Imaging at the quantum limit with convolutional neural networks

TL;DR

This paper demonstrates that deep convolutional neural networks can achieve image reconstruction and parameter estimation at the fundamental quantum limits of precision, surpassing classical bounds like shot-noise and reaching the Heisenberg limit.

Contribution

It shows that CNNs trained on quantum-illuminated images can reach the ultimate quantum limits of measurement precision, a novel intersection of deep learning and quantum metrology.

Findings

CNNs surpass the standard quantum limit in image reconstruction

CNNs reach the Heisenberg limit for certain images

Predictions match quantum Cramér-Rao bounds across parameters

Abstract

Deep neural networks have been shown to achieve exceptional performance for computer vision tasks like image recognition, segmentation, and reconstruction or denoising. Here, we evaluate the ultimate performance limits of deep convolutional neural network models for image reconstruction, by comparing them against the standard quantum limit set by shot-noise and the Heisenberg limit on precision. We train U-Net models on images of natural objects illuminated with coherent states of light, and find that the average mean-squared error of the reconstructions can surpass the standard quantum limit, and in some cases reaches the Heisenberg limit. Further, we train models on well-parameterized images for which we can calculate the quantum Cram\'er-Rao bound to determine the minimum possible measurable variance of an estimated parameter for a given probe state. We find the mean-squared error of the model predictions reaches these bounds calculated for the parameters, across a variety of parameterized images. These results suggest that deep convolutional neural networks can learn to become the optimal estimators allowed by the laws of physics, performing parameter estimation and image reconstruction at the ultimate possible limits of precision for the case of classical illumination of the object.