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arXiv:1904.10392 · Physical Review Letters

Calibration of Quantum Sensors by Neural Networks

Valeria Cimini, Ilaria Gianani, Nicolò Spagnolo, Fabio Leccese, Fabio Sciarrino, Marco Barbieri

Published Dec 4, 2019• 58 citations
arXivHTMLPDF

Abstract

Introducing quantum sensors as a solution to real world problems demands reliability and controllability outside of laboratory conditions. Producers and operators ought to be assumed to have limited resources readily available for calibration, and yet, they should be able to trust the devices. Neural networks are almost ubiquitous for similar tasks for classical sensors: here we show the applications of this technique to calibrating a quantum photonic sensor. This is based on a set of training data, collected only relying on the available probe states, hence reducing overhead. We found that covering finely the parameter space is key to achieving uncertainties close to their ultimate level. This technique has the potential to become the standard approach to calibrate quantum sensors.

DOI
10.1103/physrevlett.123.230502

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Introducing quantum sensors as a solution to real world problems demands reliability and controllability outside of laboratory conditions. Producers and operators ought to be assumed to have limited resources readily available for calibration, and yet, they should be able to trust the devices. Neural networks are almost ubiquitous for similar tasks for classical sensors: here we show the applications of this technique to calibrating a quantum photonic sensor. This is based on a set of training data, collected only relying on the available probe states, hence reducing overhead. We found that covering finely the parameter space is key to achieving uncertainties close to their ultimate level. This technique has the potential to become the standard approach to calibrate quantum sensors.
Quantum sensing is a quantum-based process that concerns the development of principles, methods, and devices using superposition of quantum states. Quantum sensors find application in a variety of contexts, serving as a base sensitive element in high-precision synchronization systems, functioning as a key part of gravitometers, accelerometers, and electric and magnetic field sensors. They are also being utilized in quantum metrology and lidar technology. The data generated by quantum sensors can be employed for machine learning purposes. A discussed approach involves the direct utilization of quantum sensor data as input parameters in machine learning models based on photonic neural networks. It has been determined that there is an actual problem of integration for results from quantum sensing and photonic neural networks features. A photonic neural network is discussed as a hardware-implemented algorithm, that belongs to the category of artificial intelligence algorithms in general. The hardware-implemented algorithm reveals a complex interconnection between physical processes at the photonic-based neurons. This paper provides an analysis of quantum sensing in general. It discusses the main type of photonic neural networks and their applications for quantum sensing. The paper considers an integration scheme for photonic neural networks for key points control of quantum sensing processes. Furthermore, the paper presents a proposed functional scheme for quantum sensing control based on the regulator with photonic neural networks.
Abstract Artificial neural networks (NNs) bridge input data into output results by approximately encoding the function that relates them. This is achieved after training the network with a collection of known inputs and results leading to an adjustment of the neuron connections and biases. In the context of quantum detection schemes, NNs find a natural playground. In particular, in the presence of a target (e.g. an electromagnetic field), a quantum sensor delivers a response, i.e. the input data, which can be subsequently processed by a NN that outputs the target features. In this work we demonstrate that adequately trained NNs enable to characterize a target with (i) minimal knowledge of the underlying physical model (ii) in regimes where the quantum sensor presents complex responses and (iii) under a significant shot noise due to a reduced number of measurements. We exemplify the method with a development for 171 Yb + atomic sensors. However, our protocol is general, thus applicable to arbitrary quantum detection scenarios.
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Abstract Bayesian estimation is a powerful theoretical paradigm for the operation of the approach to parameter estimation. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its use to systems that can be explicitly modeled. In this theoretical study, we formulate parameter estimation as a classification task and use artificial neural networks to efficiently perform Bayesian estimation. We show that the network’s posterior distribution is centered at the true (unknown) value of the parameter within an uncertainty given by the inverse Fisher information, representing the ultimate sensitivity limit for the given apparatus. When only a limited number of calibration measurements are available, our machine-learning-based procedure outperforms standard calibration methods. Our machine-learning-based procedure is model independent, and is thus well suited to “black-box sensors”, which lack simple explicit fitting models. Thus, our work paves the way for Bayesian quantum sensors that can take advantage of complex nonclassical quantum states and/or adaptive protocols. These capabilities can significantly enhance the sensitivity of future devices.
Estimation of physical quantities is at the core of most scientific research, and the use of quantum devices promises to enhance its performances. In real scenarios, it is fundamental to consider that resources are limited, and Bayesian adaptive estimation represents a powerful approach to efficiently allocate, during the estimation process, all the available resources. However, this framework relies on the precise knowledge of the system model, retrieved with a fine calibration, with results that are often computationally and experimentally demanding. We introduce a model-free and deep-learning-based approach to efficiently implement realistic Bayesian quantum metrology tasks accomplishing all the relevant challenges, without relying on any a priori knowledge of the system. To overcome this need, a neural network is trained directly on experimental data to learn the multiparameter Bayesian update. Then the system is set at its optimal working point through feedback provided by a reinforcement learning algorithm trained to reconstruct and enhance experiment heuristics of the investigated quantum sensor. Notably, we prove experimentally the achievement of higher estimation performances than standard methods, demonstrating the strength of the combination of these two black-box algorithms on an integrated photonic circuit. Our work represents an important step toward fully artificial intelligence-based quantum metrology.