Kim, Isaac H. (2012) 3D local qupit quantum code without string logical operator. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20120713-091419180
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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 well-defined 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.
|Item Type:||Report or Paper (Discussion Paper)|
|Additional Information:||This research was supported in part by NSF under Grant No. PHY-0803371, by ARO Grant No. W911NF-09-1-0442, and DOE Grant No. DE-FG03-92-ER40701. Author would like to thank Steven Flammia, Jeongwan Haah, Robert Koenig, and John Preskill for useful dis- cussions.|
|Group:||IQIM, Institute for Quantum Information and Matter|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||19 Jul 2012 22:05|
|Last Modified:||26 Dec 2012 15:31|
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