Supplementary Information: Difference between revisions

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 <math>\ket{+}=\frac{1}{\sqrt{2}}(\ket{0}+\ket{1}),</math></br>
 <math>\ket{-}=\frac{1}{\sqrt{2}}(\ket{0}-\ket{1})</math>
-Thus, |0i, |1i are eigenstates of Z gate and |+i, |−i are eigenstates of X gate.
+</br>X (NOT gate):  <math>X\ket{0}\,\to\,\ \ket{1}, X\ket{1}\,\to\,\ \ket{0}, X\ket{+}\,\to\,\ \ket{+}, X\ket{-}\,\to\,\ -\ket{-}</math>
-</br>X (NOT gate):  <math>X\ket{0}\,\to\,\ \ket{1},\quad X\ket{1}\,\to\,\ \ket{0},\quad X\ket{+}\,\to\,\ \ket{+}, X\ket{-}\,\to\,\ -\ket{-}</math>
+</br>Z (Phase gate): <math>Z\ket{+}\,\to\,\ \ket{-}, Z\ket{-}\,\to\,\ \ket{+}, Z\ket{0}\,\to\,\ \ket{0}, Z\ket{1}\,\to\,\ -\ket{1}</math></br>
-</br>Z (Phase gate): <math>Z\ket{+}\,\to\,\ \ket{-},\quad Z\ket{-}\,\to\,\ \ket{+},\quad Z\ket{0}\,\to\,\ \ket{0},\quad Z\ket{1}\,\to\,\ -\ket{1}</math></br>
 Thus, <math>\ket{0}</math>, <math>\ket{1}</math> are eigenstates of Z gate and <math>\ket{+}</math>, <math>\ket{-}</math> are eigenstates of X gate.
 </br> (Hadamard gate): <math>H\ket{0}\,\to\,\ \ket{+}</math> or <math>H\ket{1}\,\to\,\ \ket{-}</math>