Introducing structure to expedite quantum searching

We present a novel quantum algorithm for solving the unstructured search problem with one marked element. Our allows generating circuits that use asymptotically fewer additional gates than famous Grover's and may be successfully executed on NISQ devices. prove our is optimal in total number of elementary up to multiplicative constant. As many NP-hard problems are not fact unstructured, we also describe \emph{partial uncompute} technique which exploits oracle structure significant reduction required find solution. Combining these results us smaller various applications, keeping queries essentially same. show how can applied solve hard combinatorial problems, example Unique k-SAT. Additionally, reduce multiple elements.