QGI Virtual Seminar: Nick Hunter-Jones 'Models of quantum complexity growth'

The quantum complexity of a unitary or state is defined as the size of the shortest quantum computation that implements the unitary or prepares the state. The notion has far-reaching implications spanning computer science, quantum many-body physics, and high energy theory. Complexity growth in time is a phenomenon expected to occur in holographic theories and strongly-interacting many-body systems more generally, but explicitly computing the complexity of a given state or unitary is notoriously difficult. In this talk, Nick Hunter-Jones (Perimeter) proves statements about complexity growth in various models by considering an ensemble of systems, and establishing a rigorous relation between complexity and unitary designs. Specifically, Nick proves a linear growth of complexity in random quantum circuits, using a recent result about their design growth.

This talk was recorded on May 20, 2020 at the Albert Einstein Institute in Potsdam-Golm.