Journal
PHYSICAL REVIEW LETTERS
Volume 107, Issue 15, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.107.150504
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Funding
- DARPA [HR0011-09-C-0047]
- NSF [PHY-0803371]
- ARO [W911NF-09-1-0442]
- DOE [DE-FG03-92-ER40701]
- Korea Foundation for Advanced Studies
- Division Of Physics
- Direct For Mathematical & Physical Scien [0803371] Funding Source: National Science Foundation
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We explore the feasibility of a quantum self-correcting memory based on 3D spin Hamiltonians with topological quantum order in which thermal diffusion of topological defects is suppressed by macroscopic energy barriers. To this end we characterize the energy landscape of stabilizer code Hamiltonians with local bounded-strength interactions which have a topologically ordered ground state but do not have stringlike logical operators. We prove that any sequence of local errors mapping a ground state of such a Hamiltonian to an orthogonal ground state must cross an energy barrier growing at least as a logarithm of the lattice size. Our bound on the energy barrier is tight up to a constant factor for one particular 3D spin Hamiltonian.
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