Improving Quantum Search on Simple Graphs by Pretty Good Structured Oracles

Quantum search algorithms provide a way to speed up combinatorial search, and have found several applications in modern quantum technology. In particular, spatial on graphs, based continuous-time walks (CTQW), represents promising platform for the implementation of condensed matter systems. CTQW-based algorithms, however, work exactly complete while they are known perform poorly realistic graphs with low connectivity. this paper, we put forward an alternative algorithm, structuring oracle operator, which allows one improve localization properties walker by tuning only on-site energies graph, i.e., without altering its topology. As such, proposed algorithm is suitable systems connectivity, e.g., rings dots or superconducting circuits. Oracle parameters determined Hamiltonian constraints, need numerical optimization.