**Ergodic dynamics and thermalization in an isolated quantum system** - Charles Neill

Statistical mechanics is founded on the assumption that all accessible
states of a system are equally likely. This requires dynamics that explore
all configurations over time, known as ergodic dynamics. Here, using three
fully-coupled superconducting qubits, we demonstrate ergodic dynamics and
the resulting thermalization. We subject the qubits to a sequence of
periodic rotations and interactions and measure the density matrix as a
function of time. We find a striking resemblance between maps of the
entanglement entropy and the phase space dynamics in the classical limit;
classically chaotic regions coincide with regions of nearly maximum
entanglement entropy. We further show that in regions with high entropy
the qubits explore the entire accessible state space, demonstrating
quantum ergodic dynamics. In these regions, the time-averaged density
matrix approaches a microcanonical ensemble. Our work illustrates how
fundamental questions in non-equilibrium thermodynamics can be studied
using superconducting circuits.