarded afellowship at King's. In the spring of 1935, still only twenty-twoyears old, Turing was indeed elected as a Fellow of King'sfor three years, with the prospect of renewal for at least afurther three years, at a stipend of £300 per year; the successwas sufficiently remarkable that the boys at Sherborne weregiven a half-day holiday in his honor. But something muchmore significant had happened to Turing during his studentshipyear. He had been introduced to the puzzle of whetherit was possible to establish, from some kind of mathematicalfirst principles, whether or not a mathematical statement(such as Fermat's famous Last Theorem) was provable. Apartfrom the philosophical interest in the problem, if such a techniqueexisted it would save mathematicians from wasting timetrying to prove the unprovable.

A very simple example of an unprovable statement is "thisstatement is false." If it is true, then it must be false, and if it isfalse, it must be true. So it cannot be proven to be either trueor false. The mathematical examples are more tricky, for thoseof us without a Part III in math, but the principle is still thesame. Embarrassingly for mathematicians, it turns out thatthere are mathematical statements which are true, but cannotbe proven to be true, and the question is whether provablestatements (equivalent to "this statement is true") in mathematicscan be distinguished from unprovable statements usingsome set of rules applied in a certain way.

Turing's introduction to these ideas came from a series oflectures given by Max Newman on "The Foundations ofMathematics," drawing heavily on the work of the Germanmathematician David Hilbert. Newman described the applicationof this kind of set of rules as a "mechanical process,"meaning that it could be carried out by a human being (ora team of such human "computers") following the rulesblindly, without having any deep insight. As the Cambridgemathematician G. H. Hardy had commented, "it is onlythe very unsophisticated outsider who imagines that mathematiciansmake discoveries by turning the handle of somemiraculous machine." But Turing, always idiosyncratic andliteral-minded, saw that a "mechanical process" carried outby a team of people could be carried out by a machine, inthe everyday sense of the word. And he carried with him theidea, from his childhood reading, of even the human bodyas a kind of machine. In the early summer of 1935, as he layin a meadow at Grantchester taking a rest from a long run,something clicked in his mind, and he decided to try to devisea machine that could test the provability of any mathematicalstatement. By then, he had already met von Neumann, whovisited Cambridge in the spring of 1935, and had applied fora visiting fellowship at Princeton, von Neumann's base, for thefollowing year. He would not arrive empty-handed.

(Continues...)

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Dettagli dell?edizione

• Editore: Prometheus Books
• Data di pubblicazione: 2014
• Lingua: Inglese
• ISBN 10: 1616149213
• ISBN 13: 9781616149215
• Rilegatura: Copertina rigida
• Numero di pagine: 295
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile