Exactly solvable 3D quantum model with finite temperature topological order

Details Exactly solvable 3D quantum model with finite temperature topological order Exactly solvable 3D quantum model with finite temperature topological order

2010-12-03

arxiv.org/abs/1012.0859v2

Phys.Rev.A83:052308, 2011

Physics

Quantum Physics

6 pages, 7 figures. Minor revision. References updated

Scientific paper

10.1103/PhysRevA.83.052308

We present a family of exactly solvable spin-1/2 quantum hamiltonians on a 3D lattice. The degenerate ground state of the system is characterized by a quantum error correcting code whose number of encoded qubits are equal to the second Betti number of the manifold. These models 1) have solely local interactions, 2) admit a strong-weak duality relation with an Ising model on a dual lattice 3) have topological order in the ground state, some of which survive at finite temperature, 4) behave as classical memory at finite temperature. The associated quantum error correcting codes are all non-CSS stabilizer codes.

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