Classical simulation of dissipative fermionic linear optics

TL;DR

This paper demonstrates that even with dissipative processes governed by Lindblad equations, fermionic linear optics remains efficiently simulable on classical computers, extending previous results.

Contribution

It extends the classical simulability of fermionic linear optics to include dissipative evolution with Lindblad operators, providing efficient algorithms for simulation.

Findings

Simulation time for gates: O(N^3)

Simulation time for measurements: O(N^2)

Steady state computation: O(N^3)

Abstract

Fermionic linear optics is a limited form of quantum computation which is known to be efficiently simulable on a classical computer. We revisit and extend this result by enlarging the set of available computational gates: in addition to unitaries and measurements, we allow dissipative evolution governed by a Markovian master equation with linear Lindblad operators. We show that this more general form of fermionic computation is also simulable efficiently by classical means. Given a system of $N$ fermionic modes, our algorithm simulates any such gate in time $O(N^3)$ while a single-mode measurement is simulated in time $O(N^2)$. The steady state of the Lindblad equation can be computed in time $O(N^3)$.