  Relaxation dynamics of complex many-body quantum systems brought out of
equilibrium and subsequently trapped into metastable states is a very active
field of research from both the theoretical and experimental point of view with
implications in a wide array of topics from macroscopic quantum tunnelling and
nucleosynthesis to non-equilibrium superconductivity and new energy-efficient
memory devices. Understanding the dynamics of such systems is crucial for
exploring fundamental aspects of many-body non-equilibrium quantum physics. In
this work we investigate quantum domain reconfiguration dynamics in the
electronic superlattice of a quantum material where classical dynamics is
topologically constrained. The crossover from temperature to quantum
fluctuation dominated dynamics in the context of environmental noise is
investigated by directly observing charge reconfiguration with time-resolved
scanning tunneling microscopy. The process is modelled using a programmable
superconducting quantum simulator in which qubit interconnections correspond
directly to the microscopic interactions between electrons in the quantum
material. Crucially, the dynamics of both the experiment on the quantum
material and the simulation is driven by spectrally similar pink noise. We find
that the simulations reproduce the emergent time evolution and temperature
dependence of the experimentally observed electronic domain dynamics remarkably
well. The combined experiment and simulations lead to a better understanding of
noise-driven quantum dynamics in open quantum systems. From a practical
viewpoint, the results are important for understanding the origin of the
retention time in non-volatile memory devices such as those based on 1T-TaS2.
