# Testing GitHub Actions

08 May 2020Please disregard this post; it is only intended to check that GitHub Actions work correctly with jekyll-katex.

By way of context, it helps to revisit a little bit of what a quantum state is in the first place. Typically, if we have an $n$-qubit register, we think of a state $\ket{\psi}$ of that register as being a *vector* with $2^n$ complex elements; one for each possible classical bit string on $n$ bits.

For example, when we write out a state in Dirac notation like $\ket{00}$, we could have also written that same state out as a vector on four elements:

$\begin{aligned} \ket{00} = \left( \begin{matrix} 1 \\ 0 \\ 0 \\ 0 \end{matrix} \right). \end{aligned}$

As our system gets larger and larger, this gets more and more unwieldy. Even at three qubits, things get big in a hurry:

$\begin{aligned} \frac{1}{\sqrt{2}} \left( \ket{000} + \ket{111} \right) = \frac{1}{\sqrt{2}} \left( \begin{matrix} 1 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 1 \end{matrix} \right). \end{aligned}$