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User:Salix alba/sandbox

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Let be odd

  • first item
  • second item

and even.


= \cdot


SVG: MathML: n

\mathcal{A} 𝒜


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<math>q(v)=|v|^2</math> MathML/MathJax SVG

<math>q(v)=\|v\|^2</math> MathML/MathJax SVG

<math>q(v)=\|v\|_A</math> MathML/MathJax SVG

<math>x^2</math> MathML/MathJax SVG

<math>(v)^2</math> MathML/MathJax SVG


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<math>\cancel{y}</math> MathML/MathJax SVG

<math>\cancel{x}</math> MathML/MathJax SVG

<math>\cancel{xyz}</math> MathML/MathJax SVG


let be odd

  1. foo
  2. bar

and even.



Pick a random number .|Compute , the greatest common divisor of and .|If , then is a nontrivial factor of , with the other factor being and we are done.|Otherwise, use the quantum subroutine to find the order of .|If is odd, then go back to step 1.|Compute . If is nontrivial, the other factor is , and we're done. Otherwise, go back to step 1. }}It has been shown that this will be likely to succeed after a few runs.[1] In practice, a single call to the quantum order-finding subroutine is enough to completely factor with very high probability of success if one uses a more advanced reduction.[2]

  1. ^ Cite error: The named reference siam was invoked but never defined (see the help page).
  2. ^ Ekerå, Martin (June 2021). "On completely factoring any integer efficiently in a single run of an order-finding algorithm". Quantum Information Processing. 20 (6): 205. arXiv:2007.10044. Bibcode:2021QuIP...20..205E. doi:10.1007/s11128-021-03069-1.