From: Minimizing CNOT-count in quantum circuit of the extended Shor’s algorithm for ECDLP
Process | The change in value | |
---|---|---|
1.1 | CNOT\(\quad w_1,w_2,x_1,y_1\) | \(w_1\leftarrow x_1,w_2\leftarrow y_1\) |
2.1 | \({\texttt {ModAdd}}^{-1}\quad x_1,y_1,x_2,y_2\) | \(x_1\leftarrow x_1-x_2,y_1\leftarrow y_1-y_2\) |
3.1 | \({\texttt {Inv}} \quad w_3,x_1\) | \(w_3\leftarrow \frac{1}{x_1-x_2}\) |
4.1 | \({\texttt {M-Mul}} \quad w_4,y_1,w_3\) | \(w_4\leftarrow \lambda\) |
5.1 | \({\texttt {D-Mul}} \quad w_6,w_4,w_5\) | \(w_6\leftarrow \lambda ^2\) |
6.1 | CNOT\(w_7,w_6\) | \(w_7\leftarrow \lambda ^2\) |
7.1 | \({\texttt {ModAdd}}^{-1} w_7,w_1\) | \(w_7\leftarrow \lambda ^2-x_1\) |
8.1 | \({\texttt {ModAdd}}^{-1}\quad w_7,x_2\) | \(w_7\leftarrow \lambda ^2-x_1-x_2=x_3\) |
9.1 | \({\texttt {ModAdd}}^{-1}\quad w_1,w_7\) | \(w_1\leftarrow x_1-x_3\) |
10.1 | \({\texttt {D-Mul}} \quad w_8,w_1,w_4\) | \(w_8\leftarrow \lambda (x_1-x_3)\) |
11.1 | \({\texttt {ModAdd}}^{-1}\quad w_8,w_2\) | \(w_8\leftarrow \lambda (x_1-x_3)-y_1=y_3\) |