Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1711.05238

Quantum parameter estimation with a neural network

Eliška Greplová, Christian Kraglund Andersen, Klaus Mølmer

Published Nov 14, 2017• 14 citations
arXivHTMLPDF

Abstract

We propose to use neural networks to estimate the rates of coherent and incoherent processes in quantum systems from continuous measurement records. In particular, we adapt an image recognition algorithm to recognize the patterns in experimental signals and link them to physical quantities. We demonstrate that the parameter estimation works unabatedly in the presence of detector imperfections which complicate or rule out Bayesian filter analyses.

DOI
10.48550/arxiv.1711.05238

Related papers

Parameter estimation from quantum-jump data using neural networks

Enrico Rinaldi, Manuel González Lastre, Sergio García Herreros +4 more

Abstract We present an inference method utilizing artificial neural networks for parameter estimation of a quantum probe monitored through a single continuous measurement. Unlike existing approaches focusing on the diffusive signals generated by continuous weak measurements, our method harnesses quantum correlations in discrete photon-counting data characterized by quantum jumps. We benchmark the precision of this method against Bayesian inference, which is optimal in the sense of information retrieval. By using numerical experiments on a two-level quantum system, we demonstrate that our approach can achieve a similar optimal performance as Bayesian inference, while drastically reducing computational costs. Additionally, the method exhibits robustness against the presence of imperfections in both measurement and training data. This approach offers a promising and computationally efficient tool for quantum parameter estimation with photon-counting data, relevant for applications such as quantum sensing or quantum imaging, as well as robust calibration tasks in laboratory-based settings.

Quantum Science and Technology•Apr 9, 2024•9 citations

Parameter estimation by learning quantum correlations in continuous photon-counting data using neural networks

Enrico Rinaldi, Manuel González Lastre, Sergio García Herreros +4 more

We present an inference method utilizing artificial neural networks for parameter estimation of a quantum probe monitored through a single continuous measurement. Unlike existing approaches focusing on the diffusive signals generated by continuous weak measurements, our method harnesses quantum correlations in discrete photon-counting data characterized by quantum jumps. We benchmark the precision of this method against Bayesian inference, which is optimal in the sense of information retrieval. By using numerical experiments on a two-level quantum system, we demonstrate that our approach can achieve a similar optimal performance as Bayesian inference, while drastically reducing computational costs. Additionally, the method exhibits robustness against the presence of imperfections in both measurement and training data. This approach offers a promising and computationally efficient tool for quantum parameter estimation with photon-counting data, relevant for applications such as quantum sensing or quantum imaging, as well as robust calibration tasks in laboratory-based settings.

arXiv:2310.02309•Oct 3, 2023•0 citations

Quantum parameter estimation with uncertainty quantification from continuous measurement data using neural network ensembles

Amanuel Anteneh

Abstract We show that ensembles of deep neural networks, called deep ensembles, can be used to perform quantum parameter estimation while also providing a means for quantifying uncertainty in parameter estimates, which is a key advantage of using Bayesian inference for parameter estimation that is lost when using existing machine learning methods. We show that optimizing for both accurate parameter estimates and well calibrated uncertainty estimates does not lead to degradation in the former as opposed to only optimizing for accuracy. We also show that the drift detection capabilities of these ensemble models can be used to detect drift in the experimental data used during inference. This approach is also shown to provide much faster inference time than both likelihood-based and likelihood-free Bayesian inference. These results suggest that such models could enable accurate, real-time parameter estimation with quantified uncertainty, making them promising candidates for deployment in experimental settings.

arXiv:2509.10756•Journal of Physics B Atomic Molecular and Optical Physics•Oct 5, 2026•0 citations

Using a Recurrent Neural Network to Reconstruct Quantum Dynamics of a Superconducting Qubit from Physical Observations

