Figure 42.

Circuit diagram of the quantum subroutine used in Shor’s algorithm. A $2n$-qubit register is initiated in the zero-state $\left|0\right.〉$, and an n-qubit register in $\left|1\right.〉$. Basis change of the input-register part of the controlled modular exponentiation operator allow for sampling a probability distribution with peaks at $s/r$.