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Encoded qubits with generalized toric codes and Kitaev honeycomb models

Speaker: Stefano Chesi RIKEN (Japan)
Time: 2013-05-20 15:00-2013-05-16 16:00
Venue: FIT 1-222


 We discuss the encoding of qubits in extended spin lattices which are generalizations of the Kitaev toric code and honeycomb model. More specifically, we introduce repulsive long-range interactions between the diffusing anyons of the toric code and establish, with a combination of analytic methods and numerical simulations, that the memory lifetime has a favorable polynomial scaling with system size. Such toric code with long-range interactions can be realized as an effective theory of the honeycomb model, by introducing suitable couplings to extended cavity fields. By making use of the Schrieffer-Wolff transformation, we discuss how the cavity modes affect the low-energy toric code Hamiltonian via their frequencies, photon occupations, and coupling strengths. The quantized cavity modes can also be used to detect the presence of anyons through frequency shifts. Finally, we present an alternative encoding in the honeycomb model in the limit of a one-dimensional spin ladder. Here, through an exact mapping of the spins to fermions, the ground-state degeneracy can be interpreted as due to isolated Majorana modes. Introducing inhomogeneous couplings along the ladder makes the ground state degeneracy insensitive to a larger family of external perturbations than the homogeneous ladder.

Short Bio:

 Stefano Chesi main interests are in the theory of spin manipulation and many-body phenomena in semiconductor nanostructures, topologically protected models, and solid-state implementations of quantum computing. He received his PhD from Purdue University (US) in 2007. Afterwards, he held postdoctoral positions in the group of Prof. Danial Loss (University of Basel, Switzerland) in 2007-2010 and at McGill University (Canada) in 2011-2013. He recently joined the Emergent Materials Department of RIKEN (Japan) as Research Scientist.