Forecasting temporal dynamics underpins many areas of science and engineering, from large-scale atmospheric prediction to nanoscale quantum control. Classical approaches, including autoregressive models and deep neural networks, have advanced sequential learning often at the expense of known model order, or large dataset and parameters, resulting in computational cost. Here, we investigate whether quantum entanglement can serve as a resource for temporal pattern learning using shallow and structured quantum circuits. We have proposed a Quantum Time Series (QTS) framework that encodes normalised sequential data into single-qubit rotations and captures temporal correlations through forward and cross-entanglement layers. Among several encoding schemes, phase encoding-based sparse entanglement provides hardware efficiency by scaling to larger qubit systems with linear circuit depth and two-qubit complexity of [Formula: see text] for qubit size n. This offers a reduction in parameters and depth compared with deep variational quantum circuits such as Heisenberg-inspired circuits, and random-parametric unitary architectures. Experiments on synthetic and geophysical datasets show that shallow QTS circuits reproduce complex temporal pattern from limited data by leveraging structured quantum entanglement. Executions on IBM's Heron and Eagle-class processors demonstrate robustness and scalability up to 100 qubits. These results suggest that structured entanglement may offer a short-term memory effect for time-series analysis, providing a scalable route for near-term quantum applications.
Forecasting temporal dynamics underpins many areas of science and engineering, from large-scale atmospheric prediction to nanoscale quantum control. Classical approaches, including autoregressive models and deep neural networks, have advanced sequential learning often at the expense of known model order, or large dataset and parameters, resulting in computational cost. Here, we investigate whether quantum entanglement can serve as a resource for temporal pattern learning using shallow and structured quantum circuits. We have proposed a Quantum Time Series (QTS) framework that encodes normalised sequential data into single-qubit rotations and captures temporal correlations through forward and cross-entanglement layers. Among several encoding schemes, phase encoding-based sparse entanglement provides hardware efficiency by scaling to larger qubit systems with linear circuit depth and two-qubit complexity of [Formula: see text] for qubit size n. This offers a reduction in parameters and depth compared with deep variational quantum circuits such as Heisenberg-inspired circuits, and random-parametric unitary architectures. Experiments on synthetic and geophysical datasets show that shallow QTS circuits reproduce complex temporal pattern from limited data by leveraging structured quantum entanglement. Executions on IBM's Heron and Eagle-class processors demonstrate robustness and scalability up to 100 qubits. These results suggest that structured entanglement may offer a short-term memory effect for time-series analysis, providing a scalable route for near-term quantum applications.
Time series forecasting is foundational in scientific and technological domains, from climate modelling to molecular dynamics. Classical approaches have significantly advanced sequential prediction, including autoregressive models and deep learning architectures such as temporal convolutional networks (TCNs) and Transformers. Yet, they remain resource-intensive and often scale poorly in data-limited or hardware-constrained settings. We propose a quantum-native time series forecasting framework that harnesses entanglement-based parameterized quantum circuits to learn temporal dependencies. Our Quantum Time Series (QTS) model encodes normalized sequential data into single-qubit rotations and embeds temporal structure through structured entanglement patterns. This design considers predictive performance with logarithmic complexity in training data and parameter count. We benchmark QTS against classical models on synthetic and real-world datasets, including geopotential height fields used in numerical weather prediction. Experiments on the noisy backend and real IBM quantum hardware demonstrate that QTS can capture temporal patterns using fewer data points. Hardware benchmarking results establish quantum entanglement as a practical computational resource for temporal modelling, with potential near-term applications in nano-scale systems, quantum sensor networks, and other forecasting scenarios.
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.
