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Topological subsystem color codes (TSCCs) are an important class oftopological subsystem codes that allow for syndrome measurement with only2-body measurements. It is expected that such low complexity measurements canhelp in fault tolerance. While TSCCs have been studied over depolarizing noisemodel, their performance over the erasure channel has not been studied as much.Recently, we proposed erasure decoders for TSCCs and reported a threshold of9.7%. In this paper, we continue our study of TSCCS over the erasure channel.We propose two erasure decoders for topological subsystem color codes. Thesedecoders use the technique of gauge fixing where some of the gauge operators ofthe subsystem code are promoted to stabilizers. We perform gauge fixing using4-body and 8-body gauge operators. With partial gauge fixing we obtained athreshold of 17.7% on a TSCC derived from the square octagon lattice. Using anorder maximal gauge fixing decoder we were able to improve the threshold to44%. The previously known decoder for TSCC over the erasure channel had athreshold of 9.7%. We also study the correctability of erasures on thesubsystem codes.

Decoding Topological Subsystem Color Codes Over the Erasure Channel using Gauge Fixing