  Engineered, highly-controllable quantum systems hold promise as simulators of
emergent physics beyond the capabilities of classical computers. An important
problem in many-body physics is itinerant magnetism, which originates purely
from long-range interactions of free electrons and whose existence in real
systems has been subject to debate for decades. Here we use a quantum simulator
consisting of a four-site square plaquette of quantum dots to demonstrate
Nagaoka ferromagnetism. This form of itinerant magnetism has been rigorously
studied theoretically but has remained unattainable in experiment. We load the
plaquette with three electrons and demonstrate the predicted emergence of
spontaneous ferromagnetic correlations through pairwise measurements of spin.
We find the ferromagnetic ground state is remarkably robust to engineered
disorder in the on-site potentials and can induce a transition to the low-spin
state by changing the plaquette topology to an open chain. This demonstration
of Nagaoka ferromagnetism highlights that quantum simulators can be used to
study physical phenomena that have not yet been observed in any system before.
The work also constitutes an important step towards large-scale quantum dot
simulators of correlated electron systems.
