  Domains are homogeneous areas of discrete symmetry, created in nonequilibrium
phase transitions. They are separated by domain walls, topological objects
which prevent them from fusing together. Domains may reconfigure by
thermally-driven microscopic processes, and in quantum systems, by macroscopic
quantum tunnelling. The underlying microscopic physics that defines the
system's energy landscape for tunnelling is of interest in many different
systems, from cosmology and other quantum domain systems, and more generally to
nuclear physics, matter waves, magnetism, and biology. A unique opportunity to
investigate the dynamics of microscopic correlations leading to emergent
behaviour, such as quantum domain dynamics is offered by quantum materials.
Here, as a direct realization of Feynman's idea of using a quantum computer to
simulate a quantum system, we report an investigation of quantum electron
reconfiguration dynamics and domain melting in two matching embodiments: a
prototypical two-dimensionally electronically ordered solid-state quantum
material and a simulation on a latest-generation quantum simulator. We use
scanning tunnelling microscopy to measure the time-evolution of electronic
domain reconfiguration dynamics and compare this with the time evolution of
domains in an ensemble of entangled correlated electrons in simulated quantum
domain melting. The domain reconfiguration is found to proceed by tunnelling in
an emergent, self-configuring energy landscape, with characteristic step-like
time evolution and temperature-dependences observed macroscopically. The
remarkable correspondence in the dynamics of a quantum material and a quantum
simulation opens the way to an understanding of emergent behaviour in diverse
interacting many-body quantum systems at the microscopic level.
