No offense, but that is really handwavy. In what way does constructive mathematics unlock the door to being closer to all the quantum shit?
Not being a physicist I have no idea whether this is "the way forward" for quantum physics or anything, but the results that I do understand are non-trivial so there seems to be something there...
https://arxiv.org/pdf/0805.2859.pdf Page 14. But do a google search “constructive mathematics” “quantum” or “linear logic” “quantum”, a lot has been written.