Quantum search can beat Grover's depth when oracle and diffusion depths are comparable by mixing global and local diffusion operators in one or more stages.
For convenience, we denote the oracleUf as Ut = 1 12n− 2|t⟩⟨t| (3) if the ancillary qubitH|1⟩ is prepared
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Depth optimization of quantum search algorithms beyond Grover's algorithm
Quantum search can beat Grover's depth when oracle and diffusion depths are comparable by mixing global and local diffusion operators in one or more stages.