Pede a few months away from finishing a Ph.D. in computer science, here. I felt like jumping in to point out two interesting consequences of if this were true:
Not so great consequence: The un-crackability of pretty much all modern encryption algorithms depends on prime factorization being in NP (hasn't been officially proven NP-hard or NP-complete, but it's presumed to not be in P). A quantum computer being able to bypass that means that any kind of computer security, as we know it, would be rendered useless. No more online banking, secure digital communications, etc. We're not prepared as a society for such an overnight-rendered impotency of all such systems.
A maybe good, maybe bad consequence: The automated theorem proving problem is co-NP-complete. The problem essentially boils down to this: given a set of axioms and a proposition, generate a proof for the proposition from those axioms (or conclude that it's impossible).A quantum computer, again being able to bypass that, could in theory be able to discover everything that's discoverable from what's already been discovered.
So, step 1: feed the quantum computer all human knowledge. Step 2: ask it any question. If it's possible at all to answer that question from all existing knowledge, it'll answer it (with a proof, to boot!).
That second consequence would enable the scenario put forth by the OP.
Pede a few months away from finishing a Ph.D. in computer science, here. I felt like jumping in to point out two interesting consequences of if this were true:
Not so great consequence: The un-crackability of pretty much all modern encryption algorithms depends on prime factorization being in NP (hasn't been officially proven NP-hard or NP-complete, but it's presumed to not be in P). A quantum computer being able to bypass that means that any kind of computer security, as we know it, would be rendered useless. No more online banking, secure digital communications, etc. We're not prepared as a society for such an overnight-rendered impotency of all such systems.
A maybe good, maybe bad consequence: The automated theorem proving problem is co-NP-complete. The problem essentially boils down to this: given a set of axioms and a proposition, generate a proof for the proposition from those axioms (or conclude that it's impossible).A quantum computer, again being able to bypass that, could in theory be able to discover everything that's discoverable from what's already been discovered.
So, step 1: feed the quantum computer all human knowledge. Step 2: ask it any question. If it's possible at all to answer that question from all existing knowledge, it'll answer it (with a proof, to boot!).
That second consequence would enable the scenario put forth by the OP.