String Theory Journal Club

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. By considering an ensemble of systems, and establishing a rigorous relation between complexity and unitary designs, we will prove statements about complexity growth in various models. Specifically, we prove a linear growth of complexity in random quantum circuits, using a recent result about their design growth. Link: https://mpi-aei.zoom.us/j/99064635917. GQFI-WST is a common online seminar series organized by "Gravity, Quantum Fields and Information" (GQFI) group at the Max Planck Institute (Potsdam) and String Theory group at the University of Warsaw (WST).