I cannot attend this conference... though ... what a pity... Japan is located

too far from Canada. I'll go to US in this August. Toooooo hard schedule.

There will be a session by Erdahl....

(At CSC2009, Garnet and Ayers kindly told me about this conference, thanks!)

http://atlas-conferences.com/cgi-bin/abstract/cazc-03

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Non-commutative polynomial optimization and the varianional RDM method by Stefano Pironio

**http://atlas-conferences.com/cgi-bin/abstract/cazc-03**

A standard problem in optimization theory is to find the minimum of a polynomial function subject to polynomial inequality constraints. We introduce a generalization of this problem where the optimization variables are not real numbers, but non-commutative variables, i.e., operators acting on Hilbert spaces of arbitrary dimension. We show how semidefinite programming (SDP) can be used to solve this problem. Specifically, we introduce a sequence of SDP relaxations of the original problem, whose optima converge monotically to the global optimum.

Our method can find applications to compute the ground state energy of quantum many-body systems. In particular, it gives a new interpretation to and should strengthens the RDM method used in quantum chemistry to compute electronic energies. Our method provides a computation technique for many-body systems that is not based on states (and thus directly linked to entanglement) but that is rather based on the algebraic structure of quantum operators.

---------------------------------------------------------------------------------------------I asked him to send me a preprint!

Maybe I cannot sleep until their preprint is sent to me.

What they are doing? Some magic? Yes I'm sure!

SDP now become very popular indeed!!!

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