The quantum component of Shor's prime factorization algorithm is the order-finding algorithm. The video details the process of reducing it into the phase estimation algorithm, offering a comprehensive presentation of the requisite mathematics and logical reasoning behind the algorithm.

References
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1) John Watrous, Quantum Computation Lecture notes, University of Waterloo https://cs.uwaterloo.ca/~watrous/QC-notes/
2) Nielsen, Michael A., and Isaac L. Chuang. Quantum computation and quantum information. Cambridge university press, 2010. .

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