We report on pure-quantum-state polariton condensates in optical annular traps. The study of the underlying mechanism reveals that the polariton wave function always coalesces in a single pure quantum state that, counterintuitively, is always the uppermost confined state with the highest overlap with the exciton reservoir. The tunability of such states combined with the short polariton lifetime allows for ultrafast transitions between coherent mesoscopic wave functions of distinctly different symmetries, rendering optically confined polariton condensates a promising platform for applications such as many-body quantum circuitry and continuous-variable quantum processing.