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We study the two-dimensional toric code Hamiltonian with effective long-range interactions between its anyonic excitations induced by coupling the toric code to external fields.
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Sergey Bravyi and Alexei Kitaev · 1998
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David J. C. MacKay · 2002
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Sergey Bravyi and Jeongwan Haah · 2011
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A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
Sergey Bravyi and Barbara Terhal · 2009
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Alioscia Hamma, Claudio Castelnovo, and Claudio Chamon · 2009
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V. Kolmogorov · 2009
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Self-correcting quantum memory in a thermal environment
Stefano Chesi, Beat Röthlisberger, and Daniel Loss · 2010
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Let the ‘height’ h h be given by the number of plaquette operators from top to bottom and the ‘width’ w w by the number of star operators from left to right. The total number of qubits is then given by 2 h w + h + w + 1 2hw+h+w+1 , the number of plaquette operators by h ( w + 1 ) h(w+1) and the number of star operators by ( h + 1 ) w (h+1)w . Since each stabilizer condition eliminates half of all 2 2 h w + h + w + 1 2^{2hw+h+w+1} degrees of freedom, we are left with 2 2 of them
Cited in the paper.
Note that for a super-Ohmic bath we have γ ( 0 ) = 0 \gamma(0)=0 , forbidding the direct hopping of anyons and heavily suppressing their diffusion. In this case, only ‘indirect hopping’ [ 5 ] is possible, in which a new pair of anyons is created next to an existing one and the existing one fuses with one of them, leading to an effective movement of the already existing anyon
Cited in the paper.
Fabio L. Pedrocchi, Stefano Chesi, and Daniel Loss · 2011
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Jeongwan Haah, private communication, Jan. 2012
2012
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Incoherent dynamics in the toric code subject to disorder
Beat Röthlisberger, James R. Wootton, Robert M. Heath, Jiannis K. Pachos, and Daniel Loss · 2012
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A witness for topological order and stable quantum memories in abelian anyonic systems
James R. Wootton · 2012
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