Local stabilizer codes in three dimensions without string logical operators

  title={Local stabilizer codes in three dimensions without string logical operators},
  author={Jeongwan Haah},
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… CONTINUE READING
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