Stuttgart 2012 – wissenschaftliches Programm
Q 8.8: Vortrag
Montag, 12. März 2012, 15:45–16:00, V38.04
An algorithm for permutationally invariant state reconstruction for larger qubit numbers — •Tobias Moroder1, Philipp Hyllus2,3, Géza Tóth2,3,4, Christian Schwemmer5,6, Alexander Niggebaum5,6, Stefanie Gaile7, Otfried Gühne1,8, and Harald Weinfurter5,6 — 1IQOQI, Innsbruck — 2Department Theoretical Physics, Bilbao — 3IKERBASQUE, Bilbao — 4Research Institute for Solid State Physics and Optics, Budapest — 5MPQ, Garching — 6Fakultät Physik, LMU, München — 7DTU Mathematics, Lyngby — 8Department Physik, Siegen
Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, also an efficient way to reconstruct the density operator from the observed finite data set. Since this state reconstruction task typically requires the solution of a non-linear large-scale optimization problem, this becomes another major challenge in the design of scalable tomography schemes.
In this talk we present an efficient state reconstruction scheme for permutationally invariant tomography [PRL 105, 250403]. It works for common state-of-the-art reconstruction principles, including, among others, maximum likelihood and least squares which are the preferred choices in experiments. This is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin-coupling and moreover by using convex optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed numerical routines. First prototype implementations allow state reconstruction of 20 qubits in about 20 minutes on a standard computer.