Contextuality and Wigner function negativity in qubit quantum computation

TL;DR

This paper explores the fundamental role of contextuality and Wigner function negativity as necessary resources for quantum computation with magic states on qubits, establishing their interconnection and underlying structure.

Contribution

It introduces a framework linking contextuality, Wigner function negativity, and classical simulation hardness in qubit quantum computation with magic states, under simple postulates.

Findings

Contextuality is necessary for quantum advantage with magic states.

Negativity of Wigner functions correlates with computational hardness.

The paper reveals structural conditions connecting these quantum resources.

Abstract

We describe a scheme of quantum computation with magic states on qubits for which contextuality is a necessary resource possessed by the magic states. More generally, we establish contextuality as a necessary resource for all schemes of quantum computation with magic states on qubits that satisfy three simple postulates. Furthermore, we identify stringent consistency conditions on such computational schemes, revealing the general structure by which negativity of Wigner functions, hardness of classical simulation of the computation, and contextuality are connected.