Statistical Analysis for Quantum Adiabatic Computations: Quantum Monte Carlo Annealing

Quantum adiabatic computations are designed to determine the ground state configurations of an classical problem Hamiltonian H3SAT within quantum theory and at imaginary time allow statistical mechanics studies for the computational e_ciency of the ground state search. We mention a recent determination of the quantum complexity, i.e. the mass-gap _mGAP for a specific ensemble of three-satisfiability (3SAT) problems with a unique satisfiability assignment, which shows an exponential increase of the gap correlation length _GAP with _GAP = 1=_mGAP. In 3SAT we present numerical data for the behavior of quantum Monte Carlo annealing cycles in search for the ground state. The findings show, that for the specific set of realizations quantum Monte Carlo searches in 3SAT fail above a sharp cut-o_ Kcut in the complexity K, which exemplifies the intractable nature of 3SAT.