3D local qupit quantum code without string logical operator
Abstract
Recently Haah introduced a new quantum error correcting code embedded on a cubic lattice. One of the defining properties of this code is the absence of string logical operator. We present new codes with similar properties by relaxing the condition on the local particle dimension. The resulting code is welldefined when the local Hilbert space dimension is prime. These codes can be divided into two different classes: the local stabilizer generators are either symmetric or antisymmetric with respect to the inversion operation. These is a nontrivial correspondence between these two classes. For any symmetric code without string logical operator, there exists a complementary antisymmetric code with the same property and vice versa. We derive a sufficient condition for the absence of string logical operator in terms of the algebraic constraints on the defining parameters of the code. Minimal number of local particle dimension which satisfies the condition is 5. These codes have logarithmic energy barrier for any logical error.
 Publication:

arXiv eprints
 Pub Date:
 January 2012
 DOI:
 10.48550/arXiv.1202.0052
 arXiv:
 arXiv:1202.0052
 Bibcode:
 2012arXiv1202.0052K
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 9 pages, 7 figures