2 research outputs found
Monte Carlo Search for Very Hard KSAT Realizations for Use in Quantum Annealing
Using powerful Multicanonical Ensemble Monte Carlo methods from statistical
physics we explore the realization space of random K satisfiability (KSAT) in
search for computational hard problems, most likely the 'hardest problems'. We
search for realizations with unique satisfying assignments (USA) at ratio of
clause to spin number that is minimal. USA realizations are found
for -values that approach from above with increasing number
of spins . We consider small spin numbers in . The ensemble
mean exhibits very special properties. We find that the density of states of
the first excited state with energy one is consistent with an
exponential divergence in : . The rate
constants for and of KSAT with USA realizations at
are determined numerically to be in the interval at and
at . These approach the unstructured search value
with increasing . Our ensemble of hard problems is expected to provide a
test bed for studies of quantum searches with Hamiltonians that have the form
of general Ising models.Comment: non