Resourcefulness of non-classical continuous-variable quantum gates

TL;DR

This paper introduces a versatile phase-space quasiprobability approach to evaluate the resourcefulness of continuous-variable quantum gates, highlighting their potential for quantum advantage and robustness to losses.

Contribution

It develops a new method using $(s)$-ordered quasiprobabilities to analyze the resourcefulness of quantum gates in continuous-variable quantum computation.

Findings

Identifies the resourcefulness of Gaussian and non-Gaussian gates.

Highlights the robustness of certain gates to losses.

Provides insights into the role of non-Gaussianity in quantum advantage.

Abstract

In continuous-variable quantum computation, identifying key elements that enable a quantum computational advantage is a long-standing issue. Starting from the standard results on the necessity of Wigner negativity, we develop a comprehensive and versatile approach in which the techniques of $(s)$-ordered quasiprobabilities are exploited to identify the contribution of each quantum gate to the potential achievement of quantum computational advantage. This is achieved by means of an analysis of the so-called transfer function, allowing us to highlight the resourcefulness of a gate set. As such this technique can be straightforwardly applied to current continuous-variables quantum circuits, while also constraining the tolerable amount of losses above which any potential quantum advantage can be ruled out. We use $(s)$-ordered quasiprobability distributions on phase-space to capture the non-classical features in the protocol, and focus our technique entirely on the ordering parameter $s$. This allows us to highlight the resourcefulness and robustness to loss of a universal set of unitary gates comprising three distinct Gaussian gates, and a fourth one, the cubic gate, providing important insight on the role of non-Gaussianity.