Origin of the soft-measurement threshold discrepancy

Determine whether the discrepancy between the entropy-threshold prediction and simulated threshold improvement for soft measurements is caused by the suboptimality of the matching-graph update procedure or by the entropy threshold’s neglected terms.

Background

The paper extends its entropy-based threshold framework to soft measurement information, in which analog measurement reliability is supplied to the decoder in addition to hard detector outcomes. For the surface code with phenomenological noise, the entropy method predicts an increase in threshold when soft information is used.

However, the predicted threshold improvement is larger than the improvement obtained in simulations using a decoding-graph update procedure followed by matching. The paper explicitly leaves unresolved whether this difference arises from the decoder procedure being suboptimal or from the entropy heuristic being overly optimistic because it neglects terms such as correlations and degeneracy entropy.