  We propose a strategy for modeling the behavior of an adiabatic quantum
computer described by an Ising Hamiltonian with $N$ sites and the coordination
number $Z$. The method is based on the $1/Z$ expansion for the density matrix
of the system. In each order, the ground state energy is found neglecting the
higher-order correlations between the sites, as long as the set of equations
remains non-singular. The conditions of the appearance of a singularity,
equivalent to the disappearance of energy gap in the given approximation, can
be directly obtained from the equations. Then the next order in the expansion
must be used, at the price of an $N$-fold increase in computational resources.
This "martingale" strategy allows reducing the computational costs to a power
of $N$ rather than $2^N$, with a finite probability of success. The strategy is
illustrated by the case of a two-spin system and extended to a large number of
qubits. Comparing the predictions to the experimental results obtained by using
an adiabatic quantum computer would help quantify the importance of multi-site
correlations, and the influence of decoherence, on its operation.
