To make predictions on the future states of engineering systems, prognostics has been increasingly relying on data-driven models and machine learning. Recent work has also looked at the potential of quantum machine learning to provide insight on the health state of systems. Nevertheless, these approaches treated the quantum component only as a deterministic predictor, in fact disregarding the uncertainty information. In this work, we propose a different approach to exploiting quantum circuits in prognostics. We focus on Bayesian learning of neural networks for Remaining Useful Life (RUL) prediction and uncertainty quantification. Here, the quantum circuit is introduced not as a data-driven model, but as a generator of neural network weights. Using Variational Inference, the quantum circuit can be trained to approximate the true posterior of the classical machine learning predictor. The overall method retains the data-processing ability of state-of-the-art machine learning models, while exploiting the quantum circuit to introduce uncertainty by sampling the modelspace from a distribution that is classically nontrivial. We validate our approach on the task of predicting the End of Discharge of Li-ion batteries, using data generated from a simulator with tunable process uncertainty, and we compare the predictions obtained through quantum sampling with those from Flipout Bayesian neural networks, heteroscedastic neural networks and Monte Carlo Dropout. The results show that our quantum circuits learn to approximate the weight posterior and that the resulting data-driven models demonstrate accuracy and uncertainty quantification that is comparable if not superior to the baselines. Overall, our work demonstrates the potential of quantum computing for uncertainty-aware prognostics, and sets the stage for further investigations in this area.
To make predictions on the future states of engineering systems, prognostics has been increasingly relying on data-driven models and machine learning. Recent work has also looked at the potential of quantum machine learning to provide insight on the health state of systems. Nevertheless, these approaches treated the quantum component only as a deterministic predictor, in fact disregarding the uncertainty information. In this work, we propose a different approach to exploiting quantum circuits in prognostics. We focus on Bayesian learning of neural networks for Remaining Useful Life (RUL) prediction and uncertainty quantification. Here, the quantum circuit is introduced not as a data-driven model, but as a generator of neural network weights. Using Variational Inference, the quantum circuit can be trained to approximate the true posterior of the classical machine learning predictor. The overall method retains the data-processing ability of state-of-the-art machine learning models, while exploiting the quantum circuit to introduce uncertainty by sampling the modelspace from a distribution that is classically nontrivial. We validate our approach on the task of predicting the End of Discharge of Li-ion batteries, using data generated from a simulator with tunable process uncertainty, and we compare the predictions obtained through quantum sampling with those from Flipout Bayesian neural networks, heteroscedastic neural networks and Monte Carlo Dropout. The results show that our quantum circuits learn to approximate the weight posterior and that the resulting data-driven models demonstrate accuracy and uncertainty quantification that is comparable if not superior to the baselines. Overall, our work demonstrates the potential of quantum computing for uncertainty-aware prognostics, and sets the stage for further investigations in this area.
Uncertainty quantification (UQ) is essential for deploying machine learning models in safety-critical physical systems, yet classical Bayesian approaches incur substantial computational overhead. We establish a formal connection between Born-rule measurement statistics from variational quantum circuits (VQCs) and Bayesian posterior uncertainty, proving that repeated quantum measurements naturally produce calibrated prediction intervals without requiring explicit Bayesian neural network (BNN) machinery. We demonstrate this framework on physics-constrained VQCs trained on PDE residuals. Systematic experiments comparing quantum shot-based UQ against MC Dropout and Deep Ensemble baselines show that quantum UQ achieves coverage probabilities within 1-3% of target confidence levels at N >= 5000 shots, while MC Dropout systematically over-covers by 4-5%. Physics-constrained circuits reduce the expected calibration error (ECE) by 34-40% compared to unconstrained counterparts, with interval widths 14-30% narrower at equivalent coverage. Information-theoretic analysis reveals that quantum circuits extract ~15% more bits of UQ information per evaluation than MC Dropout and ~42% more than Deep Ensembles (M = 10), owing to the exponential Hilbert space accessible through Born-rule sampling. These results establish quantum measurement statistics as a principled, computationally efficient framework for uncertainty quantification in physics-informed learning.
In this work, we are introducing a Quantum-Classical Bayesian Neural Network (QCBNN) that is capable to perform uncertainty-aware classification of classical medical dataset. This model is a symbiosis of a classical Convolutional NN that performs ultra-sound image processing and a quantum circuit that generates its stochastic weights, within a Bayesian learning framework. To test the utility of this idea for the possible future deployment in the medical sector we track multiple behavioral metrics that capture both predictive performance as well as model’s uncertainty. It is our ambition to create a hybrid model that is capable to classify samples in a more uncertainty aware fashion, which will advance the trustworthiness of these models and thus bring us step closer to utilizing them in the industry. We test multiple setups for quantum circuit for this task, and our best architectures display bigger uncertainty gap between correctly and incorrectly identified samples than its classical benchmark at an expense of a slight drop in predictive performance. The innovation of this paper is two-fold: (1) combining of different approaches that allow the stochastic weights from the quantum circuit to be continues thus allowing the model to classify application-driven dataset; (2) studying architectural features of quantum circuit that make-or-break these models, which pave the way into further investigation of more informed architectural designs.
