Efficient quantum algorithm for solving structured problems via multistep quantum computation

In classical computation, a problem can be solved in multiple steps where calculated results of each step copied and used repeatedly. While quantum it is difficult to realize similar multi-step computation process because the no-cloning theorem forbids making copies an unknown state perfectly. We find method based on resonant transition protect reuse that encodes intermediate without state, present algorithm solves via process. This achieve exponential speedup over algorithms solving type structured search problems.