That is a bit too strong a claim (even taking "NP" to mean "NP - P", since all P problems are also in NP).
First of all, while not proven, it is considered most likely that integer factorization is not in P, so potentially we already know of 1 NP-P problem which can have an exponential speed-up from a QC (Shor's algorithm).
Secondly, there is one non-exponential speedup that can potentially apply to even NP-complete problems - using Grover's algorithm to find an element in an unordered list with complexity O(sqrt(n)) instead of the classical O(n).
Isn't the whole problem in there - as n - somehow this assumes that n-qubits can magically grow without a fuss - what if to entangle more quibits you need to cool the whole system down exponentially/using exponentially more energy? All those O(...) notations flip over, don't they?
Assuming the current version of Quantum Mechanics is correct, no. Given that we know QM is not compatible with General Relativity, which means one or both of them must be wrong, we could potentially discover some limitation of QM while investigating this.
Ironically, if that were to happen, it would probably be a much more important boon for humanity than if we successfully build a working QC.
There isn’t actually any reason to believe one of them “is wrong” (we know they’re both approximations.) We just think that the macro and micro should follow the same fundamental laws because that’s how things have been thought to work so far.
It could very well be that they are both great approximations and it’s actually the underlying information structure that shifts depending on scale. This doesn’t seem likely to us perhaps, but only because of existing intuition which we know is likely wrong at some level.
Sure,"wrong" is a bit strong. I mean "wrong" in the same sense as Newtonian mechanics is wrong, which is exactly that it is an excellent approximation in some domains, but fails in others.
> It could very well be that they are both great approximations and it’s actually the underlying information structure that shifts depending on scale.
Right now, both QM and GR claim that they apply at any scale. If it turns out that the laws of physics change with scale, that means that both QM and GR are wrong, even though they may each be perfectly correct at the scale they have been seen to work so far.
>both QM and GR claim that they apply at any scale
the thing is I don't believe that either does make such a claim. I believe certain people have said that and the untrained masses may assume that's the case. But I don't think the scholarly proponents or intellectual founders of either system made such a claim (in fact Newton was religious and Einstein believed we were way off by his death.)
>that means that both QM and GR are wrong
How though? They are both right for their use case so are likely subsets of a greater theory.
The equations of both GR, QM and classical mechanics have no "scale" parameter, so they are in fact claiming they apply at every scale in the most important way - in the math.
Not only does the math apply at any scale, but no one has any idea how to add a scale parameter to prevent it from doing so, or what value that parameter should have. QM at least has the Measurement Postulate that could allow this to fit, but no scale is added.
Note that when I say "a scale parameter", I'm referring to something like the sqrt(1-v²/c²) of special relativity, but for "size", added to the Schrodinger equation and to Einstein's equations, that would mean they take the "scale" of the phenomenon into account. Without such a parameter, the equation says that it applies to a star as well as to a neutron. The only reason we don't apply them that way is that we have already tried and we know they give the wrong results.
Also, both GR and QM give the right results if applied at the scales of day to day life. You can use the Schrodinger equation and the Born postulate to compute where two trains traveling in opposite direction with some speed will meet, or you can use Einstein's field equations, and you'll get the same response within some small margin or error (with some reasonable assumptions, such as an almost flat spacetime in the area).
Furthermore, there are at least significant numbers of QM practitioners who do believe that QM applies at any scale - those who believe in the Many Worlds Interpretation, which states this very explicitly. On the GR side, the limitations of GR if applied at subatomic scales are well accepted and considered a flaw in the theory - which is why people hope to replace it with a theory of quantum gravity.
