A physical process can never solve a mathematical problem in Hilbert's sense, unless the process is 100% deterministic. Thus quantum algorithms have only a heuristic value unless they happen to produce a solution that can be verified independently.

A quantum algorithm produces answers with certain probabilities only. So instead of answering yes or no a quantum decision algorithm gives a probability that tends (with probability 1) to 0 or 1. At any fixed time, we have no certainty. In particular, unless the algorithm spits out a proof of nonexistence - which Kieu's algorithm doesn't - that can be checked by hand or with a deterministic proof checker, we'll never know whether a solution exist in case in fact none exists.

The same applies for occasionally proposed quantum solutions of the still unsolved 'P=NP?' problem, one of the Clay Millennium problems.