# Stuttgart 2012 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 8: Quanteninformation: Konzepte und Methoden 2

### 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 Moroder^{1}, Philipp Hyllus^{2,3}, Géza Tóth^{2,3,4}, Christian Schwemmer^{5,6}, Alexander Niggebaum^{5,6}, Stefanie Gaile^{7}, Otfried Gühne^{1,8}, and Harald Weinfurter^{5,6} — ^{1}IQOQI, Innsbruck — ^{2}Department Theoretical Physics, Bilbao — ^{3}IKERBASQUE, Bilbao — ^{4}Research Institute for Solid State Physics and Optics, Budapest — ^{5}MPQ, Garching — ^{6}Fakultät Physik, LMU, München — ^{7}DTU Mathematics, Lyngby — ^{8}Department 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.