# How are magic states defined in the context of quantum computation?

Quoting from this blog post by Earl T. Campbell:

Magic states are a special ingredient, or resource, that allows quantum computers to run faster than traditional computers.

One interesting example that is mentioned in that blog post is that, in the case of a single qubit, any state apart from the eigenstates of the Pauli matrices is magic.

How are these magic states more generally defined? Is it really just any state that is not a stabilizer state, or is it something else?

The standard example is that if you can produce the state $(|0\rangle+e^{i\pi/4}|1\rangle)/\sqrt{2}$, then you can combine this with Clifford operations in order to apply a $T$ gate (see Fig. 10.25 in Nielsen and Chuang), and we know that $T$+Clifford is universal.