Abstract

Whether a given target quantum state can be prepared by starting with a simple product state and acting with a finite-depth quantum circuit is a key question in condensed matter physics and quantum information science. It underpins the classification of topological phases and the understanding of topological quantum codes and has obvious relevance for device implementations. Traditionally, this question assumes that (1) the quantum circuit consists of unitary gates that are geometrically local and (2) when the circuit depth is linear, there are no restrictions on the number of gates acting on each degree of freedom. In this talk, I discuss the classification of quantum states under two classes of quantum circuits: finite-depth circuits, where gates are allowed to be geometrically non-local, and sequential linear-depth circuits, where only a constant number of gates are allowed to act on each degree of freedom. Such classes of quantum circuits establish a hierarchy among many-body entangled states.