  Bilayer graphene is a nanomaterial that allows for well-defined, separated
quantum states to be defined by electrostatic gating and, therefore, provides
an attractive platform to construct tunable quantum dots. When a magnetic field
perpendicular to the graphene layers is applied, the graphene valley degeneracy
is lifted, and splitting of the energy levels of the dot is observed. Given the
experimental ability to engineer this energy valley splitting, bilayer graphene
quantum dots have a great potential for hosting robust qubits. Although bilayer
graphene quantum dots have been recently realized in experiments, it is
critically important to devise robust methods that can identify the observed
quantum states from accessible measurement data. Here, we develop an efficient
algorithm for extracting the model parameters needed to characterize the states
of a bilayer graphene quantum dot completely. We introduce a Hamiltonian-guided
random search method and demonstrate robust identification of quantum states on
both simulated and experimental data.
