Link to research paper: https://doi.org/10.12743/quanta.v12i1.235
These are pedagogical notes on Shor's factoring algorithm. They derive the Shor factorization circuit in a rigors but self-contained manner. We have assumed no prior knowledge of the algorithm, except a familiarity with the circuit model of quantum computing, and we have walked the reader through the framework required to understand the algorithm. The manuscript goes on to factor the numbers N=15, 21, 33, 35, 143, 247. We derive a general method by which the appropriate modular exponentiation operator can be constructed.
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