Table 4 The steps to restore the auxiliary bits. The states in the table represent the change of the quantum registers corresponding to each step and the unwritten states are the same as the states in the previous step
From: Minimizing CNOT-count in quantum circuit of the extended Shor’s algorithm for ECDLP
Process | The change in value | |
|---|---|---|
11.2 | \({\texttt {ModAdd}}\quad w_8,w_2\) | \(w_8\leftarrow \lambda (x_1-x_3)\) |
10.2 | \({\texttt {D-Mul}} ^{-1}\quad w_8,w_1,w_4\) | \(w_8\leftarrow 0\) |
9.2 | \({\texttt {ModAdd}}\quad w_1,w_7\) | \(w_1\leftarrow x_1\) |
8.2 | \({\texttt {ModAdd}}\quad w_7,x_2\) | \(w_7\leftarrow \lambda ^2-x_1\) |
7.2 | \({\texttt {ModAdd}}\quad w_7,w_1\) | \(w_7\leftarrow \lambda ^2\) |
6.2 | CNOT\(\quad w_7,w_6\) | \(w_7\leftarrow 0\) |
5.2 | \({\texttt {D-Mul}} ^{-1} \quad w_6,w_4,w_5\) | \(w_6\leftarrow 0\) |
4.2 | \({\texttt {M-Mul}} ^{-1}\quad w_4,y_1,w_3\) | \(w_4\leftarrow 0\) |
3.2 | \({\texttt {Inv}} ^{-1}\quad w_3,x_1\) | \(w_3\leftarrow 0\) |
2.2 | \({\texttt {ModAdd}}\quad x_1,y_1,x_2,y_2\) | \(x_1\leftarrow x_1,y_1\leftarrow y_1\) |
1.2 | CNOT\(\quad w_1,w_2,x_1,y_1\) | \(w_1\leftarrow 0,w_2\leftarrow 0\) |