Quantum Computation
Fall 2006, Hebrew University
Instructor: Dorit Aharonov
Office: Ross 72, Hebrew University, Jerusalem, 02-6584611.
Reception hour: Monday 5-6
TA: Elad Eban
Announcements:
General Information:
General Information:
Time and Place:
Hebrew University: Monday, 12:00-13:45, Shprintsak
201, Wednesday 14:00-14:45, Shprintzak 114
Tirgul:
Wednesday 13:00-13:45, Shprintzak 114
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.
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.
-
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.
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.
Exercises:
Ex 1
Ex 2
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.
Ex 3
Ex 4
Ex 1
Ex 2 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.
Ex 3
Ex 4
References:
There are a few good places to look at:
Quantum Computation and Quantum Information, By Michael Nielsen and Ike Chuang,Cambridge University Press. (Two copies preserved in the (math) library.)
Quantum Theory : Concepts and Methods (Fundamental
Theories of Physics, Vol 57), by Asher Peres, Kluwer Academic Pub. (Two copies preserved in the library.)
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.
Quantum Computation and Quantum Information, By Michael Nielsen and Ike Chuang,Cambridge University Press. (Two copies preserved in the (math) library.)
Quantum Theory : Concepts and Methods (Fundamental
Theories of Physics, Vol 57), by Asher Peres, Kluwer Academic Pub. (Two copies preserved in the library.)
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.
Quantum Theory : Concepts and Methods (Fundamental Theories of Physics, Vol 57), by Asher Peres, Kluwer Academic Pub. (Two copies preserved in the library.)
Links to quantum computation web pages.
John Preskill's Home page.
John's quantum course contains excellent and very coherent
lecture notes.
Umesh Vazirani's
Course web page.
We will follow Umesh's course quite closely, so you might find the
lecture notes very useful.
Isaac Chuang's
Course web page
at MIT.
The Los-Alamos Archive.
Also called quant-ph.
You can find most papers on quantum computation there.
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.
Isaac Chuang's
Course web page
at MIT.
The Los-Alamos Archive.
Also called quant-ph.
You can find most papers on quantum computation there.
at MIT.
The Los-Alamos Archive.
Also called quant-ph.
You can find most papers on quantum computation there.
Also called quant-ph.
You can find most papers on quantum computation there.
Lecture notes
of a similar course given in the Hebrew University in 2001.
Note that these notes are very poorly edited by me and may very well
contain mistakes!
Week1 (postscript file)
Additional Material (to be used later on in the course):
Basics about complex numbers and linear algebra
Proofs of Fermat's little theorem
Completing the reduction from factoring to order finding
Something about Continued Fractions (and pianos...) and something about Continued fractions and Chaos