Emmanuel Flurin, Leigh S. Martin, Shay Hacohen-Gourgy +1 more

At its core, quantum mechanics is a theory developed to describe fundamental observations in the spectroscopy of solids and gases.Despite these practical roots, however, quantum theory is infamous for being highly counterintuitive, largely due to its intrinsically probabilistic nature.Neural networks have recently emerged as a powerful tool that can extract nontrivial correlations in vast datasets.These networks routinely outperform state-of-the-art techniques in language translation, medical diagnosis, and image recognition.It remains to be seen if neural networks can be trained to predict stochastic quantum evolution without a priori specifying the rules of quantum theory.Here, we demonstrate that a recurrent neural network can be trained in real time to infer the individual quantum trajectories associated with the evolution of a superconducting qubit under unitary evolution, decoherence, and continuous measurement from physical observations only.The network extracts the system Hamiltonian, measurement operators, and physical parameters.It is also able to perform tomography of an unknown initial state without any prior calibration.This method has the potential to greatly simplify and enhance tasks in quantum systems such as noise characterization, parameter estimation, feedback, and optimization of quantum control.

arXiv:1811.12420•Physical Review X•Jan 9, 2020•88 citations

Neural-Network Heuristics for Adaptive Bayesian Quantum Estimation

Lukas J. Fiderer, Jonas Schuff, Daniel Braun

Quantum metrology promises unprecedented measurement precision but suffers in practice from the limited availability of resources such as the number of probes, their coherence time, or nonclassical quantum states.The adaptive Bayesian approach to parameter estimation allows an efficient use of resources because of adaptive experiment design.For its practical success, fast numerical solutions for the Bayesian update and the adaptive experiment design are crucial.Here we show that neural networks can be trained to become fast and strong experiment-design heuristics using a combination of an evolutionary strategy and reinforcement learning.Neural-network heuristics are shown to outperform established heuristics for the technologically important example of frequency estimation of a qubit that suffers from dephasing.Our method of creating neural-network heuristics is very general and complements the well-studied sequential Monte Carlo method for Bayesian updates to form a complete framework for adaptive Bayesian quantum estimation.

arXiv:2003.02183•PRX Quantum•Apr 7, 2021•62 citations

Uncertainty of feed forward neural networks recognizing quantum contextuality

Jan Wasilewski, Tomasz Paterek, Karol Horodecki

Abstract The usual figure of merit characterizing the performance of neural networks applied to problems in the quantum domain is their accuracy, being the probability of a correct answer on a previously unseen input. Here we append this parameter with the uncertainty of the prediction, characterizing the degree of confidence in the answer. A powerful technique for estimating uncertainty is provided by Bayesian neural networks (BNNs). We first give simple illustrative examples of advantages brought forward by BNNs, out of which we wish to highlight their ability of reliable uncertainty estimation even after training with biased datasets. Then we apply BNNs to the problem of recognition of quantum contextuality, which shows that the uncertainty itself is an independent parameter identifying the chance of misclassification of contextuality.

