This paper presents a unified quantum-classical hybrid framework for multi-horizon time-series forecasting, introducing two model variants Quantum Reservoir Forecaster (QRC-F) and Variational Quantum Forecaster (VQF-F). The proposed framework investigates the complexity-fidelity trade-off of quantum forecasting under near-term NISQ hardware constraints. Continuous time-series signals are transformed into binary representations through uniform quantization and encoded into quantum states using angle encoding with parameterized RY rotation gates. Cross-channel entanglement layers capture dependencies among multiple variables. QRC-F utilizes a fixed random unitary quantum reservoir for stable, gradient-free temporal feature extraction, whereas VQF-F employs a trainable variational quantum circuit optimized through the parameter-shift rule to learn temporal and inter-variable patterns from Pauli expectation values. Both models replace computationally expensive quadratic self-attention with efficient linear transformations, reducing parameter complexity. A shared MIMO-based multi-horizon prediction head simultaneously generates forecasts across multiple horizons, avoiding error accumulation in recursive forecasting. Experimental evaluations on benchmark datasets, including ETTh1, ETTh2, ETTm1, ETTm2, Weather, electricity, and exchange-rate, demonstrate that VQF-F achieves superior training stability and parameter efficiency, while QRC-F provides enhanced robustness and circuit fidelity under quantum noise. The results establish a practical quantum-native forecasting framework with strong potential for deployment on near-term NISQ devices.
This paper presents a unified quantum-classical hybrid framework for multi-horizon time-series forecasting, introducing two model variants Quantum Reservoir Forecaster (QRC-F) and Variational Quantum Forecaster (VQF-F). The proposed framework investigates the complexity-fidelity trade-off of quantum forecasting under near-term NISQ hardware constraints. Continuous time-series signals are transformed into binary representations through uniform quantization and encoded into quantum states using angle encoding with parameterized RY rotation gates. Cross-channel entanglement layers capture dependencies among multiple variables. QRC-F utilizes a fixed random unitary quantum reservoir for stable, gradient-free temporal feature extraction, whereas VQF-F employs a trainable variational quantum circuit optimized through the parameter-shift rule to learn temporal and inter-variable patterns from Pauli expectation values. Both models replace computationally expensive quadratic self-attention with efficient linear transformations, reducing parameter complexity. A shared MIMO-based multi-horizon prediction head simultaneously generates forecasts across multiple horizons, avoiding error accumulation in recursive forecasting. Experimental evaluations on benchmark datasets, including ETTh1, ETTh2, ETTm1, ETTm2, Weather, electricity, and exchange-rate, demonstrate that VQF-F achieves superior training stability and parameter efficiency, while QRC-F provides enhanced robustness and circuit fidelity under quantum noise. The results establish a practical quantum-native forecasting framework with strong potential for deployment on near-term NISQ devices.
Time-series forecasting is vital across sectors such as finance, energy, and environmental science, where accurate future predictions drive informed decision-making. Traditional statistical methods and deep learning models like LSTM and Transformers, while effective, often struggle with high-dimensional data and long-term dependencies. In this paper, we propose a hybrid quantum-classical model that utilizes Parameterized Quantum Circuits (PQCs) to capture complex temporal patterns in multivariate time-series data. Our architecture integrates a classical encoder, a quantum variational processor, and a classical decoder, trained end-to-end using gradient-based optimization. Experiments conducted on benchmark datasets—electricity load, stock prices, and weather forecasting—demonstrate that the hybrid model consistently outperforms classical baselines in terms of Mean Squared Error (MSE), Mean Absolute Error (MAE), and R² score. Robustness analysis confirms the model’s resilience to moderate quantum noise, while an ablation study highlights the performance gain from quantum components. This work showcases the potential of hybrid quantum-classical approaches on Noisy Intermediate-Scale Quantum (NISQ) devices and lays a foundation for scalable, real-world quantum machine learning applications.
