Table 6 The number of T gates and CNOT gates for Clifford+T implementations
From: Minimizing CNOT-count in quantum circuit of the extended Shor’s algorithm for ECDLP
The basic arithmetic operations | #T gates | #CNOTs for Clifford+T |
|---|---|---|
\({\texttt {1-Add}} _y\) (unknown state y) | 14n | \(16n+1\) |
\({\texttt{ctrl}}\)-\({\texttt {1-Add}} _y\) (unknown state y) | \(28n+7\) | \(26n+6\) |
\({\texttt{2-Add}}_y\) (known constant y) | \(14n-7\) | \(14n-5.5\) |
\({\texttt{ctrl}}\)-\({\texttt{2-Add}}_y\) | 14n | \(17n+1\) |
\({\texttt{1-Comp}}\) | 14n | \(12n+1\) |
\({\texttt{2-Comp}}_y\) (known constant y) | 14n | \(12n+1\) |
\({\texttt{ctrl}}\)-\({\texttt{2-Comp}}_y\) (known constant y) | \(14n+7\) | \(12n+7\) |
\({\texttt{2-Comp}}_y\) (unknown state y) | 14n | \(16n+1\) |
\({\texttt{ctrl}}\)-\({\texttt{2-Comp}}_y\) (unknown state y) | \(14n+7\) | \(16n+7\) |
\({\texttt {ModSub}} _y\) or \({\texttt {ModAdd}}_y\) (known constant y) | \(42n-7\) | \(43n-2.5\) |
\({\texttt{ctrl}}\)-\({\texttt {ModSub}} _y\) (known constant y) | \(42n+7\) | \(46n+11\) |
\({\texttt {ModAdd}}_y\) (unknown state y) | 56n | \(61n+6\) |
\({\texttt{ctrl}}\)-\({\texttt {ModAdd}}_y\) (unknown state y) | \(70n+14\) | \(71n+17\) |
\({\texttt {Neg}}\) | \(14n-7\) | \(14n-5.5\) |
\({\texttt{ctrl}}\)-\({\texttt {Neg}}\) | 14n | \(18n+1\) |
\({\texttt{ctrl}}\)-\({\texttt {1-Shift}}\) | 14n | 12n |
\({\texttt{ctrl}}\)-\({\texttt{2-Shift}}\) | 7n | 8n |
\({\texttt {ShiftMod}}\) | 28n | \(31n+15\) |
\({\texttt {M-Mul}}\) (half) | \(42n^2+35n-7\) | \(45n^2+39n-4.5\) |
\({\texttt {D-Mul}}\) (half) | \(56n^2\) | \(57n^2+2.5n\) |