Simulating arbitrary Gaussian circuits with linear optics

TL;DR

This paper introduces a method to simulate any Gaussian quantum circuit using only passive linear optics and two-mode squeezed vacuum states, eliminating the need for active nonlinear transformations.

Contribution

The authors present a novel technique to emulate Gaussian unitaries with passive interferometers and resource states, bypassing active transformations via a clever use of partial time reversal.

Findings

Able to simulate any Gaussian circuit with passive optics and squeezed states

Provides a linear optics-based approach to extended boson sampling

Circumvents the need for nonlinear optical media in Gaussian circuit simulation

Abstract

Linear canonical transformations of bosonic modes correspond to Gaussian unitaries, which comprise passive linear-optical transformations as effected by a multiport passive interferometer and active Bogoliubov transformations as effected by a nonlinear amplification medium. As a consequence of the Bloch-Messiah theorem, any Gaussian unitary can be decomposed into a passive interferometer followed by a layer of single-mode squeezers and another passive interferometer. Here, it is shown how to circumvent the need for active transformations. Namely, we provide a technique to simulate sampling from the joint input and output distributions of any Gaussian circuit with passive interferometry only, provided two-mode squeezed vacuum states are available as a prior resource. At the heart of the procedure, we exploit the fact that a beam splitter under partial time reversal simulates a two-mode squeezer, which gives access to an arbitrary Gaussian circuit without any nonlinear optical medium. This yields, in particular, a procedure for simulating with linear optics an extended boson sampling experiment, where photons jointly propagate through an arbitrary multimode Gaussian circuit, followed by the detection of output photon patterns.