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Rui Soares Barbosa

International Iberian Nanotechnology Laboratory, Portugal,

Causal contextuality and adaptive MBQC

(joint work with Cihan Okay)

contextuality vs causality

Contextuality has been linked to quantum advantage in various setups. In particular, Raussendorf [1] considered a specific model of measurement-based quantum computation where a (possibly adaptive) classical control is restricted to performing $\mathbb{Z}_2$-linear operations, being supplemented by access to a resource in the form of an empirical model (i.e.~correlation table) in an $(n,2,2)$ Bell-type scenario ($n$ sites, $2$ measurement settings, $2$ outcomes). It is shown that if the MBQC program \textit{deterministically} implements a non-linear Boolean function then the resource correlation must be strongly contextual. However, in the presence of adativity -- and if one is interested in a specific computation with a given dependency structure between sites rather than in the whole class of computations achievable with a single resource -- there is arguably no reason to assume no-signalling to sites in the past, or to expect a classical counterpart to yield measurement outcomes independently of such prior measurements. For a fixed causal/adaptivity structure, we give sufficient conditions on the computed function that imply the resource displays strong causal non-classicality in the sense of Gogioso and Pinzani [2]. This result generalises Raussendorf's in the case of a flat causal order.

[1] R. Raussendorf, Contextuality in measurement-based quantum computation, Physical Review A 88: 022322 (2013).

[2] S. Gogioso and N. Pinzani, The sheaf-theoretic structure of definite causality, 18th International Conference on Quantum Physics and Logic (QPL 2021), M. Backens and C. Heunen (eds), Electronic Proceedings in Theoretical Computer Science 343: 301–324 (2021).