The application of AI-based forecasting methods has led to great progress in the prediction of complex systems. Among the AI-methods being used reservoir computing (RC) turns out to be so far the most promising approach as it combines superior prediction results with little CPU-needs for training. In Quantum Reservoir Computing (QRC) the reservoir that is commonly a random network, is replaced by a system of entangled qubits. Using a spin-network as ad hoc quantum reservoir it was demonstrated that a NARMA process can be well predicted using as few as 10 qubits [1]. Our recent first results suggest that even a 4-6 qubit system may be sufficient to predict the Lorenz-system as well as with “conventional” RC [2]. In the forthcoming research project “Neuromorphic Quantum Computing (NeMoQC)” within the framework of the DLR Quantum Computing Initiative (QCI) we will now investigate systematically which quantum reservoirs are best suited for prediction and optimization tasks. In a software/hardware codesign we will seek for hardware realizations of QRC. Further, these newly developed QC-based forecasting and optimization methods are to be utilized in real world applications. Industrial partners for both the hardware design and the applications in real world use cases are welcome to join our project. [1] R. Martinez-Pena et al., PRL, 127, 100502 (2021) [2] J. Steinegger, Masterthesis LMU (ongoing)
The application of AI-based forecasting methods has led to great progress in the prediction of complex systems. Among the AI-methods being used reservoir computing (RC) turns out to be so far the most promising approach as it combines superior prediction results with little CPU-needs for training. In Quantum Reservoir Computing (QRC) the reservoir that is commonly a random network, is replaced by a system of entangled qubits. Using a spin-network as ad hoc quantum reservoir it was demonstrated that a NARMA process can be well predicted using as few as 10 qubits [1]. Our recent first results suggest that even a 4-6 qubit system may be sufficient to predict the Lorenz-system as well as with “conventional” RC [2]. In the forthcoming research project “Neuromorphic Quantum Computing (NeMoQC)” within the framework of the DLR Quantum Computing Initiative (QCI) we will now investigate systematically which quantum reservoirs are best suited for prediction and optimization tasks. In a software/hardware codesign we will seek for hardware realizations of QRC. Further, these newly developed QC-based forecasting and optimization methods are to be utilized in real world applications. Industrial partners for both the hardware design and the applications in real world use cases are welcome to join our project. [1] R. Martinez-Pena et al., PRL, 127, 100502 (2021) [2] J. Steinegger, Masterthesis LMU (ongoing)
This paper investigates the application of quantum reservoir computing (QRC) to time series prediction. Classical reservoir computing (RC) utilizes a complex, high-dimensional system – the 'reservoir' – as a non-linear feature extractor, followed by a linear regression model for prediction. QRC extends this concept by leveraging the inherent dynamics of a quantum system as the reservoir. We hypothesize that quantum systems, due to their superposition and entanglement properties, can provide richer and more complex dynamics than classical reservoirs, potentially leading to improved prediction accuracy. This work outlines the theoretical framework for QRC, detailing the setup of a suitable quantum reservoir (e.g., a superconducting qubit array), the measurement process, and the training strategy involving a classical machine learning model. We demonstrate a conceptual approach, focusing on the potential advantages and challenges of employing quantum systems for this task. The core claim is that QRC can achieve superior time series prediction accuracy compared to classical RC methods. Key elements explored include the input signal's influence on the quantum reservoir, the selection of appropriate measurement schemes, and the choice of classical learning algorithms. The paper concludes with a discussion of future research directions and the potential impact of QRC on various time series prediction applications.
Recent developments in quantum computing and machine learning have propelled the interdisciplinary study of quantum machine learning. Sequential modeling is an important task with high scientific and commercial value. Existing VQC or QNN-based methods require significant computational resources to perform the gradient-based optimization of a larger number of quantum circuit parameters. The major drawback is that such quantum gradient calculation requires a large amount of circuit evaluation, posing challenges in current near-term quantum hardware and simulation software. In this work, we approach sequential modeling by applying a reservoir computing (RC) framework to quantum recurrent neural networks (QRNN-RC) that are based on classical RNN, LSTM and GRU. The main idea to this RC approach is that the QRNN with randomly initialized weights is treated as a dynamical system and only the final classical linear layer is trained. Our numerical simulations show that the QRNN-RC can reach results comparable to fully trained QRNN models for several function approximation and time series prediction tasks. Since the QRNN training complexity is significantly reduced, the proposed model trains notably faster. In this work we also compare to corresponding classical RNN-based RC implementations and show that the quantum version learns faster by requiring fewer training epochs in most cases. Our results demonstrate a new possibility to utilize quantum neural network for sequential modeling with greater quantum hardware efficiency, an important design consideration for noisy intermediate-scale quantum (NISQ) computers.
