I don’t suppose you could spend a post or two explaining in your nice easy to understand way exactly what it is a quantum computer is supposed to do and how this might impact the NP problems.
Grover’s algorithm provides a quadratic speedup over brute-force algorithms for solving NP-complete problems, but that still leaves them as exponential-time. BQP (Bounded error, quantum, polynomial-time; basically the complexity class of quantum computers) is suspected to be disjoint from NP and a superset of P, but neither is known for sure.
I don’t suppose you could spend a post or two explaining in your nice easy to understand way exactly what it is a quantum computer is supposed to do and how this might impact the NP problems.
It’s not exactly known.
Grover’s algorithm provides a quadratic speedup over brute-force algorithms for solving NP-complete problems, but that still leaves them as exponential-time. BQP (Bounded error, quantum, polynomial-time; basically the complexity class of quantum computers) is suspected to be disjoint from NP and a superset of P, but neither is known for sure.