Abstract In this paper, we address the challenge of multivariate time-series forecasting through quantum-enhanced machine learning architectures. We propose adaptation strategies that extend variational quantum circuit models (VQC), traditionally constrained to univariate data, toward the multivariate setting, exploring both purely quantum and hybrid quantum-classical formulations. First, we extend and benchmark several VQC-based and hybrid models to systematically evaluate their ability to capture cross-variable dependencies. Building on these foundations, we introduce the iQTransformer, a novel quantum transformer architecture that integrates a quantum self-attention mechanism within the iTransformer framework, enabling a quantum-native representation of inter-variable relationships. Finally, we present a comprehensive empirical evaluation on both synthetic and real-world datasets, demonstrating that quantum-enhanced models can achieve competitive or superior forecasting accuracy with fewer trainable parameters and faster convergence than state-of-the-art classical and quantum baselines. These findings highlight the potential of quantum-enhanced architectures as efficient and scalable tools for advancing multivariate time-series forecasting.
In this paper, we address the challenge of multivariate time-series forecasting using quantum machine learning techniques. We introduce adaptation strategies that extend variational quantum circuit models, traditionally limited to univariate data, toward the multivariate setting, exploring both purely quantum and hybrid quantum-classical formulations. First, we extend and benchmark several VQC-based and hybrid architectures to systematically evaluate their capacity to model cross-variable dependencies. Second, building upon these foundations, we introduce the iQTransformer, a novel quantum transformer architecture that integrates a quantum self-attention mechanism within the iTransformer framework, enabling a quantum-native representation of inter-variable relationships. Third, we provide a comprehensive empirical evaluation on both synthetic and real-world datasets, showing that quantum-based models may achieve competitive or superior forecasting accuracy with fewer trainable parameters and faster convergence than state-of-the-art classical and quantum baselines in some cases. These contributions highlight the potential of quantum-enhanced architectures as efficient and scalable tools for advancing multivariate time-series forecasting.
Multi-output time-series forecasting in energy systems is challenging because of nonlinear dynamics, multi-scale seasonality, and strong dependencies across correlated series. In this work, we investigate two hybrid quantum-classical frameworks for multi-stream time-series forecasting on a real Smart Meter dataset comprising 103 household electricity consumption time-series, with experiments executed on the ibm_marrakesh superconducting quantum processor. The first model, Kernelized Quantum Reservoir Computing with Repeated Measurement (KQRC-RM), combines coupled quantum reservoirs, ancilla-assisted repeated measurement, and kernelized readouts to model temporal dynamics and cross-stream correlations jointly. For a 3-stream time-series input and output, the KQRC-RM model using 114 qubits achieves an MAE of 0.0811 on MPS simulator (36.92\% improvement over its classical analog) whereas performance degrades to an MAE of 0.1524 on hardware. The second, a Projected Quantum Kernel Gaussian Process (QGP), replaces fidelity-based kernels with projected kernels constructed from local reduced-state statistics. Using a topology-aware 100-qubit QGP model to predict 100 multi-output time-series values, we observe 49\% of time-series outputs achieve high-accuracy predictions (MAE <0.15), with an average MAE of 0.082 for this low-error group. The medium-error regime (MAE 0.15-0.35) has an average MAE of 0.229, while the high-error regime (MAE >0.35) has an average MAE of 0.664. Overall, this reduces the average MAE relative to the classical GP baseline by 62.01\% on MPS simulator and 40.37\% on hardware. Together, these results demonstrate the feasibility of hybrid quantum machine learning for multi-input, multi-output time-series forecasting at the 100+ qubit scale on NISQ devices.
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. The code is available at https://github.com/arco-group/quantum-ml.
We investigate a digital quantum reservoir computing (QRC) framework for multi-step forecasting of automated teller machine (ATM) cash demand time series on near-term quantum devices. The proposed approach uses parametrized four-qubit reservoirs with a fixed structure exploiting partial measurement and reset, where temporal data is encoded in rotation angles. Training is restricted to a classical Ridge-regression readout. We systematically analyze the impact of the circuit ansatzë, reservoir memory, measurement-derived observables, and the execution backend on the forecasting performance. Experiments are performed with noiseless simulation, noise-aware emulation, and a real IQM Spark quantum processor. Although the QRC models do not outperform the classical Prophet benchmark in terms of Mean Absolute Error and Normalized Mean Squared Error metrics, they achieve more competitive results in Dynamic Time Warping metric, indicating a partial ability to capture temporal structure. These findings provide an empirical assessment of digital QRC for realistic financial forecasting and highlight both its current limitations and its potential on near-term quantum hardware.