New answers tagged nielsen-and-chuang
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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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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-\...
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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 ...
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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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