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Local stabilizer codes in three dimensions without string logical operators

Haah, Jeongwan (2011) Local stabilizer codes in three dimensions without string logical operators. Physical Review A, 83 (4). Art No. 042330. ISSN 1050-2947. doi:10.1103/PhysRevA.83.042330.

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We suggest concrete models for self-correcting quantum memory by reporting examples of local stabilizer codes in 3D that have no string logical operators. Previously known local stabilizer codes in 3D all have stringlike logical operators, which make the codes non-self-correcting. We introduce a notion of “logical string segments” to avoid difficulties in defining one-dimensional objects in discrete lattices. We prove that every stringlike logical operator of our code can be deformed to a disjoint union of short segments, each of which is in the stabilizer group. The code has surfacelike logical operators whose partial implementation has unsatisfied stabilizers along its boundary.

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Additional Information:© 2011 American Physical Society. Received 27 January 2011; published 22 April 2011. This research was supported in part by the NSF under Grant No. PHY-0803371, by ARO Grant No. W911NF-09-1-0442, by DOE Grant No. DE-FG03-92-ER40701, and by the Korea Foundation for Advanced Studies. I thank Salman Beigi, Liang Jiang, and especially John Preskill for useful discussions.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-09-1-0442
Department of Energy (DOE) DE-FG03-92-ER40701
Korea Foundation for Advanced StudiesUNSPECIFIED
Issue or Number:4
Classification Code:PACS: 03.67.Pp, 03.67.Lx
Record Number:CaltechAUTHORS:20110519-140600236
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Official Citation:Local stabilizer codes in three dimensions without string logical operators Jeongwan Haah Published 22 April 2011 (16 pages) 042330
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23738
Deposited By: Ruth Sustaita
Deposited On:19 May 2011 21:41
Last Modified:09 Nov 2021 16:17

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