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

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. 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.

Figures (10)

• Figure 1: Diagram of quantum parameter estimation procedure using continuous photon counting measurement of a two-level system (qubit) coupled to an external bath (the environment) with coupling strength $\gamma$ and continuously driven by an external laser field.
• Figure 2: Diagram of using deep ensemble of $M=3$ NNs for estimating the detuning parameter $\Delta$ from a set of input time delay measurements $x=[\tau_1,\dots, \tau_N]$ from a quantum trajectory.
• Figure 3: Performance of different estimators on $\Delta$ estimation task.
• Figure 4: Performance of single network and deep ensemble in the presence of time jitter noise in the training and testing data following a Gaussian distribution $\mathcal{N}(0, \sigma_\tau=0.76)$.
• Figure 5: Performance of different estimators on $\Delta$ estimation task with noise present in training labels.