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How to choose a suitable number of iterations for Grover's algorithm?

Note that grover algorithm's iterations depends on the number of solutions the problem have (More than the optimal creates a really bad result). We can know this by the Quantum Counting Algorithm.
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Is there a criteria to ensure a one-qubit operator is exactly of the form $R_n(\theta)$ (i.e without a global phase $e^{i\alpha}$)?

As to your first question, I believe global phases can always be ignored, and we generally only concern ourselves with relative phases. So we don't really require that $\alpha=0$, we just ignore it. ...
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2 votes

Why is dual-rail encoding called an error-detecting code for amplitude damping?

Equation 1 misses the Kraus operator on the right. The results are ok. You may obtain the same results by considering E acting on a single qubit: $$E_0|0> =|0>,\tag{1}$$ $$E_0|1> =\sqrt{1-\...
1 vote

Quick conditions to see that $I - E_1 -E_2$ is positive for $E_1, E_2$ positives (example from Nielsen and Chuang)

You obtain the factor by defining \begin{gather} E_1 = \alpha |1\rangle \langle 1| \\ E_2 = \alpha \frac{(|0\rangle-|1\rangle)(\langle 0|-\langle 1|)}{2} \\ E_3 = I - E_1 - E_2 \\ \end{gather} and ...
2 votes

Solution to Nielsen & Chuang Exercise 5.3 (FFT)

It seems like a homework question so I will not give full details. First, the question asks to show that a straightforward application of DFT takes $\Theta(2^{2n})$ operations on an input with $2^n$ ...
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