Solution of SAT problems with the adaptive-bias quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) is a promising method for solving certain classical combinatorial problems on near-term devices. When employing the QAOA to 3-SAT and Max-3-SAT problems, cost exhibits an easy-hard-easy or easy-hard pattern respectively as clause density changed. resources needed in hard-region are out of reach current NISQ We show by numerical simulations with up 14 variables analytical arguments that adaptive-bias (ab-QAOA) greatly improves performance hard region problems. For similar accuracy, average, ab-QAOA needs 3 levels 10-variable compared 22 QAOA. numbers 7 62 levels. improvement comes from more targeted limited generation entanglement during evolution. demonstrate not strictly necessary since local fields used guide This leads us propose optimization-free can solve effectively significantly fewer gates original ab-QAOA. Our work paves way realizing advantages