Testing GitHub Actions

Please 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 nn-qubit register, we think of a state ψ\ket{\psi} of that register as being a vector with 2n2^n complex elements; one for each possible classical bit string on nn bits.

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

00=(1000). \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:

12(000+111)=12(10000001). \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}