Contextuality as a resource for measurement-based quantum computation beyond qubits

TL;DR

This paper explores how contextuality serves as a resource in measurement-based quantum computation beyond qubits, emphasizing the role of system partitioning and the necessity of strong non-locality in qudit systems.

Contribution

It identifies the conditions under which high-degree polynomial functions can be computed in qudit measurement-based models, introducing local universality and analyzing the role of system partitioning.

Findings

Strong non-locality is necessary for high-degree polynomial computation in qudits.

System partitioning influences the computational power of measurement-based quantum models.

Resources enabling qubit and qudit computations are fundamentally similar, avoiding qubit-specific pathologies.

Abstract

Contextuality - the obstruction to describing quantum mechanics in a classical statistical way - has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality as a computational resource, as follows. If local measurements on a multi-qubit state can be used to evaluate non-linear boolean functions with only linear control processing, then this computation constitutes a proof of strong contextuality - the possible local measurement outcomes cannot all be pre-assigned. However, this connection is restricted to the special case when the local measured systems are qubits, which have unusual properties from the perspective of contextuality. A single qubit cannot allow for a proof of contextuality, unlike higher-dimensional systems, and multiple qubits can allow for state-independent contextuality with only Pauli observables, again unlike higher-dimensional generalisations. Here we identify precisely that strong non-locality is necessary in a qudit measurement-based computation that evaluates high-degree polynomial functions with only linear control. We introduce the concept of local universality, which places a bound on the space of output functions accessible under the constraint of single-qudit measurements. Thus, the partition of a physical system into subsystems plays a crucial role for the increase in computational power. A prominent feature of our setting is that the enabling resources for qubit and qudit measurement-based computations are of the same underlying nature, avoiding the pathologies associated with qubit contextuality.