Hybrid Quantum Neural Network for Multivariate Clinical Time Series Forecasting

TL;DR

This work addresses multivariate multi-horizon forecasting of physiological time series by jointly predicting heart rate, oxygen saturation, pulse rate, and respiratory rate at forecasting horizons of 15, 30, and 60 seconds by proposing a hybrid quantum-classical architecture that integrates a Variational Quantum Circuit within a recurrent neural backbone.

Abstract

Forecasting physiological signals can support proactive monitoring and timely clinical intervention by anticipating critical changes in patient status. In this work, we address multivariate multi-horizon forecasting of physiological time series by jointly predicting heart rate, oxygen saturation, pulse rate, and respiratory rate at forecasting horizons of 15, 30, and 60 seconds. We propose a hybrid quantum-classical architecture that integrates a Variational Quantum Circuit (VQC) within a recurrent neural backbone. A GRU encoder summarizes the historical observation window into a latent representation, which is then projected into quantum angles used to parameterize the VQC. The quantum layer acts as a learnable non-linear feature mixer, modeling cross-variable interactions before the final prediction stage. We evaluate the proposed approach on the BIDMC PPG and Respiration dataset under a Leave-One-Patient-Out protocol. The results show competitive accuracy compared with classical and deep learning baselines, together with greater robustness to noise and missing inputs. These findings suggest that hybrid quantum layers can provide useful inductive biases for physiological time series forecasting in small-cohort clinical settings.

Figures (5)

• Figure 1: Proposed hybrid GRU--VQC forecaster. The encoder $E$ maps the input window to $z$, projected to VQC angles $\theta$. The VQC acts as a learnable non-linear feature mixer and outputs quantum features $q$ via Pauli-$Z$ measurements. The hybrid vector $[z\|q]$ is used to predict HR, $SpO_2$, Pulse, and RR at $h\in\{15,30,60\}$ s.
• Figure 2: Noise sensitivity analysis under increasing Gaussian perturbations applied to the test inputs. Performance is reported in terms of macro-MAE and macro-RMSE under the LOPO protocol ($N=53$).
• Figure 3: Missing-data sensitivity analysis under increasing missing rates applied to the test inputs. Performance is reported in terms of macro-MAE and macro-RMSE under the LOPO protocol ($N=53$).
• Figure 4: Patient-wise ranking comparison across physiological tasks under the LOPO protocol ($N=53$). For each subject, RMSE is first averaged across prediction horizons ($h15$, $h30$, $h60$), models are ranked by increasing error, and scores are normalized to $[0,1]$.
• Figure 5: Patient-wise ranking comparison across prediction horizons ($h15$, $h30$, $h60$). For each subject, RMSE is averaged across the four physiological tasks (HR, Pulse, RR, SpO$_2$), models are ranked by increasing error, and scores are normalized to $[0,1]$.