Error correcting Bacon-Shor code with continuous measurement of non-commuting operators

We analyze the nine-qubit Bacon-Shor code (smallest Bacon-Shor code capable of correcting any single-qubit error) with simultaneous continuous measurement of non-commuting gauge operators. Error syndromes are determined by cross-correlations of three measurement signals. During continuous operation of the code, such error syndromes can be monitored via running time averages of the measurement signals with a certain weighting function. We investigate how various parameters of the latter affect the performance of the code operation. We calculate the logical error rates due to environmental decoherence, and compare the performances of the continuous and discrete implementation of the nine-qubit Bacon-Shor code.