QMATH Lecture: Logical paradoxes in deterministic quantum state injection

Speaker: Nadish de Silva, University College, London

Title: Logical paradoxes in deterministic quantum state injection

While quantum computers are expected to yield considerable advantages over classical devices, the precise features of quantum theory accounting for these advantages remain unclear.  Contextuality---the denial of a notion of classical physical reality---has emerged as a promising hypothesis. 

Howard et al. showed that single-qudit magic states, resources critical to achieving quantum universality, exhibit a standard form of contextuality known to facilitate probabilistic advantages in computational and communicational tasks.  Strong contextuality is a logical form of contextuality describing systems, e.g. the GHZ state, that exhibit paradoxical behaviour: the true statements describing their response to measurement are inconsistent.  

We consider the role of paradoxes in deterministically achieving quantum universality.  Via elementary number-theoretic arguments, we present large families of strongly contextual multiqudit magic states admitting deterministic implementation of gates from the third level of the Clifford hierarchy.  Our results contribute to the computational resource theory of contextuality by applying logical tools towards a structural understanding of quantum information theory.