Stabilizer Slicing: Coherent Error Cancellations in LDPC Codes

In this paper we propose a scheme to cancel coherent overrotation errors when implementing quantum error correcting codes. These are considered to be among the most damaging errors due to the way they grow rapidly when combined. Due to their unitary nature, these errors have inverse operations and through our technique the errors due to different parts of the circuit create pairs of errors which cancel over the logical subspace. When considering a simplified error model and allowing native 3 qubit gates we can completely eliminate error in the purely coherent case for Surface-17, and show 135-fold improvement at 0.99 unitarity. For an ion trap gate set and only two qubit interactions, we can observe an 89-fold improvement in Bacon-Shor-13. This second implementation takes advantage of the prepared gauge of the code, and is the first implementation to our knowledge in which the state of the gauge affects the robustness of our memory.