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Errors in heavy hexagonal code and other topological codes like surface codewere usually decoded using the Minimum Weight Perfect Matching (MWPM) baseddecoders. Recent advances have shown that topological codes can be efficientlydecoded by deploying machine learning (ML) techniques, for example, neuralnetworks. In this work, we first propose an ML based decoder and show that thisdecoder can decode heavy hexagonal code efficiently, in terms of the values ofthreshold and pseudo-threshold, for various noise models. We show that theproposed ML based decoding method achieves $\sim 5$ times higher values ofthreshold than that by MWPM. Next, exploiting the property of subsystem codes,we define gauge equivalence in heavy hexagonal code, by which two differenterrors can belong to the same error class. We obtain a quadratic reduction inthe number of error classes for both bit flip and phase flip errors, thusachieving a further improvement of $\sim 14\%$ in the threshold o ver the basicML decoder. A novel technique of rank based gauge equivalence minimization tominimize the number of classes is further proposed, which is empirically fasterthan the previously mentioned gauge equivalence minimization.

Efficient Machine-Learning-based decoder for Heavy Hexagonal QECC