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Trapped Ion Quantum Computing

On the energy landscape of 3D spin Hamiltonians with topological order

arXiv
Authors: Sergey Bravyi, Jeongwan Haah

Year

2011

Paper ID

8728

Status

Preprint

Abstract Read

~2 min

Abstract Words

117

Citations

N/A

Abstract

We explore 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 string-like logical operators. We prove that any sequence of local errors mapping a ground state of such 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 shown to be tight up to a constant factor for one particular 3D spin Hamiltonian.

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  • We explore feasibility of a quantum self-correcting memory based on 3D spin Hamiltonians with topological quantum order in which thermal diffusion of topological defects is...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1105.4159 [2] arXiv https://arxiv.org/abs/1105.4159 [3] Publisher https://arxiv.org/abs/1105.4159

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