Editing Hadamard transform (section)

===Hadamard gate===
{{further|Quantum gate#Hadamard gate}}
In quantum computing, the Hadamard gate is a one-[[qubit]] [[rotation]], mapping the qubit-basis states <math>|0 \rangle </math> and <math>|1 \rangle </math> to two superposition states with equal weight of the computational [[Basis (linear algebra)|basis]] states <math>|0 \rangle </math> and <math>|1 \rangle </math>. Usually the phases are chosen so that
<math display="block">H=\frac{|0\rangle+|1\rangle}{\sqrt{2}}\langle0|+\frac{|0\rangle-|1\rangle}{\sqrt{2}}\langle1|</math>

in [[Dirac notation]]. This corresponds to the [[transformation matrix]]
<math display="block">H_1=\frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}</math>
in the <math>|0 \rangle , |1 \rangle </math> basis, also known as the [[computational basis]]. The states <math display="inline"> \frac{\left|0\right\rangle + \left|1\right\rangle}{\sqrt{2}}</math> and <math display="inline">\frac{\left|0\right\rangle - \left|1\right\rangle}{\sqrt{2}}</math> are known as <math>\left|\boldsymbol{+}\right\rangle</math> and <math>\left|\boldsymbol{-}\right\rangle</math> respectively, and together constitute the [[polar basis]] in [[quantum computing]].