Simplifying quantum double Hamiltonians using perturbative gadgets

Details Simplifying quantum double Hamiltonians using perturbative gadgets Simplifying quantum double Hamiltonians using perturbative gadgets

2009-01-09

arxiv.org/abs/0901.1333v2

Quant. Inf. Comp., vol. 10, no. 3, pp. 292-324, 2010

Physics

Quantum Physics

34 pages, v2: updated to match published version

Scientific paper

Perturbative gadgets were originally introduced to generate effective k-local interactions in the low-energy sector of a 2-local Hamiltonian. Extending this idea, we present gadgets which are specifically suited for realizing Hamiltonians exhibiting non-abelian anyonic excitations. At the core of our construction is a perturbative analysis of a widely used hopping-term Hamiltonian. We show that in the low-energy limit, this Hamiltonian can be approximated by a certain ordered product of operators. In particular, this provides a simplified realization of Kitaev's quantum double Hamiltonians.

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