Researchers map quantum phase transition to classical percolation

Researchers have demonstrated a surprising and mathematically exact connection between quantum mechanics and a classical model of connected networks. James Allen of Université de Montréal and William Witczak-Krempa report that a measurement-induced phase transition in a one-dimensional quantum circuit precisely maps to classical percolation, a phenomenon describing how things spread through connected spaces. The work details an “infinite hierarchy of entanglement exponents” characterizing long-range, genuine multiparty entanglement in these transitions, and extends this mapping to a two-dimensional system linked to classical three-dimensional percolation. These results provide a firm ground to understand the multiparty entanglement of measurement-induced phase transitions and broader ensembles of quantum circuits. A one-dimensional measurement-induced phase transition (MIPT) exhibits a mathematically exact correspondence to classical percolation, a surprising result detailed in recent work by…