Optimizing photon-number distributions of Gaussian states in the presence of loss: Towards minimizing the impact of loss in Gaussian boson sampling

TL;DR

This paper investigates methods to mitigate photon loss effects on Gaussian states in quantum photonic systems, aiming to preserve photon-number distributions crucial for Gaussian boson sampling, by redefining state parameters based on known loss.

Contribution

It introduces and evaluates strategies to adjust Gaussian state parameters to counteract photon loss, focusing on fidelity, vacuum overlap, and moments, enhancing the robustness of quantum photonic computations.

Findings

Optimizing fidelity alone does not ensure photon-number distribution similarity.

Correcting vacuum overlap effectively minimizes photon-number deviations.

Proposed methods improve the feasibility of Gaussian boson sampling in lossy environments.

Abstract

We analyze the impact of photon loss on the photon-number statistics of Gaussian states. Specifically, we propose and carefully evaluate several methods to mitigate deviations in the photon-number distributions of lossy (displaced) squeezed vacuum states from those of their lossless counterparts. These methods rely on appropriately redefining the parameters of Gaussian states when the loss budget is known in order to recover, as closely as possible, the desired photon-number distribution associated with each target state. While it is intrinsically hard to directly optimize the photon-number distribution of high-dimensional, correlated multimode Gaussian states, the proposed methods are instead based on optimizing specific key properties such as fidelity, phase-space functions, low-order moments of the underlying photon-number statistics, or overlap with the vacuum state. In particular, our results show that optimizing the fidelity between a pure Gaussian target state and a modified Gaussian state that has passed through a loss channel does typically not result in closeness of the corresponding photon-number distributions. Furthermore, we show that correcting for the vacuum overlap minimizes the deviation in the photon-number distribution for large parameter ranges which we explicitly prove for single-mode squeezed vacuum and provide numerical evidence for general (displaced) squeezed vacuum states. As photon loss is a key limitation for Gaussian boson sampling, our results provide insights into the feasibility and limitations of such photonic quantum simulations in lossy environments and offer guidelines for mitigating these imperfections.