1209.3539 (Austin G. Fowler)

Accurate simulations of planar topological codes cannot use cyclic
boundaries    [PDF]

Austin G. Fowler

Cyclic boundaries are used in many branches of physics and mathematics, typically to assist the approximation of a large space. We show that when determining the performance of planar, fault-tolerant, topological quantum error correction, using cyclic boundaries leads to a significant underestimate of the logical error rate. We present cyclic and non-cyclic surface code simulations exhibiting this discrepancy, and analytic formulae precisely reproducing and explaining the observed behavior in the limit of low physical error.

View original: http://arxiv.org/abs/1209.3539