The Deutsch-Jozsa circuit,

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

The Deutsch-Jozsa circuit, H⊗nH^{\otimes n}, phase oracle, H⊗nH^{\otimes n}, is run on n=2n=2 input qubits for a function that breaks the constant-or-balanced promise: f(00)=1f(00)=1 and f(x)=0f(x)=0 for the other three inputs. Using the general amplitude formula amplitude of ∣00⟩=2−n∑x(−1)f(x),\text{amplitude of }|00\rangle=2^{-n}\sum_x(-1)^{f(x)}, calculate the probability that a measurement of the two output qubits returns 0000.

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