Simulating lossy and partially distinguishable quantum optical circuits: theory, algorithms and applications to experiment validation and state preparation

TL;DR

This paper introduces efficient algorithms for simulating noisy and partially distinguishable quantum optical circuits, enabling accurate and scalable calculations crucial for experimental validation and state preparation in quantum optics.

Contribution

It provides a novel exponential-time algorithm for computing coarse-grained photon distributions, significantly improving speed and accuracy over previous methods.

Findings

Achieved exponential speedup in computing photon distributions.

Enabled exact simulations of larger, more realistic quantum optical circuits.

Improved validation techniques for boson sampling experiments.

Abstract

To understand quantum optics experiments, we must perform calculations that consider the principal sources of noise, such as losses, spectral impurity and partial distinguishability. In both discrete and continuous variable systems, these can be modeled as mixed Gaussian states over multiple modes. The modes are not all resolved by photon-number measurements and so require calculations on coarse-grained photon-number distribution. Existing methods can lead to a combinatorial explosion in the time complexity, making this task unfeasible for even moderate sized experiments of interest. In this work, we prove that the computation of this type of distributions can be done in exponential time, providing a combinatorial speedup. We develop numerical techniques that allow us to determine coarse-grained photon number distributions of Gaussian states, as well as density matrix elements of heralded non-Gaussian states prepared in the presence of spectral impurity and partial distinguishability. These results offer significant speed-up and accuracy improvements to validation tests of both Fock and Gaussian boson samplers that rely on binned probability distributions. Moreover, they pave the way to a more efficient simulation of realistic photonic circuits, unlocking the ability to perform exact calculations at scales which were previously out of reach. In addition to this, our results, including loop Hafnian master theorems, may be of interest to the fields of combinatorics and graph theory.