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Q: Fachverband Quantenoptik und Photonik
Q 41: Quanteninformation (Konzepte und Methoden III)
Q 41.3: Talk
Thursday, March 13, 2008, 14:30–14:45, 1B
Completeness of classical spin systems and universal quantum computation — •Gemma De las Cuevas1, Robert Hübener1, Maarten Van den Nest1, Wolfgang Dür1,2, and Hans J. Briegel1,2 — 1Institut für Quantenoptik und Quanteninformation der Österreichischen Akademie der Wissenschaften, Innsbruck, Austria — 2Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria
It was recently shown [quant-ph/0708.2275] how classical spin models, such as the Ising and Potts models on arbitrary graphs, can be mapped onto the stabilizer formalism from quantum information theory. Moreover, by invoking the universality of the one-way quantum computer it was proven how the partition function on an arbitrary graph can be expressed as a special instance of the Ising partition function on a 2D square lattice. However, in order to obtain this result the coupling strengths and local magnetic fields on the 2D square lattice had to be complex, and thus did not allow for a physical interpretation. In this talk, we will first present the completeness of the 2D Ising model with complex parameters and we will then show that a complete model with real parameters is obtained when the 3D Ising model is considered. We will further investigate how generalizations of the 2D Ising model allow us to strengthen the completeness results, and will consider other possible mappings between the partition function and the quantum stabilizer formalism.