  It has been demonstrated that small plaquettes of quantum dot spin qubits are
capable of simulating condensed matter phenomena which arise from the Hubbard
model, such as the collective Coulomb blockade and Nagaoka ferromagnetism.
Motivated by recent materials developments, we investigate a bilayer
arrangement of quantum dots with four dots in each layer which exhibits a
complex ground state behavior. We find using a generalized Hubbard model with
long-range Coulomb interactions, several distinct magnetic phases occur as the
Coulomb interaction strength is varied, with possible ground states that are
ferromagnetic, antiferromagnetic, or having both one antiferromagnetic and one
ferromagnetic layer. We map out the full phase diagram of the system as it
depends on the inter- and intra-layer Coulomb interaction strengths, and find
that for a single layer, a similar but simpler effect occurs. We also predict
interesting contrasts among electron, hole, and electron-hole bilayer systems
arising from complex correlation physics. Observing the predicted magnetic
configuration in already-existing few-dot semiconductor bilayer structures
could prove to be an important assessment of current experimental quantum dot
devices, particularly in the context of spin-qubit-based analog quantum
simulations.
