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Journal of Physics Communications

Deep-learning-based quantum imaging using NOON states

Fengrong Li, Yifan Sun, Xiangdong Zhang

Published Mar 1, 2022• 9 citations
Publisher

Abstract

Abstract The phase sensitivity of photonic NOON states scales O(1/N), which reaches the Heisenberg limit and indicates a great potential in high-quality optical phase sensing. However, the NOON states with large photon number N are experimentally difficult both to prepare and to operate. Such a fact severely limits their practical use. In this article, we soften the requirements for high-quality imaging based on NOON states with large N by introducing deep-learning methods. Specifically, we show that, with the help of deep-learning network, the fluctuation of the images obtained by the NOON states when N = 2 can be reduced to that of the currently infeasible imaging by the NOON states when N = 8. We numerically investigate our results obtained by two types of deep-learning models—deep neural network and convolutional denoising autoencoders, and characterize the imaging quality using the root mean square error. By comparison, we find that small-N NOON state imaging data is sufficient for training the deep-learning models of our schemes, which supports its direct application to the imaging processes.

DOI
10.1088/2399-6528/ac5e25

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Abstract The phase sensitivity of photonic NOON states scales O(1/N), which reaches the Heisenberg limit and indicates a great potential in high-quality optical phase sensing. However, the NOON states with large photon number N are experimentally difficult both to prepare and to operate. Such a fact severely limits their practical use. In this article, we soften the requirements for high-quality imaging based on NOON states with large N by introducing deep-learning methods. Specifically, we show that, with the help of deep-learning network, the fluctuation of the images obtained by the NOON states when N = 2 can be reduced to that of the currently infeasible imaging by the NOON states when N = 8. We numerically investigate our results obtained by two types of deep-learning models—deep neural network and convolutional denoising autoencoders, and characterize the imaging quality using the root mean square error. By comparison, we find that small-N NOON state imaging data is sufficient for training the deep-learning models of our schemes, which supports its direct application to the imaging processes.
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 Cramér-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.
Quantum imaging using photon pairs with strong quantum correlations has been harnessed to bring quantum advantages to various fields from biological imaging to range finding. Such inherent non-classical properties support the extraction of more valid signals to build photon-limited images, even in low-light conditions where the shot noise becomes dominant as light decreases to a single-photon level. Numerical optimization algorithms are possible but require thousands of photon-sparse frames, and they are thus unavailable in real time. We demonstrate fast correlated-photon imaging enhanced by deep learning as an intelligent computational strategy to discover a deeper structure in big data. Our work verifies that a convolutional neural network can efficiently solve inverse imaging problems associated with strong shot noise and background noise (electronic noise, scattered light). Our results show that we can overcome limitations due to the trade-off between imaging speed and image quality by pushing the low-light imaging technique to the single-photon level in real time, which enables deep-learning-enhanced quantum imaging for real-life applications.
The sensitivity of optical measurement is ultimately constrained by the shot noise to the standard quantum limit.It has become a common concept that beating this limit requires quantum resources.A deep-learning neural network free of quantum principle has the capability of removing classical noise from images, but it is unclear in reducing quantum noise.In a coincidence-imaging experiment, we show that quantum-resource-free deep learning can be exploited to surpass the standard quantum limit via the photon-number-dependent nonlinear feedback during training.Using an effective classical light with photon flux of about 9 × 10 4 photons per second, our deep-learning-based scheme achieves a 14 dB improvement in signal-to-noise ratio with respect to the standard quantum limit.
Quantum imaging systems produce images with distinctive noise patterns that conventional denoising algorithms cannot effectively process. We present an innovative neural network architecture that merges quantum physics principles with deep learning to address this challenge. Our hybrid approach adapts standard image processing techniques to handle quantum-specific noise while preserving critical image features. Experimental validation demonstrates a consistent 12.6% improvement in output quality compared to existing methods, with efficient performance on standard computing hardware. Additionally, the model exhibits strong generalization capabilities, achieving robust performance across varying noise levels. This advancement represents an important step toward practical quantum imaging applications in fields ranging from medical diagnostics to secure communications.
Quantum computing is a new computational paradigm that promises applications in several fields, including machine learning. In the last decade, deep learning, and in particular Convolutional neural networks (CNN), have become essential for applications in signal processing and image recognition. Quantum deep learning, however remains a challenging problem, as it is difficult to implement non linearities with quantum unitaries. In this paper we propose a quantum algorithm for applying and training deep convolutional neural networks with a potential speedup. The quantum CNN (QCNN) is a shallow circuit, reproducing completely the classical CNN, by allowing non linearities and pooling operations. The QCNN is particularly interesting for deep networks and could allow new frontiers in image recognition, by using more or larger convolution kernels, larger or deeper inputs. We introduce a new quantum tomography algorithm with ℓ∞\ell_{\infty}ℓ∞​ norm guarantees, and new applications of probabilistic sampling in the context of information processing. We also present numerical simulations for the classification of the MNIST dataset to provide practical evidence for the efficiency of the QCNN.
Correlated photon pairs, carrying strong quantum correlations, have been harnessed to bring quantum advantages to various fields from biological imaging to range finding. Such inherent non-classical properties support extracting more valid signals to build photon-limited images even in low flux-level, where the shot noise becomes dominant as light source decreases to single-photon level. Optimization by numerical reconstruction algorithms is possible but require thousands of photon-sparse frames, thus unavailable in real time. Here, we present an experimental fast correlated-photon imaging enhanced by deep learning, showing an intelligent computational strategy to discover deeper structure in big data. Convolutional neural network is found being able to efficiently solve image inverse problems associated with strong shot noise and background noise (electronic noise, scattered light). Our results fill the key gap in incompatibility between imaging speed and image quality by pushing low-light imaging technique to the regime of real-time and single-photon level, opening up an avenue to deep leaning-enhanced quantum imaging for real-life applications.