A database with entries has exactly one entry,

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 database with N=4096N=4096 entries has exactly one entry, M=1M=1, satisfying a search criterion tested by a phase oracle. ((a)) Find the optimal number of Grover iterations R=round ⁣(π2θ−12)R = \mathrm{round}\!\left(\dfrac{\pi}{2\theta} - \dfrac{1}{2}\right), where sin⁡(θ/2)=M/N\sin(\theta/2) = \sqrt{M/N}. ((b)) Find the success probability after RR iterations and check it is consistent with the failure bound M/NM/N.

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