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| Main Authors: | , , |
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| Format: | Preprint |
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2021
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| Online Access: | https://arxiv.org/abs/2105.12302 |
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| _version_ | 1866916291501096960 |
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| author | Nolan, Samuel P. Pezzè, Luca Smerzi, Augusto |
| author_facet | Nolan, Samuel P. Pezzè, Luca Smerzi, Augusto |
| contents | Recently there has been a great deal of interest surrounding the calibration of quantum sensors using machine learning techniques. In this work, we explore the use of regression to infer a machine-learned point estimate of an unknown parameter. Although the analysis is neccessarily frequentist - relying on repeated esitmates to build up statistics - we clarify that this machine-learned estimator converges to the Bayesian maximum a-posterori estimator (subject to some regularity conditions). When the number of training measurements are large, this is identical to the well-known maximum-likelihood estimator (MLE), and using this fact, we argue that the Cram{é}r-Rao sensitivity bound applies to the mean-square error cost function and can therefore be used to select optimal model and training parameters. We show that the machine-learned estimator inherits the desirable asymptotic properties of the MLE, up to a limit imposed by the resolution of the training grid. Furthermore, we investigate the role of quantum noise the training process, and show that this noise imposes a fundamental limit on number of grid points. This manuscript paves the way for machine-learning to assist the calibration of quantum sensors, thereby allowing maximum-likelihood inference to play a more prominent role in the design and operation of the next generation of ultra-precise sensors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_12302 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Frequentist Parameter Estimation with Supervised Learning Nolan, Samuel P. Pezzè, Luca Smerzi, Augusto Quantum Physics Recently there has been a great deal of interest surrounding the calibration of quantum sensors using machine learning techniques. In this work, we explore the use of regression to infer a machine-learned point estimate of an unknown parameter. Although the analysis is neccessarily frequentist - relying on repeated esitmates to build up statistics - we clarify that this machine-learned estimator converges to the Bayesian maximum a-posterori estimator (subject to some regularity conditions). When the number of training measurements are large, this is identical to the well-known maximum-likelihood estimator (MLE), and using this fact, we argue that the Cram{é}r-Rao sensitivity bound applies to the mean-square error cost function and can therefore be used to select optimal model and training parameters. We show that the machine-learned estimator inherits the desirable asymptotic properties of the MLE, up to a limit imposed by the resolution of the training grid. Furthermore, we investigate the role of quantum noise the training process, and show that this noise imposes a fundamental limit on number of grid points. This manuscript paves the way for machine-learning to assist the calibration of quantum sensors, thereby allowing maximum-likelihood inference to play a more prominent role in the design and operation of the next generation of ultra-precise sensors. |
| title | Frequentist Parameter Estimation with Supervised Learning |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2105.12302 |