  Adaptive quantum design identifies the best broken-symmetry configurations of
atoms and molecules that enable a desired target function response. In this
work, numerical optimization is used to design atomic clusters with specified
quasiparticle densities of states. The dominant self-assembled building blocks
of these engineered quantum systems are found to depend on the symmetry of the
target function. For example, particle-hole symmetric spectra can be
constructed from a dilute configuration of atomic dimers, whereas more complex
structures such as trimers and quadrumers are required for asymmetric target
functions. The convergence of the optimization algorithms depends on the shape
of the target function, the density of atoms, and constraints due to substrates
and boundary conditions. Hybrids of steepest descent methods, simulated
annealing, and genetic algorithms are found to be most efficient.
