Contextuality as a resource for measurement-based quantum computation beyond qubits. (10th October 2018)

• Record Type: Journal Article
• Authors: Frembs, Markus; Roberts, Sam; Bartlett, Stephen D
• Is Part Of: New journal of physics. Volume 20:Number 10(2018:Oct.)
• Publication Date: 2018-10-10
• Subjects: quantum information -- quantum computing -- contextuality -- Bell nonlocality; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/aae3ad
• Languages: English
• ISSNs: 1367-2630

Abstract

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 nonlinear 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 (MBC) 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 MBC are of the same underlying nature, avoiding the pathologies associated with qubit contextuality.