2015/09/14 by Tomas Jochym-O'Connor, Stephen D. Bartlett · 1 voice
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physreva.93.022323
published as Phys. Rev. A 93, 022323 (2016) · 14 pages, 6 figures, comments welcome. Note our construction is very similar to recent results by Bravyi and Cross reported in arXiv:1509.03239. Version 2 contains minor changes
arxiv published 2015/09/14 · arxiv created 2016/03/04 · arxiv updated 2016/03/07
We introduce a class of 3D color codes, which we call stacked codes, together with a fault-tolerant transformation that will map logical qubits encoded in two-dimensional (2D) color codes into stacked codes and back. The stacked code allows for the transversal implementation of a non-Clifford π/8 logical gate, which when combined with the logical Clifford gates that are transversal in the 2D color code give a gate set which is both fault-tolerant and universal without requiring nonstabilizer magic states. We then show that the layers forming the stacked code can be unfolded and arranged in a 2D layout. As only Clifford gates can be implemented transversally for 2D topological stabilizer codes, a non-local operation must be incorporated in order to allow for this transversal application of a non-Clifford gate. Our code achieves this operation through the transformation from a 2D color code to the unfolded stacked code induced by measuring only geometrically local stabilizers and gauge operators within the bulk of 2D color codes together with a nonlocal operator that has support on a one-dimensional boundary between such 2D codes. We believe that this proposed method to implement the non-local operation is a realistic one for 2D stabilizer layouts and would be beneficial in avoiding the large overheads caused by magic state distillation.