Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part One Reference Frame Columns, Physics Today 1988–2009
- 1 What's wrong with this Lagrangean, April 1988
- 2 What's wrong with this library, August 1988
- 3 What's wrong with these prizes, January 1989
- 4 What's wrong with this pillow, April 1989
- 5 What's wrong with this prose, May 1989
- 6 What's wrong with these equations, October 1989
- 7 What's wrong with these elements of reality, June 1990
- 8 What's wrong with these reviews, August 1990
- 9 What's wrong with those epochs, November 1990
- 10 Publishing in Computopia, May 1991
- 11 What's wrong with those grants, June 1991
- 12 What's wrong in Computopia, April 1992
- 13 What's wrong with those talks, November 1992
- 14 Two lectures on the wave–particle duality, January 1993
- 15 A quarrel we can settle, December 1993
- 16 What's wrong with this temptation, June 1994
- 17 What's wrong with this sustaining myth, March 1996
- 18 The golemization of relativity, April 1996
- 19 Diary of a Nobel guest, March 1997
- 20 What's wrong with this reading, October 1997
- 21 How not to create tigers, August 1999
- 22 What's wrong with this elegance, March 2000
- 23 The contemplation of quantum computation, July 2000
- 24 What's wrong with these questions, February 2001
- 25 What's wrong with this quantum world, February 2004
- 26 Could Feynman have said this? May 2004
- 27 My life with Einstein, December 2005
- 28 What has quantum mechanics to do with factoring? April 2007
- 29 Some curious facts about quantum factoring, October 2007
- 30 What's bad about this habit, May 2009
- Part Two Shedding Bad Habits
- Part Three More from Professor Mozart
- Part Four More to be Said
- Part Five Some People I've Known
- Part Six Summing it Up
- Index
28 - What has quantum mechanics to do with factoring? April 2007
from Part One - Reference Frame Columns, Physics Today 1988–2009
Published online by Cambridge University Press: 05 January 2016
- Frontmatter
- Dedication
- Contents
- Preface
- Part One Reference Frame Columns, Physics Today 1988–2009
- 1 What's wrong with this Lagrangean, April 1988
- 2 What's wrong with this library, August 1988
- 3 What's wrong with these prizes, January 1989
- 4 What's wrong with this pillow, April 1989
- 5 What's wrong with this prose, May 1989
- 6 What's wrong with these equations, October 1989
- 7 What's wrong with these elements of reality, June 1990
- 8 What's wrong with these reviews, August 1990
- 9 What's wrong with those epochs, November 1990
- 10 Publishing in Computopia, May 1991
- 11 What's wrong with those grants, June 1991
- 12 What's wrong in Computopia, April 1992
- 13 What's wrong with those talks, November 1992
- 14 Two lectures on the wave–particle duality, January 1993
- 15 A quarrel we can settle, December 1993
- 16 What's wrong with this temptation, June 1994
- 17 What's wrong with this sustaining myth, March 1996
- 18 The golemization of relativity, April 1996
- 19 Diary of a Nobel guest, March 1997
- 20 What's wrong with this reading, October 1997
- 21 How not to create tigers, August 1999
- 22 What's wrong with this elegance, March 2000
- 23 The contemplation of quantum computation, July 2000
- 24 What's wrong with these questions, February 2001
- 25 What's wrong with this quantum world, February 2004
- 26 Could Feynman have said this? May 2004
- 27 My life with Einstein, December 2005
- 28 What has quantum mechanics to do with factoring? April 2007
- 29 Some curious facts about quantum factoring, October 2007
- 30 What's bad about this habit, May 2009
- Part Two Shedding Bad Habits
- Part Three More from Professor Mozart
- Part Four More to be Said
- Part Five Some People I've Known
- Part Six Summing it Up
- Index
Summary
A quantum computer is a digital computer capable of exploiting quantum coherence among the physical two-state systems that store the binary arithmetic information.
To factor an integer is to find its (unique) expression as a product of prime numbers.
The most impressive, most important, and best-known thing a quantum computer can do is to factor with spectacular efficiency the product of two enormous prime numbers. But what on earth can quantum mechanics have to do with factoring?
This question bothered me for four years, from the time I heard about the discovery that a quantum computer was spectacularly good at factoring until I finally took the trouble to find out how it was done. The answer, you will be relieved—but, if you're like me, also a little disappointed—to learn, is that quantum mechanics has nothing at all directly to do with factoring. But it does have a lot to do with waves. Many important waves are periodic, so it is not very surprising that quantum mechanics might be useful in efficiently revealing features associated with periodicity.
Quantum mechanics is connected to factoring through periodicity. It turns out, for purely arithmetic reasons having nothing to do with quantum mechanics, that if we have an efficient way to find the period of a periodic function, then, as we shall see below, we can easily factor the product of two enormous prime numbers. And a quantum computer provides an extremely efficient way to find periods.
All of the above is of considerable practical importance, because the great difficulty in factoring such a product—where the two enormous prime numbers are typically each several hundred digits long—is the basis for the security of the most widely used encryption scheme (called RSA [1] encryption) for protecting private information sent over the internet. In 1994 Peter Shor discovered [2] that a quantum computer would be super-efficient at period finding and thereby pose a potential threat to innumerable secrets. Whence the explosion of interest in developing quantum computation. The threat is only potential because no quantum computer capable of anything like serious period finding currently exists.
I suspect the emphasis has been put on factoring rather than period finding because factoring is more famously associated with RSA code breaking, although, as it happens, period finding can be used directly to crack the RSA code, without any need for a detour into factoring.
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- Why Quark Rhymes with PorkAnd Other Scientific Diversions, pp. 195 - 200Publisher: Cambridge University PressPrint publication year: 2016