Uncontrolled unitaries plus controlled preparations replace controlled unitaries in phase estimation, cutting two-qubit gates exponentially when eigenstate preparation is known.
In other words, if the ancilla is|1⟩ a, we performW|ϕ⟩ s =|ψ⟩ s, and if the ancilla is|0⟩ a, we do nothing, leaving the system in|ϕ⟩ s
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Exponentially cheaper coherent phase estimation via uncontrolled unitaries
Uncontrolled unitaries plus controlled preparations replace controlled unitaries in phase estimation, cutting two-qubit gates exponentially when eigenstate preparation is known.