In the context of current Noisy Intermediate-Scale Quantum (NISQ) computers, the application of quantum circuits is hampered by various sources of noise, resulting in errors between the actual output and the ideal output. To mitigate these errors, this study investigates a method for predicting the expected output of quantum circuits. In order to enhance the precision of the experiments, a fixed-scale quantum circuit dataset is randomly collected, and one-hot encoding is applied to represent the data. To eliminate redundant noise in the dataset, a Quantum auto-encoder (QAE) reconstruction encoding model is designed to separate and reconstruct the descriptions of quantum circuits in the dataset. The operation process of a quantum circuit is a sequence of quantum gate operations, and gate operations are gradually realized to change the state of qubits. We regard the process of quantum circuit implementation as a process of evolution with time, so it has the nature of timing. We build an additive fusion prediction model based on temporal neural network, the model can be trained to learn the relationship between sequences to predict the output of quantum circuit, and a loss function based on maximum likelihood estimation is employed to optimize the model parameters. Additionally, a dual approach is verified to optimize the computational indicators in the ensemble model. To validate the effectiveness of the proposed method, experiments are conducted on quantum circuits of varying scales, and the results are compared with the quantum system framework provided by IBM Quantum Experience. The experimental results show that the time series neural network integration can better highlight timing information and noise information in quantum circuits, the proposed method outperforms the IBM Quantum Experience framework in terms of circuit depth and network depth for quantum circuits of different scales, exhibiting robustness and stability.
We propose a single-qubit Quantum Machine Learning (QML) model for time series forecasting, built around the concept of a Quantum Reupload Unit (QRU), a hardwareefficient quantum circuit architecture with shallow depth. The proposed model demonstrates enhanced predictive power compared to variational methods such as quantum circuits (VQC), parameterized quantum circuits (PQC), and quantum residual blocks (QRB). The proposed QRU outperforms classical learning models such as Recurrent Neural Networks (RNNs) and Long-Short Term Memory (LSTM) with the same number of parameters. The novelty of this approach is its ability to model temporal patterns without relying on an extensive memory state, which reduces resource demands while preserving forecast accuracy. The expressivity of the model is evaluated through Fourier spectral decomposition. We analyze the trainability of our model using the absorption witness metric. We benchmarked the proposed model on the Mackey-Glass chaotic time series and the real-world river level dataset from TAIAO. The proposed model consistently exhibits enhanced expressivity over both of the datasets. These results highlight the significance of QRUs as promising candidates for learning models that can be conveniently deployed on noisy intermediate-scale quantum (NISQ) hardware.
Variational quantum circuits (VQCs) have been proposed as promising models for nonlinear learning tasks in the noisy intermediate-scale quantum (NISQ) era. This study presents a hybrid classical-quantum framework for nonlinear time-series forecasting that integrates causally-filtered Hidden Markov regime detection with multiple VQC architectures. Four circuit architectures are defined as an explicit [Formula: see text] factorial design that isolates circuit depth from entanglement topology (shallow: depth 1/linear; ring: depth 1/ring; deep: depth 4/linear; heavy: depth 4/ring), each with reported qubit count, parameter count and gate count, and are evaluated under an analytic depolarizing/readout noise model. Three nonlinear classical baselines (support-vector regression, gradient boosting, and a multilayer perceptron) are compared alongside a linear autoregressive (AR) baseline, and the Hidden Markov Model (HMM) regime feature is fit only on training data and propagated causally into the test set to remove look-ahead leakage. Across 20 Monte Carlo replicates, we find that every VQC architecture is outperformed by every classical baseline, including plain linear AR (paired t-tests, all [Formula: see text]; Cohen’s d up to 4.8). Within the VQC family, circuit depth - not shallowness - is associated with better performance (deep/heavy [Formula: see text] shallow/ring), while entanglement topology alone has little independent effect once depth is controlled. An ablation removing the HMM-derived feature shows it contributes negligibly to forecast accuracy in this setting. Under this confound-controlled design, we find no evidence of a forecasting advantage for the tested VQC architectures over classical linear or nonlinear baselines, which we report as a cautionary result for claims of near-term quantum advantage in forecasting.
We proposed a time-delayed quantum extreme learning machine (TD-QELM) for efficient time-series prediction on noisy intermediate-scale quantum (NISQ) devices. By encoding multiple past inputs simultaneously, TD-QELM achieves shallow circuit depth independent of sequence length, thereby, mitigating noise accumulation and reducing computational complexity. Experiments using the NARMA benchmark on both noiseless simulations and IBM's 127-qubit processor demonstrate that TD-QELM consistently outperforms conventional quantum reservoir computing in prediction accuracy and noise robustness. These results highlight TD-QELM as a practical and scalable framework for time-series learning on current NISQ hardware.