Quantum Bayesian inference for parameter estimation using quantum generative model

Jon Frost, Carlos Madeira, Harald Uhlig

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.

Theodore J. Yoder, Guang Hao Low, Isaac L. Chuang

Jincheng Zhang

Quantum-enhanced Bayesian inference represents a significant advancement in statistical modeling, leveraging the unique properties of quantum computing to accelerate probabilistic computations and improve model accuracy. This paper explores the potential of quantum mechanics to revolutionize Bayesian inference, focusing on the implementation of quantum-assisted probability calculations, quantum entanglement and superposition for enhanced data processing, and quantum-enhanced parameter estimation and model prediction. This investigation addresses the limitations of classical Bayesian inference by introducing a novel framework centered on quantum computing. We detail the core mechanism behind this approach, emphasizing the utilization of quantum bits (qubits) to improve the efficiency and accuracy of Bayesian inference. This work presents a substantial contribution to the field of statistical modeling and explores the practical implications of quantum-enhanced Bayesian inference.

Jincheng Zhang

This paper introduces an adaptive quantum sampling method designed to enhance the efficiency of Bayesian inference in complex, high-dimensional spaces. Traditional Bayesian inference methods often struggle with the computational complexity of exploring the vast parameter space, leading to slow convergence and limited accuracy. We propose a novel quantum sampling algorithm that dynamically adjusts the sampling process based on uncertainty estimates generated by quantum computations. This adaptive approach mitigates the inherent challenges of sampling in high-dimensional spaces, resulting in significantly faster convergence and improved inference accuracy. The core mechanism leverages quantum algorithms to identify promising regions of the parameter space, thereby reducing the computational burden and enhancing the effectiveness of Bayesian modeling. The paper details the theoretical framework underpinning the algorithm, outlines the implementation of the quantum sampling process, and provides a comprehensive analysis of its performance compared to traditional sampling techniques. Finally, we present preliminary experimental results demonstrating the effectiveness of the proposed method across a range of complex scenarios.

Hiroshi Ohno