Curator's Take
AI Commentary
This article offers the first microscopic picture of how decoherence can drive a topological phase transition by framing it as a percolation problem, introducing quasi‑local topological entanglement negativity (QLTEN) to map where logical order survives or collapses. By showing that biased “explosive” decoherence can suppress large error clusters and that color‑code and toric‑code lattices respond differently, the work sharpens our understanding of fault‑tolerance thresholds for leading quantum error‑correcting hardware. The findings give designers a concrete tool to predict and mitigate logical qubit loss in realistic noisy environments, while also highlighting that a universal theory of decoherence‑induced transitions remains an open challenge.
— Mark Eatherly
Summary
We investigate microscopic mechanisms underlying decoherence-induced transitions between topologically ordered states. As a first case study, we analyze the color code using topological entanglement negativity (TEN) and a disorder parameter associated with 1-form symmetry. We interpret these quantities as first- and zeroth-dimensional simplicial homological objects, respectively, and show that the transition can be understood in terms of decoherence percolation. To resolve its local structure, we introduce quasi-local TEN (QLTEN), which visualizes the spatial distribution of local topological properties and the growth of decohered regions. We further introduce explosive percolation (EP), corresponding here to biased decoherence that suppresses the formation of large decohered clusters. As a second case study, we consider the toric code on a triangular lattice under external-field-type decoherence. Numerical results show that QLTEN faithfully captures the emergence of Higgs regions and the survival of logical qubits. Although global TEN, QLTEN clusters, and string operators are strongly correlated in both models, the color code and toric code respond differently to EP patterns. This difference indicates that a universal microscopic description of decoherence-induced topological phase transitions remains challenging even for closely related systems.