The astounding acceleration in Artificial Intelligence and Quantum Computing advances naturally gives rise to a line of research, which unrolls the potential advantages of quantum computing on classical Machine Learning tasks, known as Quantum Machine Learning or Quantum Machine Intelligence. The typical objectives are either (1) exploring the potential quantum advantages on classical learning tasks or (2) levering well-established classical ML algorithms to tackle quantum-related problems on Noisy Intermediate-Scale Quantum (NISQ) devices. Along the second research direction, we study Quantum Neural Networks (QNNs) to accomplish the purpose of Bayesian learning. By observing a wide range of studies on QNNs, in which the sole training method is based on frequentist training, we find that Bayesian learning benefits QNNs from two aspects. First, Bayesian-trained models enjoy a high level of generalization due to the prior and posterior distribution usage compared to frequentist training, which will be justified by this paper’s theoretical study of model capacity. Second, Bayesian Inference offers epistemic uncertainty estimation, which merits the decision-making process. It is worth mentioning that frequentist-trained QNNs generally lack this desirable property. Under the Bayesian training procedure, our derived models can be considered a new class of QNNs (called BayesianQNNs) which possesses both desirable properties of Bayesian Inference while maintaining comparable predictive performance as frequentist counterparts. The proposed Bayesian Quantum Neural Networks is justified by empirical evidence from numerical experiments.
While the Graybox characterization method allows for implicit noise models and is platform-agnostic, the method lacks uncertainty quantification. Characterization of quantum devices is a crucial process that enables researchers to gain insight from experimental settings. Graybox characterization combines known system dynamics with unknown transformations, where the latter is modeled using machine learning. Prediction uncertainty helps researchers make informed decisions. It allows valuable insights from the devices without overconfidence. We therefore develop a probabilistic Graybox characterization model using probabilistic machine learning, specifically Bayesian Neural Networks, and utilize binary measurement outcomes directly for inference. With stochastic noise in a quantum device, we analyze statistical properties of the measurement data. Our results show that the model's prediction performance solely depends on its ability to capture the expected value of the true expectation value. Our proposed probabilistic Graybox model outperforms the original model by up to 1.9 times in capturing the distribution of observed data. We expect that our results will serve as an additional tool for characterizing quantum devices with uncertainty estimation, as they provide a flexible choice that can be utilized even without extensive prior knowledge of the noise model of the devices.
Given their high power density, low discharge rate, and decreasing cost, rechargeable lithium-ion batteries (LiBs) have found a wide range of applications such as power grid-level storage systems, electric vehicles (EVs), and mobile devices. Developing a framework to accurately model the nonlinear degradation process of LiBs, which is indeed a supervised learning problem, becomes an important research topic. This paper presents a classical-quantum hybrid machine learning approach to capture the LiB degradation model that assesses the loss of battery cell life from the operating profiles. Our work is motivated by recent advances in quantum computers as well as the similarity between neural networks and quantum circuits. Similarly to adjusting weight parameters in conventional neural networks, the parameters of the quantum circuit, namely, the degree of freedom of the qubits, can be tuned to learn a nonlinear function in a supervised learning fashion. As a proof of concept paper, our obtained numerical results with the battery dataset provided by NASA demonstrate the ability of the quantum neural networks in modeling the nonlinear relationship between the degraded capacity and the operating cycles. We also discuss the potential advantage of the quantum approach compared to conventional neural networks in classical computers in dealing with massive data, especially in the context of future penetration of EVs and energy storage.
Quantum machine learning on noisy intermediate-scale quantum (NISQ) devices often suffers from noise sensitivity, small-data overfitting, and miscalibrated predictive confidence. We propose an uncertainty-aware hybrid Bayesian quantum neural network (BQNN) that couples a Bayesian convolutional front-end with a parameterized quantum circuit (PQC), forming a three-stage pipeline: Bayesian feature extraction, quantum state evolution, and classical decision making. For 28 ×28 grayscale inputs, the front-end uses an 8-filter 3 ×3 Bayesian convolution followed by 2 ×2 max-pooling and a fully connected layer to produce a 10-dimensional embedding, which is mapped to four rotation angles and encoded on 4 qubits. Two parameterized quantum circuit designs are considered for the quantum classification layer. On MNIST and Fashion-MNIST, repeated experiments over five independent random seeds show that the proposed BQNN variants consistently outperform the corresponding QCNN baselines. On MNIST, BQNN-2 achieves a mean best test accuracy of 95.46 ± 0.36%, a mean final test accuracy of 95.44 ± 0.38%, and a mean final test loss of 0.169 ± 0.012. On Fashion-MNIST, BQNN-1 attains the best mean overall performance, with a mean best test accuracy of 87.59 ± 0.62%, a mean final test accuracy of 87.49 ± 0.73%, and a mean final test loss of 0.385 ± 0.017, while BQNN-2 exhibits slightly smaller run-to-run variation. Additional representative comparisons with QNN baselines under the same training configuration further suggest faster convergence and higher peak accuracy for BQNN. Using 30 Monte-Carlo forward passes, BQNN achieves better calibration (ECE 0.007-0.009) than QCNN (ECE 0.016-0.020), thereby reducing overconfident predictions. Additional robustness experiments under noisy mixed-state simulation further show that, under depolarizing noise, BQNN consistently preserves higher peak test accuracy than QCNN across both circuit variants on MNIST, demonstrating improved robustness in NISQ-like noisy settings.