Printing version
25th School in Theoretical Physics JERUSALEM, December 26, 2007 - January 4, 2008
Lecturer's Notes
AdY Stern - (PDF file )
Gora Shlyapnikov: talk1 talk2 talk3
Ignacio Cirac: talk1 talk2 talk3
Subir Sachdev: talk1 talk2 talk3 ( boson Hubbard model)
References for Dorit Aharonov's lectures on Quantum computation, Quantum error correction and universality of one dimensional adiabatic evolution:
General references:
A text book on quantum computation and quantum information, which contains essentially all basic results in the area,
is the book "Quantum Computation and Quantum information" by Michael Nielsen and Isaac Chuang.
A review paper that I have written on quantum algorithms might be useful to introduce you gently to the area of quantum
computation: http://arxiv.org/abs/quant-ph/9812037
Preskill's lecture notes on the subject are a wonderful source of information on quantum computation, quantum error
correction, quantum fault tolerance, topological quantum computation and more: http://www.theory.caltech.edu/~preskill/ph229/
Quantum algorithms
You can read about Shor's algorithm in any of the texts mentioned above.
A nice exposition of the Fast Fourier transform on a quantum computer can be found here;
http://www.cs.berkeley.edu/~vazirani/s07quantum/notes/lecture7.pdf
The Jones polynomial algorithm in its more mathematical version (without using TQFT) is explained here
http://arxiv.org/abs/quant-ph/0511096
See references therein for the TQFT and Anyonic approaches to the issue; As well as Preskill's notes.
Quantum error correction and fault tolerance:
A version of the threshold theorem for fault tolerant quantum computation, updated recently, can be found in
http://arxiv.org/abs/quant-ph/9906129 Its introduction contains the main references about fault tolerance and error correction therein,
including discussions of extensions of the noise model to correlated noise etc.
See the introduction and especially the related work part.
Adiabatic computation
For discussion of the universality of adiabatic evolution for quantum computation, with general geometry,
as well as the connection to quantum NP, see
http://portal.acm.org/citation.cfm?id=1033159
Adiabatic in 1Dim is universal:
For the proof that Adiabatic evolution in 1dim with nearest neighbor interactions can simulate universal quantum computation,
see our recent paper "The power of quantum systems on a line" http://arxiv.org/abs/0705.4077
it discusses many questions related to the computational complexity of ground states.