  We describe a scheme of quantum computation with magic states on qubits for
which contextuality is a necessary resource possessed by the magic states. More
generally, we establish contextuality as a necessary resource for all schemes
of quantum computation with magic states on qubits that satisfy three simple
postulates. Furthermore, we identify stringent consistency conditions on such
computational schemes, revealing the general structure by which negativity of
Wigner functions, hardness of classical simulation of the computation, and
contextuality are connected.
