Subsystem Fault Tolerance with the Bacon-Shor Code

Abstract

We discuss how the presence of gauge subsystems in the Bacon-Shor code [D. Bacon , Phys. Rev. A 73, 012340 (2006)] leads to remarkably simple and efficient methods for fault-tolerant error correction (FTEC). Most notably, FTEC does not require entangled ancillary states, and it can be implemented with nearest-neighbor two-qubit measurements. By using these methods, we prove a lower bound on the quantum accuracy threshold, $1.94\times {10}^{-4}$ for adversarial stochastic noise, that improves previous lower bounds by nearly an order of magnitude.