Forecasting neural activity from short recordings remains a fundamental challenge. Reservoir computing may offer an efficient paradigm for temporal prediction, however classical reservoirs typically underperform in small-data regimes. Here we investigate whether quantum reservoir computing (QRC) can help overcome this limitation. Building on recent advances, we introduce a quantum reservoir based on a transverse-field Ising model, combined with heterogeneous quantum measurements and polynomial ridge regression. On a standard benchmark task, results show that the quantum reservoir outperforms a classical counterpart overall, with prediction accuracy strongly dependent on reservoir parameters. We further demonstrate feasibility by running the same task on quantum hardware. To assess performance on biological signals, we evaluate QRC on simulated human electroencephalography (EEG) data with a parallel reservoir architecture. On this challenging task, the tested quantum reservoir did not match the performance of the classical one, but it produced stable, convergent predictions. This is a meaningful first step toward forecasting of biologically realistic neural data using a quantum reservoir. Overall, our findings indicate that although current quantum hardware and parallel reservoir architectures do not yet surpass classical methods on complex neural signals, QRC can be executed on near-term devices and does converge with realistic EEG-like data. This work establishes a practical baseline for future algorithmic and hardware developments aimed at clinical time-series forecasting with quantum systems.
Quantum reservoir computing (QRC) exploits the information-processing capabilities of quantum systems to tackle time-series forecasting tasks, which is expected to be superior to their classical counterparts. By far, many QRC schemes have been theoretically proposed. However, most of these schemes involve long-time evolution of quantum systems or networks with quantum gates. This poses a challenge for practical implementation of these schemes, as precise manipulation of quantum systems is crucial, and this level of control is currently hard to achieve with the existing state of quantum technology. Here we propose a different QRC scheme, which is friendly to experimental realization. It implements the quantum version of nonlinear vector autoregression, extracting linear and nonlinear features of quantum data by measurements. Thus, the evolution of complex networks of quantum gates can be avoided. Compared to other QRC schemes, our proposal also achieves an advance by effectively reducing the necessary training data for reliable predictions in time-series forecasting tasks. Furthermore, we experimentally verify our proposal by performing the forecasting tasks, and the observation matches well with the theoretical ones. Our work opens up a different way for complex tasks to be solved by using QRC, which can herald the next generation of QRC.
This paper explores the application of quantum reservoir computing (QRC) to time-series forecasting. Traditional reservoir computing methods, while effective for certain time-series, often face limitations when dealing with complex, high-dimensional data. This research proposes a novel approach utilizing a quantum system, such as a driven oscillator, as the reservoir, capitalizing on the inherent quantum properties for enhanced temporal processing. The core idea involves mapping the input time series onto the quantum reservoir, allowing the reservoir's quantum state to evolve dynamically. A linear readout layer is then trained to predict future values based on the evolved state. We investigate the potential advantages of QRC, specifically its ability to capture non-linear relationships and high-dimensional correlations within the time series data. The theoretical framework is presented, outlining the key components and the training methodology. Simulation results (described in detail below) demonstrate the feasibility and potential performance gains of QRC compared to classical reservoir computing. This research contributes to the growing field of quantum computing applied to time-series analysis.
Quantum computing and neural networks show great promise for the future of information processing. In this paper we study a quantum reservoir computer (QRC), a framework harnessing quantum dynamics and designed for fast and efficient solving of temporal machine learning tasks such as speech recognition, time series prediction and natural language processing. Specifically, we study memory capacity and accuracy of a quantum reservoir computer based on the fully connected transverse field Ising model by investigating different forms of inter-spin interactions and computing timescales. We show that variation in inter-spin interactions leads to a better memory capacity in general, by engineering the type of interactions the capacity can be greatly enhanced and there exists an optimal timescale at which the capacity is maximized. To connect computational capabilities to physical properties of the underlaying system, we also study the out-of-time-ordered correlator and find that its faster decay implies a more accurate memory. Furthermore, as an example application on real world data, we use QRC to predict stock values.