| Abstract: | The dynamics of information in a quantum circuit is shaped by two competing elements: unitary evolution scrambles and hides quantum information in increasingly non-local correlations, while local measurements attempt to reveal the encoded information. This competition leads to a phase transition at a critical measurement rate, beyond which the circuit cannot encode and propagate quantum information coherently. In this talk I will show that an intriguing substructure of “encoding” and “non-encoding” phases emerges if symmetry or other constraints are imposed on the circuit elements. The new phases can be understood and classified via symmetry and topology through a mapping to more familiar quantum ground state problems. As a surprising bonus, the mapping also predicts a new kind of phase transition that occurs at a critical evolution time. Time permitting, I will show numerical evidence for the new transition and discuss its implications. |