Local stabilizer codes in three dimensions without string logical operators

Jeongwan Haah
Phys. Rev. A 83, 042330 – Published 22 April 2011

Abstract

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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  • Received 27 January 2011

DOI:https://doi.org/10.1103/PhysRevA.83.042330

©2011 American Physical Society

Authors & Affiliations

Jeongwan Haah*

  • Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125, USA

  • *jwhaah@caltech.edu

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Issue

Vol. 83, Iss. 4 — April 2011

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