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There is a strong interest in quantum search algorithms, particularly inproblems with multiple adjacent solutions. In the hypercube, part of the energyof the quantum system is retained in states adjacent to the target states,decreasing the chances of the target states being observed. This paper appliesthe Multiself-loop Lackadaisical Quantum Walk with Partial Phase Inversion tosearch for multiple adjacent marked vertices on the hypercube. Aspects like thetype of marked vertices are considered in addition to using multiple self-loopsand weight compositions. Two scenarios are analyzed. Firstly, the relativeposition of non-adjacent marked vertices together with adjacent markedvertices. Secondly, only adjacent marked vertices are analyzed. Here, we showexperimentally that, with partial phase inversion, a quantum walk can amplifythe probability amplitudes of the target states, reaching success probabilitiesof values close to $1$. We also show that the relative position of non-adjacentmarked vertices does not significantly influence the search results. Ourresults demonstrate that the partial phase inversion of target states is apromising alternative to search adjacent solutions with quantum walks, which isa key capacity for real search applications.

Search for Multiple Adjacent Marked Vertices on the Hypercube by a Quantum Walk with Partial Phase Inversion