  The computational complexity conjecture of NP $\nsubseteq$ BQP implies that
there should be an exponentially small energy gap for Quantum Annealing (QA) of
NP-hard problems. We aim to verify how this computation originated gapless
point could be understood based on physics, using the quantum Monte Carlo
method. As a result, we found a phase transition detectable only by the
divergence of fidelity susceptibility. The exponentially small gapless points
of each instance are all located in the phase found in this study, which
suggests that this phase transition is the physical cause of the failure of QA
for NP-hard problems.
