 Deutsch algorithm

The one-input Deutsch algorithm determines whether a Boolean function is constant or balanced using one Boolean quantum oracle call. Initialize the input qubit in $|+⟩$ and the answer qubit in $|-⟩$. Quantum phase kickback changes the input to $(-1{)}^{f(0)}(|0⟩+(-1{)}^{f(0)\oplus f(1)}|1⟩)/\sqrt{2}$. A Hadamard gate and computational-basis measurement therefore return the parity $f(0)\oplus f(1)$ with certainty.