Classical simulation of fermionic linear optics augmented with noisy ancillas

TL;DR

This paper investigates the classical simulability of fermionic linear optics when augmented with noisy ancillas, providing a characterization of convex-Gaussian states in a four-mode system to understand the boundaries of classical simulation.

Contribution

It offers an analytic characterization of convex-Gaussian states in a four-mode Fock space, addressing an open problem and analyzing the geometry of these states.

Findings

Convex-Gaussian states enable classical simulation of augmented fermionic linear optics.

Analytic characterization of convex-Gaussian states in four-mode systems.

Resolution of an open problem regarding the structure of convex-Gaussian states.

Abstract

Fermionic linear optics is a model of quantum computation which is efficiently simulable on a classical probabilistic computer. We study the problem of a classical simulation of fermionic linear optics augmented with noisy auxiliary states. If the auxiliary state can be expressed as a convex combination of pure Fermionic Gaussian states, the corresponding computation scheme is classically simulable. We present an analytic characterisation of the set of convex-Gaussian states in the first non-trivial case, in which the Hilbert space of the ancilla is a four-mode Fock space. We use our result to solve an open problem recently posed by De Melo et al. and to study in detail the geometrical properties of the set of convex-Gaussian states.