arXiv:2212.13564•Journal of Physics A Mathematical and Theoretical•Sep 26, 2023•4 citations
We propose to use neural networks to estimate the rates of coherent and incoherent processes in quantum systems from continuous measurement records. In particular, we adapt an image recognition algorithm to recognize the patterns in experimental signals and link them to physical quantities. We demonstrate that the parameter estimation works unabatedly in the presence of detector imperfections which complicate or rule out Bayesian filter analyses.
Abstract We present an inference method utilizing artificial neural networks for parameter estimation of a quantum probe monitored through a single continuous measurement. Unlike existing approaches focusing on the diffusive signals generated by continuous weak measurements, our method harnesses quantum correlations in discrete photon-counting data characterized by quantum jumps. We benchmark the precision of this method against Bayesian inference, which is optimal in the sense of information retrieval. By using numerical experiments on a two-level quantum system, we demonstrate that our approach can achieve a similar optimal performance as Bayesian inference, while drastically reducing computational costs. Additionally, the method exhibits robustness against the presence of imperfections in both measurement and training data. This approach offers a promising and computationally efficient tool for quantum parameter estimation with photon-counting data, relevant for applications such as quantum sensing or quantum imaging, as well as robust calibration tasks in laboratory-based settings.
We present an inference method utilizing artificial neural networks for parameter estimation of a quantum probe monitored through a single continuous measurement. Unlike existing approaches focusing on the diffusive signals generated by continuous weak measurements, our method harnesses quantum correlations in discrete photon-counting data characterized by quantum jumps. We benchmark the precision of this method against Bayesian inference, which is optimal in the sense of information retrieval. By using numerical experiments on a two-level quantum system, we demonstrate that our approach can achieve a similar optimal performance as Bayesian inference, while drastically reducing computational costs. Additionally, the method exhibits robustness against the presence of imperfections in both measurement and training data. This approach offers a promising and computationally efficient tool for quantum parameter estimation with photon-counting data, relevant for applications such as quantum sensing or quantum imaging, as well as robust calibration tasks in laboratory-based settings.
Abstract We show that ensembles of deep neural networks, called deep ensembles, can be used to perform quantum parameter estimation while also providing a means for quantifying uncertainty in parameter estimates, which is a key advantage of using Bayesian inference for parameter estimation that is lost when using existing machine learning methods. We show that optimizing for both accurate parameter estimates and well calibrated uncertainty estimates does not lead to degradation in the former as opposed to only optimizing for accuracy. We also show that the drift detection capabilities of these ensemble models can be used to detect drift in the experimental data used during inference. This approach is also shown to provide much faster inference time than both likelihood-based and likelihood-free Bayesian inference. These results suggest that such models could enable accurate, real-time parameter estimation with quantified uncertainty, making them promising candidates for deployment in experimental settings.
At its core, quantum mechanics is a theory developed to describe fundamental observations in the spectroscopy of solids and gases.Despite these practical roots, however, quantum theory is infamous for being highly counterintuitive, largely due to its intrinsically probabilistic nature.Neural networks have recently emerged as a powerful tool that can extract nontrivial correlations in vast datasets.These networks routinely outperform state-of-the-art techniques in language translation, medical diagnosis, and image recognition.It remains to be seen if neural networks can be trained to predict stochastic quantum evolution without a priori specifying the rules of quantum theory.Here, we demonstrate that a recurrent neural network can be trained in real time to infer the individual quantum trajectories associated with the evolution of a superconducting qubit under unitary evolution, decoherence, and continuous measurement from physical observations only.The network extracts the system Hamiltonian, measurement operators, and physical parameters.It is also able to perform tomography of an unknown initial state without any prior calibration.This method has the potential to greatly simplify and enhance tasks in quantum systems such as noise characterization, parameter estimation, feedback, and optimization of quantum control.
Quantum metrology promises unprecedented measurement precision but suffers in practice from the limited availability of resources such as the number of probes, their coherence time, or nonclassical quantum states.The adaptive Bayesian approach to parameter estimation allows an efficient use of resources because of adaptive experiment design.For its practical success, fast numerical solutions for the Bayesian update and the adaptive experiment design are crucial.Here we show that neural networks can be trained to become fast and strong experiment-design heuristics using a combination of an evolutionary strategy and reinforcement learning.Neural-network heuristics are shown to outperform established heuristics for the technologically important example of frequency estimation of a qubit that suffers from dephasing.Our method of creating neural-network heuristics is very general and complements the well-studied sequential Monte Carlo method for Bayesian updates to form a complete framework for adaptive Bayesian quantum estimation.
Abstract The usual figure of merit characterizing the performance of neural networks applied to problems in the quantum domain is their accuracy, being the probability of a correct answer on a previously unseen input. Here we append this parameter with the uncertainty of the prediction, characterizing the degree of confidence in the answer. A powerful technique for estimating uncertainty is provided by Bayesian neural networks (BNNs). We first give simple illustrative examples of advantages brought forward by BNNs, out of which we wish to highlight their ability of reliable uncertainty estimation even after training with biased datasets. Then we apply BNNs to the problem of recognition of quantum contextuality, which shows that the uncertainty itself is an independent parameter identifying the chance of misclassification of contextuality.