Which precise features of quantum theory enable quantum computational and communicational advantages? Contextuality and nonlocality have emerged as promising hypotheses.
Magic states are quantum resources critical for achieving fault-tolerant universal quantum computation. They exhibit the standard form of contextuality that is known to enable probabilistic advantages in a variety of information-theoretic tasks. Strong contextuality is an extremal form of contextuality describing systems that exhibit logically paradoxical behaviour, e.g. the GHZ state and the PR box.
Here, we consider special magic states that deterministically enable quantum computation. After introducing number-theoretic techniques for constructing exotic quantum paradoxes, we present large families of strongly contextual magic states (in arbitrarily large dimensions) that enable deterministic injection of gates from the Clifford hierarchy. This bolsters a refinement of the resource theory of contextuality that emphasises the computational power of logical paradoxes.