- #1

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In Nielsen and Chuang p.223 we have the following situation:

$$\frac{1}{2^t} \sum\limits_{k,l=0}^{2^t-1} e^{\frac{-2\pi i k l}{2^t}} e^{2 \pi i \varphi k} |l\rangle$$

Which results from applying the inverse quantum Fourier transform to state ##\frac{1}{2^{t/2}} \sum\limits_{k=0}^{2^t-1} e^{-2\pi i \varphi k} |l\rangle##. We have more or less a sum over the basis states ##|l\rangle##. This is clear so far.

Next, the following new notation is then introduced ##|(b+l)(\text{mod } 2^t)\rangle##. Were we know from ##b## that it is an integer in the range from ##0## to ##2^t -1##.

What does this ##b+l## mean exactly, how is this to interpret? Why does one not leave it with the basic state ##|l\rangle##?

$$\frac{1}{2^t} \sum\limits_{k,l=0}^{2^t-1} e^{\frac{-2\pi i k l}{2^t}} e^{2 \pi i \varphi k} |l\rangle$$

Which results from applying the inverse quantum Fourier transform to state ##\frac{1}{2^{t/2}} \sum\limits_{k=0}^{2^t-1} e^{-2\pi i \varphi k} |l\rangle##. We have more or less a sum over the basis states ##|l\rangle##. This is clear so far.

Next, the following new notation is then introduced ##|(b+l)(\text{mod } 2^t)\rangle##. Were we know from ##b## that it is an integer in the range from ##0## to ##2^t -1##.

What does this ##b+l## mean exactly, how is this to interpret? Why does one not leave it with the basic state ##|l\rangle##?

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