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Quantum Computation
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** Fall 2006, Hebrew University
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Instructor:
Dorit Aharonov

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Office: Ross 72, Hebrew University, Jerusalem, 02-6584611.
Reception hour: Monday 5-6

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TA: Elad Eban

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Announcements:

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General Information:

Time and Place:

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Hebrew University: Monday, 12:00-13:45, Shprintsak
201, Wednesday 14:00-14:45, Shprintzak 114

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Tirgul:
Wednesday 13:00-13:45, Shprintzak 114

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Homework:
There will be 5-6 exercises during the semester.
Only the first exercise, which concentrates on definitions,
needs to be submitted individually, so that each one of you gets
a handle of the model.
The rest of the exercises can be done in pairs or triplets.

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Exam:
The exam will be done by each student picking a (different)
paper that interests him or her, from the following
list .
See instructions regarding meeting me before the talk, and how to prepare for it, in the above link.

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Exercises:

Hint for ex2 question 4:
Write the state as the sum over j, of |aj>|j>
where |aj> is unnormalized. Forget about the coefficients
for this exercise - just use unnormalized states, to simplify notation.
Find out the probability for Bob to measure j in terms of the
norm of the state |aj>. Call this term Dj.
Now, consider Alice measuring in any orthonormal
basis, say |bk> for k running over all basis states.
Find the state of the system if Alice had measured |bk>, and also find
the probability for this event, Pk, again, without using coefficients
but just with inner products of unnormalized states.
Now write the probability for Bob to measure j, as a sum of
the probability for alice to measure |bk>, times the probability
for Bob to measure j conditioned that alice measured |bk>.
You should get a simple expression, which you should be able to show is
equal to T.

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References:

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There are a few good places to look at:

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Quantum Computation and Quantum Information, By Michael Nielsen and Ike Chuang,Cambridge University Press. (Two copies preserved in the (math) library.)
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Quantum Theory : Concepts and Methods (Fundamental
Theories of Physics, Vol 57), by Asher Peres, Kluwer Academic Pub. (Two copies preserved in the library.)

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Other than this, the lecture notes by Preskill (a link below) and my
review article which can be found on my web page can be very helpful.
The lecture notes of Vazirani below are probably the closest material to
ours.

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Links to quantum computation web pages.

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John Preskill's Home page.
#### John's quantum course contains excellent and very coherent
lecture notes.

We will follow Umesh's course quite closely, so you might find the
lecture notes very useful.

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Also called quant-ph.
You can find most papers on quantum computation there.
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Lecture notes

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Note that these notes are very poorly edited by me and may very well
contain mistakes!

Week2 (postscript file)

Week3 (postscript file)

Week4 (postscript file)

Week5 (postscript file)

Week6 (postscript file)

Week7 (postscript file)

Week8 (pdf file)

Week9 (postscript file)

Week10 (postscript file)

Week11 (postscript file)

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Additional Material (to be used later on in the course):

Proofs of Fermat's little theorem