A quantum genetic algorithm with quantum crossover and mutation operations

In the context of evolutionary quantum computing in the literal meaning, a quantum crossover operation has not been introduced so far. Here, we introduce a novel quantum genetic algorithm which has a quantum crossover procedure performing crossovers among all chromosomes in parallel for each generation. A complexity analysis shows that a quadratic speedup is achieved over its classical counterpart in the dominant factor of the run time to handle each generation.Comment: 21 pages, 1 table, v2: typos corrected, minor modifications in sections 3.5 and 4, v3: minor revision, title changed (original title: Semiclassical genetic algorithm with quantum crossover and mutation operations), v4: minor revision, v5: minor grammatical corrections, to appear in QI