Table 4.

Decoder comparison for 2 round data

Basis	Init. State	Round Schedule	Matching Uniform (Full)	Matching Uniform (PS)	Matching Analytical (Full)	Matching Analytic (PS)	Maximum likelihood (Full)	Maximum likelihood (PS)	Shots (PS)
Z	${∣0⟩}_L$	XZXZX	0.1187(5)	0.0978(5)	0.1160(5)	0.0940(5)	0.1045(4)	0.0843(5)	322,165
Z	${∣1⟩}_L$	XZXZX	0.1151(5)	0.0928(5)	0.1162(5)	0.0920(5)	0.1031(4)	0.0819(5)	306,962
X	${∣+⟩}_L$	ZXZXZ	0.2555(6)	0.2212(7)	0.2502(6)	0.2091(7)	0.2502(6)	0.2083(7)	317,672
X	${∣-⟩}_L$	ZXZXZ	0.2860(6)	0.2468(8)	0.2805(6)	0.2332(8)	0.2803(6)	0.2321(8)	295,608

Comparison of logical error extracted using matching uniform, matching analytical, and maximum likelihood decoders on both full and leakage-post selected (PS) data-sets at r = 2 rounds. Error bars denote sampling error. Each full data set corresponding to 500,000 shots before post-selection, after post-selection each data point/set will have a different number of shots that is taken into account by the error bars.