A register of qubits holds equally weighted items

PHYSICS · Multi-part · 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 Grover search, amplitude amplification and counting

Problem

A register of n=5n=5 qubits holds N=32N=32 equally weighted items, of which one is marked. Grover's iteration GG is applied k=2k=2 times starting from the uniform superposition ∣s⟩|s\rangle. ((a)) Find the rotation angle θ\theta defined by sin⁡(θ/2)=M/N\sin(\theta/2) = \sqrt{M/N}. ((b)) Hence find the probability that a measurement after the two iterations returns the marked item.

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