A new QPE-based circuit implements the Grover diffusion operator exactly on Laplacian integral graphs, giving deterministic spatial search with O(1/√ε) cost on any connected such graph.
We will later present an interesting type of Laplacian in- tegral graphs that are not vertex-transitive and 2dL = O(N )
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Deterministic quantum search on all Laplacian integral graphs
A new QPE-based circuit implements the Grover diffusion operator exactly on Laplacian integral graphs, giving deterministic spatial search with O(1/√ε) cost on any connected such graph.