Quantum optimization

We present a quantum algorithm for combinatorial optimization using the cos t structure of the search states. Its behavior is illustrated for overconst rained satisfiability (SAT) and asymmetric traveling salesman problems (ATS P). Simulations with randomly generated problem instances show each step of the algorithm shifts amplitude preferentially towards lower cost states, t hereby concentrating amplitudes into low-cost states, on average. These res ults are compared with conventional heuristics for these problems. (C) 2000 Elsevier Science Inc. All rights reserved.