Local stabilizer codes in three dimensions without string logical operators

Details Local stabilizer codes in three dimensions without string logical operators Local stabilizer codes in three dimensions without string logical operators

2011-01-10

arxiv.org/abs/1101.1962v2

Phys. Rev. A 83, 042330 (2011)

Physics

Quantum Physics

18 pages, 12 figures; clarified intermidiate steps in the proof

Scientific paper

10.1103/PhysRevA.83.042330

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 string-like 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 string-like logical operator of our code can be deformed to a disjoint union of short segments, and each segment is in the stabilizer group. The code has surface-like logical operators whose partial implementation has unsatisfied stabilizers along its boundary.

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