A comparison of decoherence-free subsystem/subspace for partially-broken symmetry

We study the performance of the 3-quhit decoherence-free subsystem and the 4-quhitdecoherence-free subspace in the presence of partially correlated noise. We characterizetheir performance in terms of the average and worst-case fidelity, as a function of the ratioof the interqubit distance to the correlation length of the noise, and find that, in general,more symmetric arrangements (triangles or squares) lead to better performance. Overall,we find the 3-quhit code to perform better than the 4-quhit code by about a factor of 2in the average infidelity. We observe that this is related to the greater robustness of thiscode against uncorrelated (independent) errors.