Compute-phase-uncompute construction

Starting the answer qubit in

∣0 ⟩

U_{f}, Z, U_{f}

∣ x ⟩ ∣0 ⟩

to

(- 1)^{f (x)} ∣ x ⟩ ∣0 ⟩

. It realizes a phase oracle with two standard-oracle queries while returning the answer register to its initial state.

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Brassard–Høyer–Tapp collision algorithm
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Pauli-string phase by parity computation

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