Berlin 2014 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 3: Quanten-Information III
MP 3.3: Vortrag
Dienstag, 18. März 2014, 11:10–11:30, SPA SR125
Unifying Fixed-Point Engineering with the Stabiliser Formalism of Graph States and Topological States — •Thomas Schulte-Herbrüggen1, Corey O’Meara1, and Gunther Dirr2 — 1Dept. Chem., TU-München (TUM) — 2Math. Inst., University of Würzburg
We present a unified practical Lie-framework for fixed-point engineering which includes as special cases the stabiliser formalisms for graph states and topological states.
Quantum evolution in open Markovian systems takes the form of an affine map with an illustrative geometry. It consists of a unital part (‘rotation and compression’) and a translational part, the latter representing the shift (if any) from the chaotic state (identity) towards fixed points of different type.
For a plethora of examples, we demonstrate how to exploit the geometry of such translations for systematic fixed-point engineering. In the framework of Lie-semigroups a unified practical view emerges: (1) It shows how to relate a desired target state via its centraliser (or commutant) to translations and, in turn, to the corresponding Lindblad noise generators driving the system into the desired targets. (2) Analogously, graph states can be obtained from their stabilisers (seen as elements of the maximally abelian subalgebra of the centraliser) cast into translations and the corresponding Lindblad generators. (3) Topological states, as for the toric code, are engineered likewise by turning the star and plaquette operators (seen as abelian centraliser elements) into translations and Lindblad generators.