Relate coherent-error polymer representations to statistical-mechanical phase transitions

Determine the connection between the correspondence relating error-correcting thresholds to phase transitions in disordered classical spin models and the polymer representation developed for coherent-error correction.

Background

The paper develops a polymer-model representation of coherent-error correction and uses a cluster expansion to prove a positive coherent-error threshold for CSS QLDPC codes with a bounded number of logical qubits. In contrast, the established statistical-mechanical correspondence between error-correcting thresholds and phase transitions has primarily been studied for stochastic Pauli errors. The relationship between that correspondence and the polymer representation introduced here is explicitly left unresolved, motivating further investigation of the statistical-mechanical structure of coherent-error correction.