What are you think of though? Chords? Tone sets? It's not just randomly hitting keys.
That is a very difficult question to answer in any easily understood fashion about my own playing Bob, and I certainly cannot answer it for quantum, or anybody else for that matter. For myself, the nearest analogy is probably mathematical chaos, a function which is completely determined but unpredictable, resulting from a very complex set of feedback loops in the brain.
At the heart of it, I suppose you could say, is the "idea", but exactly what constitutes an "idea" is necessarily vague and beyond my ability to satisfactorily define. The things you mention, chords, sets, other musical elements such as phrase and rhythm, the haptic aspect, associated images, emotions, thoughts, memories and lyrics are components of an idea but they are not ideas in themselves.
Improvisational form for me implies a totally dynamic, fully determined, unpredictable yet non-random, serial generation of ideas. The results of a priori structured form and unconscious, random playing, seem equally uninteresting to me, although this is very much a personal view, the degree of order being itself a rightful creative choice like anything else in music.
One remarkably simple mode of thought is what I term the "cellular transition", which amounts to thinking about ways in which an idea might spring from the preceding one. If I play a cell, an idea, and repeat it imprecisely (imprecision is vital) parts of it will form the musical DNA of the next cell. The sound data of a cell is transformed into the dynamic instruction for the next, then the sound of that suggests instruction for another, and so on indefinitely.
This flow can be achieved at the conscious level and does not require a transformed mental state, "inspiration" or anything like that. It can be "practised" in the same way as anything else, chords, rhythms, technique, can be practised at the instrument. When I begin an improvisation this is a conscious process, but over about ten minutes (less as I get older) it morphs into an unconscious one in which the well known effect of becoming an observer or a channel ensues. If a block should occur, and it is normal for occasional blocks to happen, then all that is necessary is to revert to the conscious process.
That is what I think about, Bob, although I'm not sure "thinking" is quite the right word for it, and it may bear little resemblance to how others go about it.