He gave this pithy summary of his answer to a memorable discussion in a Nobel Laureate panel about what it actually means to explore Hilbert space, from a more practical perspective. Their discussion may be a good complement to the title article of this thread.
Others in this thread already correctly noted that just because something --- 'thing' more precisely defined as some action that results in an observable outcome --- exists in Hilbert space doesn't mean it's possible. But what Ketterle and others were getting at is that, as we make new theories and experiments, we can explore more of Nature and what's possible within, guided by the structure that Hilbert space could give to our questions' outcomes.
That being said, Ketterle explains it much better than I do.
Ketterle's answer in context: https://youtu.be/DNhmYkTW_jI?t=4220