Table 1 Binary representation of the single-qubit Clifford group \({{\mathcal{C}}}_{1}\)
U | I | H | S | HSH | HS | SH |
|---|---|---|---|---|---|---|
UXU† | X | Z | iXZ | X | − iXZ | Z |
UZU† | Z | X | Z | − iXZ | X | iXZ |
α(0, 1) | 0 | 0 | 0 | 3 | 0 | 1 |
α(1, 0) | 0 | 0 | 1 | 0 | 3 | 0 |
\(A=\left[\begin{array}{cc}{a}^{xx}&{a}^{xz}\\ {a}^{zx}&{a}^{zz}\end{array}\right]\) | \(\left[\begin{array}{cc}1&0\\ 0&1\\ \end{array}\right]\) | \(\left[\begin{array}{cc}0&1\\ 1&0\\ \end{array}\right]\) | \(\left[\begin{array}{cc}1&0\\ 1&1\\ \end{array}\right]\) | \(\left[\begin{array}{cc}1&1\\ 0&1\\ \end{array}\right]\) | \(\left[\begin{array}{cc}1&1\\ 1&0\\ \end{array}\right]\) | \(\left[\begin{array}{cc}0&1\\ 1&1\\ \end{array}\right]\) |
