Multivariate unbounded quantum regression via log-ratio probabilities mitigating barren plateaus

TL;DR

This paper introduces a novel log-ratio probability method for multivariate quantum regression that enhances output capacity, stabilizes training, and enables uncertainty quantification, addressing key limitations of existing quantum neural network approaches.

Contribution

The paper presents a simple post-processing technique using log-ratio probabilities that significantly improves multivariate regression capabilities and training stability in quantum neural networks.

Findings

Exponential increase in regression outputs relative to qubits.

Mitigation of barren plateau issues during training.

Robust uncertainty quantification for quantum models.

Abstract

Quantum neural networks (QNNs) have shown remarkable potential due to their capability of representing complex functions within exponentially large Hilbert spaces. However, their application to multivariate regression tasks has been limited, primarily due to inherent constraints of traditional approaches that rely on Pauli expectation values. In this work, we introduce a novel and simple post-processing method utilizing log-ratio probabilities (LRPs) of quantum states, enabling efficient and unbounded multivariate regression within existing QNN architectures. Our approach exponentially expands the number of regression outputs relative to qubit count, thus significantly improving parameter and qubit efficiency. Additionally, by enhancing parameter dependencies in the cost function and leveraging gradient pumping effects from the log-ratio transformation, our method mitigates the well-known barren plateau phenomenon, thereby stabilizing training. We further demonstrate that this approach facilitates robust uncertainty quantification, capturing both epistemic and aleatoric uncertainties simultaneously. Our findings underscore the practical potential of LRP-QNNs for complex multi-output regression tasks, particularly within current resource-constrained quantum hardware environments.