Subsystem fault tolerance with the Bacon-Shor code.

We discuss how the presence of gauge subsystems in the Bacon-Shor code [D. Bacon, Phys. Rev. A 73, 012340 (2006)10.1103/PhysRevA.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 x 10(-4) for adversarial stochastic noise, that improves previous lower bounds by nearly an order of magnitude.

Effective fault-tolerant quantum computation with slow measurements.

How important is fast measurement for fault-tolerant quantum computation? Using a combination of existing and new ideas, we argue that measurement times as long as even 1000 gate times or more have a very minimal effect on the quantum accuracy threshold. This shows that slow measurement, which appears to be unavoidable in many implementations of quantum computing, poses no essential obstacle to scalability.