Abstract
We give a general method of construting quantum circuit for random \QTR\{it\}\{satisfiability\} (SAT) problems with the basic logic gates such as multi-qubit controlled-NOT and NOT gates. The sizes of these circuits are almost the same as the sizes of the SAT formulas. Further, a parallelization scheme is described to solve random SAT problems efficiently through these quantum circuits in \QTR\{it\}\{nuclear magnetic resonance\} (NMR) ensemble quantum computing. This scheme exploits truly mixed states as input states rather than pseudo-pure states, and combines with the topological nanture of the NMR spectrum to identify the solutions to SAT problems in a parallel way. Several typical SAT problems have been experimentally demonstrated by this scheme with good performances.