Quantum Computing Asked by Upstart on July 29, 2020

Suppose I have the state $|Arangle=|xrangle^lotimes |yrangle^l otimes |zrangle^l otimes |0rangle_x^lotimes |0rangle_y^lotimes |0rangle_z^l$. I perform the transformation between the $|xrangle$ register and first $0_x$ register that is $$U|x,0rangleto |x,(2x)~text{mod}~lrangle$$

Suppose if $|xrangle=|x_0x_1x_2…x_{l-1}rangle$ and $|0rangle=|0_00_1000..0_{l-1}rangle$ then the result is $|xrangle|x_1x_2x_3….x_{l-1}0rangle$.

So the tensorial notation for this operator on state $A$ is

begin{align}

U=prod_{i=0}^{l-2} left( I^{otimes 1+i}otimes P_0otimes I^{otimes 3l-2}otimes Iotimes I^{l-1-i}otimes I^{otimes 2l} right. left.+I^{otimes 1+i}otimes P_1otimes I^{otimes 3l-2}otimes Xotimes I^{l-1-i}otimes I^{otimes 2l}right)

end{align}

Is this operator correct for the operation that I want to perform?

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