First, a few simple equations:
$$ \begin{aligned} E & = mc^2 \\ e^{i \pi} + 1 & = 0 \\ \end{aligned} $$The quadratic formula: if \( ax^2 + bx + c = 0 \), then:
$$ x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{2a} $$For quantum computation, let's first define the basis vectors \( \ket{0} \) and \( \ket{1} \):
$$ \newcommand{\bmatrix}[1]{\begin{bmatrix} #1 \end{bmatrix}} \begin{aligned} \ket{0} & = \bmatrix{1 \\ 0}, & \ket{1} & = \bmatrix{0 \\ 1} \end{aligned} $$and consider a representation of a two-qubit state as follows:
$$ \alpha \ket{00} + \beta \ket{01} + \gamma \ket{10} + \delta \ket{11} $$