As someone who works on research in quantum computation... yeah, it's not gonna help you much, Hanners.
(Fellow math/physics/statistics people, plase point out my errors - looking @Skewbrow & Carl-E, especially)
I quickly went through "
multicollinearity" and ... if I recall my numerical math courses correctly, from an applied-math POV, this is 'just' the problem of finding an inverse to an ill-conditioned matrix?
Not only do Shor et. al. not help much, IIRC - the remedies, like column/row pivot-search are well-known and pretty standard undergrad classical (=non-quantum) Numerics stuff?
Furhermore, Hanners mentions "absolute" collinearity - the term isn't mentioned in the Wiki-article, but "perfect multicollinearity" would mean the Matrix has less-than-full rank?
Soooooooh ... drop the rows in questions & be glad your Linear Algebra I Prof. didn't catch you agonizing about that?

EDIT: I
guess (=arsepull) there could be issues with really, really big and really, really weirdly structured matrices - pivot search running into 'trouble' that is similar to that which some Plus it's a search problem, not a sorting problem?