Abstract

Quantum systems host fascinating phases like superconductivity, quantum Hall, topological order, etc that have no classical counterpart. Understanding what quantum phases exist and how phase transitions happen between them is the ultimate goal of condensed matter. But this is notoriously hard, especially in systems with strong interactions. We find that the Quantum Circuit, a tool in quantum computation, provides surprisingly useful insight into the many-body entanglement structure of quantum wavefunctions and correspondingly the structure of the quantum phase diagram. In this talk, we start by reviewing how a decade ago defining gapped quantum phases using finite-depth quantum circuits led us to the systematic construction and classification of Symmetry Protected Topological Phases. Recently, we took another step forward by realizing that the transition between different gapped phases can be achieved with sequential quantum circuits. This opens the door to the systematic study of defects in quantum systems, their condensation, and the induced phase transitions in strongly interacting systems.