# Questions tagged [order-finding]

For questions about the order-finding problem.

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### Why is the operator $M_a |x\rangle= |a \cdot x \pmod{N} \rangle$ unitary?

If $N\geq 2$, $a\in \mathbb{Z}_N$, and $a^r= 1$ for some $r$. Consider the operator $M_a$, which is related to order finding : $M_a |x\rangle= |a \cdot x \pmod{N} \rangle$ if $x\in \mathbb{Z}_N$ What ...
• 51
1 vote
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### Eigenvalues of a unitary U that implements a periodic function [closed]

What can be said about the eigenvalues of a unitary quantum gate $U$ which implements $f(x)=f(x+r) \forall x$, as in $U|x\rangle|0\rangle\rightarrow|x\rangle|f(x)\rangle$ ? The reason I'm asking is ...
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### In the order finding circuit, why is the equal superposition of the controlled unitary eigenstates the $|1\rangle$ state?

In Nielsen and Chuang's "Quantum Computation and Quantum Information" when the quantum order finding process is being presented (specifically page 227, equation 5.44) we are told that by &...
1 vote
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### Probability of the case when $r'\neq r$ and $r'$ is a factor $r$ in the order finding algorithm

In the Order-Finding algorithm it is stated that it might be that $s$ and $r$ have a common factor, in which case the number $r'$ returned by the continued fractions algorithm be a factor of $r$, and ...
• 831
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