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Quantum Computing

Provided as a free public service for those interested in the exciting new field of quantum computing. No guarantees as to the information here, since we're in way over our head!



Basic Information

Quantum Computing Languages

Other Reading

People sometimes used to believe that computer programmers are mathematicians gone to seed. Some years ago I purchased two books at a public library used book sale which I somehow felt that I must have and someday read. I have poked around at them over the years but never completed either. Now I find myself opening them by my bedside to refresh my mathematical grasp so as to deal with relativity and quantum physics. These two books are: Vectors is very readable and helpful in a way that gives the reader a sense that the author liked students. Tensor Calculus and Relativity seems a little less friendly to the student, but it is still very pithy and useful. I conclude I was very fortunate in these inexpensive chance purchases.

Some other books which Internet acquaintance Albert Martinez ( recommends:

Quantum Cryptography and Quantum Computation
Nielsen and Chuang
Cambridge University Press, 2000.
ISBN (hardcover): 0 521 63235 8
ISBN (softcover): 0 521 63503 9
hardcover, ~$100 US
softcover, ~$50 US

It has introductory material on quantum mechanics, and computer science.
It has a linear algebra review which uses the Dirac notation. I recomend
the following books as supplementary material for it. They are cheap but
written better than anything I had to buy for college. Dover publishing is
the king of cheap REAL math and science books. Cambrige press is good, but
a little more expensive. Schuams and REA have cheap($20US) and cheerful
solved problem books. Why should anybody spend $100 on some dumbed down,
i..e. "university", text book?

These are all by:
Dover Publications, Inc. Mineola, New York
Published in Canada by General Publishing Company LTD., 30 Lesmill Road, Don
Mills, Toronto, Ontario.

Quantum Mechanics
Albert Messiah
ISBN: 0 486 40924 4
Very well written, really good explanation of the Dirac notation and other
math needed for this subject.

Linear Algebra
Georgi E. Shilov
ISBN:0 486 63518 X
No dirac notation.

Probability, Elements of the Mathematical Theory
C. R. Heathcote
ISBN: 0 486 41149 4

Oh, hell, I'm on a roll:

Matrix Theory
Joel N. Franklin
ISBN: 0 486 41179 6

Modern Algebra
Seth Warner
ISBN: 0 486 66341 8

Set Theory and Logic
Robert Stoll
ISBN: 0 486 63829 4

One more for the road, this time, by cambridge:
Foundations of Cryptography
Oded Goldreich
Cambridge University Press, 2001
ISBN: 0 521 79172 3

More helpful links


There's a famous optical QM delayed-choice experiment in which Mitsu informs me that empirically the following result can be obtained:
Number of apparati Emitted Observed between split and recombine? View of all exposed plates superimposed
1 Continuous stream of photons No Interference
1 Continuous stream of photons Yes No interference
1 One photon per second No Interference
1 One photon per second Yes No interference
Many Continuous stream of photons No Interference
Many Continuous stream of photons Yes No interference
Many One photon per emitter once No Interference
Many One photon per emitter once Yes No interference


Mitsuhara Hadeishi made the following interesting comment:
[T]he mystery of quantum mechanics is of a very different kind from the mystery of, say, why the fine structure constant is 1/137. The QM mystery is not just "why are the equations that way and not some other way" --- but rather --- what do the equations mean? What is a measurement? What does consciousness have to do with measurement? Why do we measure anything at all?

There is a big fuzzy hole at the center of QM, and the fundamental question of why we observe collapse to the particular set of observables we observe (and not, for example, a set of superpositions of those observables) --- that's a really big question. NOTHING in the mathematics makes this clear whatsoever.

Presumably, quantum mechanics is describing physical systems, and presumably we, the physicists, are also physical systems. So what is the relationship between us and these systems that we observe? What is so special about an "observer" that they have the power to "observe" and thereby force a "collapse" of a quantum system?

Or, to put it another way, how is it that we can make the observations necessary to even determine the fine structure constant is 1/137?

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