Contextuality in Measurement-based Quantum Computation

TL;DR

This paper demonstrates that measurement-based quantum computations that reliably compute non-linear Boolean functions are inherently contextual, including a practical example with super-polynomial speedup over classical algorithms.

Contribution

It establishes a link between computational power and contextuality in MBQCs, showing that high-probability non-linear function computation implies contextuality under natural assumptions.

Findings

Contextuality is necessary for high-probability computation of non-linear Boolean functions in MBQCs.

An example of a practically relevant MBQC with super-polynomial speedup is shown to be contextual.

The results connect quantum contextuality with computational advantages in measurement-based quantum computing.

Abstract

We show, under natural assumptions for qubit systems, that measurement-based quantum computations (MBQCs) which compute a non-linear Boolean function with high probability are contextual. The class of contextual MBQCs includes an example which is of practical interest and has a super-polynomial speedup over the best known classical algorithm, namely the quantum algorithm that solves the Discrete Log problem.