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Published May 12, 2011 | Published
Journal Article Open

Local non–Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice

Kim, Isaac H.

Abstract

We present a family of non-Calderbank-Shor-Steane quantum error-correcting code consisting of geometrically local stabilizer generators on a 3D lattice. We study the Hamiltonian constructed from ferromagnetic interaction of overcomplete set of local stabilizer generators. 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 (i) have solely local interactions; (ii) admit a strong-weak duality relation with an Ising model on a dual lattice; (iii) have topological order in the ground state, some of which survive at finite temperature; and (iv) behave as classical memory at finite temperature.

Additional Information

© 2011 American Physical Society. Received 3 January 2011; published 12 May 2011. The author thanks Jeongwan Haah for his help in finding the logical operator of the system and John Preskill for many insightful discussions. This research was supported in part by NSF under Grant No. PHY-0803371 and ARO under Grant No. W911NF-09-1-0442.

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