For the two-bit function

PHYSICS · Subjective · Fermi University Physics · Quantum Information & Technology · The quantum circuit model and quantum algorithms · The quantum circuit model and quantum algorithms

Quantum Information and Technology, Ch Oracles, quantum parallelism and the first algorithms

Problem

For the two-bit function f(x1,x2)=x1⊕x2f(x_1,x_2) = x_1\oplus x_2, use phase kickback to derive the phase oracle OfO_f acting on the two input qubits alone (with the output qubit prepared in ∣−⟩|-\rangle and left aside), and show that Of=Z⊗ZO_f = Z\otimes Z.

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