Quantum Advantage from Sequential-Transformation Contextuality

TL;DR

This paper introduces a new form of contextuality specific to transformations in sequential quantum processes, demonstrating its necessity and sufficiency for quantum computational advantage under certain conditions.

Contribution

It defines a novel notion of sequential-transformation contextuality and links it directly to quantum computational advantage in a transformation-based model.

Findings

Sequential-transformation contextuality is necessary and sufficient for deterministic non-linear function computation.

It is also necessary and sufficient for probabilistic quantum advantage in the model.

The degree of quantum advantage correlates with the degree of contextuality.

Abstract

We introduce a notion of contextuality for transformations in sequential contexts, distinct from the Bell-Kochen-Specker and Spekkens notions of contextuality. Within a transformation-based model for quantum computation we show that strong sequential-transformation contextuality is necessary and sufficient for deterministic computation of non-linear functions if classical components are restricted to mod2-linearity and matching constraints apply to any underlying ontology. For probabilistic computation, sequential-transformation contextuality is necessary and sufficient for advantage in this task and the degree of advantage quantifiably relates to the degree of contextuality.