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.
The one-iteration Grover’s algo- rithm gives |0⟩ H Ut D6 |0⟩ H |0⟩ H |0⟩ H |0⟩ H |0⟩ H Measurements at the end are computational basis mea- surements
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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.