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Accueil du site > Séminaires > Séminaires 2007 > Engineering Exotic Phases for Topologically Protected Quantum Computation : Emulating Quantum Dimer Models

Mardi 27/02/2007 - 14H00

Engineering Exotic Phases for Topologically Protected Quantum Computation : Emulating Quantum Dimer Models

A. Fabricio Albuquerque (ITP, ETH-Zurich)

par Didier Poilblanc - 27 février 2007

Engineering Exotic Phases for Topologically Protected Quantum Computation : Emulating Quantum Dimer Models

A. Fabricio Albuquerque In collaboration with Helmut G. Katzgraber, Matthias Troyer and Gianni Blatter Institute for Theoretical Physics - ETH Zurich

Motivated by recent interest in engineering topologically ordered phases for achieving fault-tolerant quantum computation, we analyze a device designed for emulating the quantum dimer model on the triangular lattice using a Josephson junctions array [L. B. Ioffe et al., Nature 415, 503 (2002)]. Using a modified numerical Contractor Renormalization (CORE) technique, we are able to derive in an unbiased way an effective Hamiltonian describing the low-energy physics of the emulator. The so obtained generalized quantum dimer model incorporates resonances and interactions involving three or more dimers whose effects on the topological phase of the standard quantum dimer model, required for the implementation of a fault- tolerant quantum bit, are presently unknown. Minimization of the couplings associated to these extra terms can only be attained for junction’s capacitances that lead to exceedingly small Josephson currents and energy scales which are far beyond the ones obtainable with current technology. An alternative implementation based on cold atoms loaded into optical lattices is also discussed, but in this case the absence of sizable interactions is a major obstacle to the successful emulation of the topological phase. Besides that, given the experimental limitations in achieving large values for the hopping amplitude in such systems, the process of storing data in such hypothetical quantum bit would be extremely slow, ruling out the possibility of any practical applications. Our results suggest that the emulation of topological phases in quantum devices can only be a viable approach if special attention is paid to the design and engineering limits.