A catalogue of items contains items matching a search criterion tested by a phase oracle.

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 catalogue of

N=1024

items contains

M=3

items matching a search criterion tested by a phase oracle. ((a)) Find the rotation angle

\theta

with

\sin(\theta/2)=\sqrt{M/N}

and the optimal iteration count

R=\mathrm{round}\!\left(\frac{\pi}{2\theta}-\frac12\right)

. ((b)) Find the success probability at

k=R

and state whether it satisfies the failure bound

M/N

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