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Energy Landscape of 3D Spin Hamiltonians with Topological Order

Bravyi, Sergey and Haah, Jeongwan (2011) Energy Landscape of 3D Spin Hamiltonians with Topological Order. Physical Review Letters, 107 (15). Art. No. 150504. ISSN 0031-9007. doi:10.1103/PhysRevLett.107.150504.

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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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Additional Information:© 2011 American Physical Society. Received 6 June 2011; published 6 October 2011. S. B was supported in part by the DARPA QuEST program under Contract No. HR0011-09-C-0047, and J.H in part by NSF No. PHY-0803371, ARO No. W911NF-09-1- 0442, DOE No. DE-FG03-92-ER40701, and the Korea Foundation for Advanced Studies.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Defense Advanced Research Projects Agency (DARPA) QuEST programHR0011-09-C-0047
Army Research Office (ARO)W911NF-09-1-0442
Department of Energy (DOE)DE-FG03-92-ER40701
Korea Foundation for Advanced StudiesUNSPECIFIED
Issue or Number:15
Classification Code:PACS: 03.67.Pp, 03.65.Ud, 03.67.Ac
Record Number:CaltechAUTHORS:20111116-100256904
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Official Citation:Energy Landscape of 3D Spin Hamiltonians with Topological Order Sergey Bravyi and Jeongwan Haah Published 6 October 2011 (4 pages) 150504
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27801
Deposited By: Ruth Sustaita
Deposited On:16 Nov 2011 18:15
Last Modified:09 Nov 2021 16:51

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