The 3rd iteration:
- if(oracle(cand)){phase($\pi$);}: $cand:=\frac{1}{2}\cdot\left[\begin{array}{c}-1&-1&-1&-1\end{array}\right]^{T}$
- Diffusion 1: $cand:=H_2\cdot\frac{1}{2}\cdot\left[\begin{array}{c}-1&-1&-1&-1\end{array}\right]^{T}=\left[\begin{array}{c}-1&0&0&0\end{array}\right]^{T}$
- Diffusion 2: if(cand$\neq$0){phase($\pi$)}: $cand:=\left[\begin{array}{c}-1&0&0&0\end{array}\right]^{T}$
- Diffusion 3: $cand:=H_2\cdot\left[\begin{array}{c}-1&0&0&0\end{array}\right]^{T}=\frac{1}{2}\cdot\left[\begin{array}{c}-1&-1&-1&-1\end{array}\right]^{T}$
The 4th iteration: Like 1st iteration, but only all $\cdot(-1)$
The 5th iteration: Like 2nd iteration, but only all $\cdot(-1)$
The 6th iteration: Like 3rd iteration, but only all $\cdot(-1)$
The 7th iteration: Like 1st iteration
Takeaways:
- .darkblue[Periodic results]
- For more complex examples: .darkblue[Probability of solution increases slowly] (and afterward decreases slowly)!
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# .darkblue[Grover's Search: