Quantum reservoir computing (QRC) harnesses quantum systems to tackle intricate computational problems with exceptional efficiency and minimized energy usage. This paper presents a QRC framework that utilizes a minimalistic quantum reservoir, consisting of only a few two-level atoms within an optical cavity. The system is inherently scalable, as newly added atoms automatically couple with the existing ones through the shared cavity field. We demonstrate that the quantum reservoir outperforms traditional classical reservoir computing in both memory retention and nonlinear data processing through two tasks, namely, the prediction of time-series data using the Mackey-Glass task and the classification of sine-square waveforms. Our results show significant performance improvements with an increasing number of atoms, facilitated by nondestructive, continuous quantum measurements and polynomial regression techniques. These findings confirm the potential of QRC as a practical and efficient solution to addressing complex computational challenges in quantum machine learning.
Quantum reservoir computing (QRC) harnesses quantum systems to tackle intricate computational problems with exceptional efficiency and minimized energy usage. This paper presents a QRC framework that utilizes a minimalistic quantum reservoir, consisting of only a few two-level atoms within an optical cavity. The system is inherently scalable, as newly added atoms automatically couple with the existing ones through the shared cavity field. We demonstrate that the quantum reservoir outperforms traditional classical reservoir computing in both memory retention and nonlinear data processing through two tasks, namely, the prediction of time-series data using the Mackey-Glass task and the classification of sine-square waveforms. Our results show significant performance improvements with an increasing number of atoms, facilitated by nondestructive, continuous quantum measurements and polynomial regression techniques. These findings confirm the potential of QRC as a practical and efficient solution to addressing complex computational challenges in quantum machine learning.
Quantum Reservoir Computing (QRC) leverages quantum systems to perform complex computational tasks with exceptional efficiency and reduced energy consumption. We introduce a minimalistic QRC framework utilizing as few as five atoms in a single-mode optical cavity, combined with continuous quantum measurement. The system is conveniently scalable, as newly added atoms naturally couple with existing ones via the shared cavity field. To achieve high computational expressivity with a minimal reservoir, we include two critical elements: reservoir feedback and polynomial regression. Reservoir feedback modifies the reservoir’s dynamics without altering its internal quantum hardware, while polynomial regression nonlinearly enhances output resolution. We demonstrate significant QRC performance in memory retention and nonlinear data processing through two tasks: predicting chaotic time-series data via the Mackey-Glass task and classifying sine-square waveforms. This framework fulfills QRC’s objectives to minimize hardware size and energy consumption, marking a significant advancement in integrating quantum physics with machine learning technology.
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.
Quantum reservoir computing (QRC) is an emerging paradigm for harnessing the natural dynamics of quantum systems as computational resources that can be used for temporal machine learning tasks. In the current setup, QRC is difficult to deal with high-dimensional data and has a major drawback of scalability in physical implementations. We propose higher-order QRC, a hybrid quantum-classical framework consisting of multiple but small quantum systems that are mutually communicated via classical connections like linear feedback. By utilizing the advantages of both classical and quantum techniques, our framework enables an efficient implementation to boost the scalability and performance of QRC. Furthermore, higher-order settings allow us to implement a FORCE learning or an innate training scheme, which provides flexibility and high operability to harness high-dimensional quantum dynamics and significantly extends the application domain of QRC. We demonstrate the effectiveness of our framework in emulating large-scale nonlinear dynamical systems, including complex spatiotemporal chaos, which outperforms many of the existing machine learning techniques in certain situations.
Reservoir computing (RC) is an effective method for predicting chaotic systems by using a high-dimensional dynamic reservoir with fixed internal weights, while keeping the learning phase linear, which simplifies training and reduces computational complexity compared to fully trained recurrent neural networks (RNNs). Quantum reservoir computing (QRC) uses the exponential growth of Hilbert spaces in quantum systems, allowing for greater information processing, memory capacity, and computational power. However, the original QRC proposal requires coherent injection of inputs multiple times, complicating practical implementation. We present a hybrid quantum-classical approach that implements memory through classical post-processing of quantum measurements. This approach avoids the need for multiple coherent input injections and is evaluated on benchmark tasks, including the chaotic Mackey-Glass time series prediction. We tested our model on two physical platforms: a fully connected Ising model and a Rydberg atom array. The optimized model demonstrates promising predictive capabilities, achieving a higher number of steps compared to previously reported approaches.
Quantum reservoir computing has emerged as a promising paradigm within the field of quantum machine learning, harnessing the inherent properties of quantum systems to optimise and enhance information processing capabilities. Here, we explore the potential of quantum-inspired machine learning methodologies by leveraging the complex dynamics of quantum reservoirs to address computationally challenging tasks with enhanced efficiency and accuracy. To this end, we employ an open quantum system model comprising two-level atomic ensembles coupled to Lorentzian photonic cavities to construct a quantum physical reservoir computer layer for a recurrent neural network. We evaluate the effectiveness of this approach by applying it to a standard machine learning image-recognition problem and benchmarking its performance against a conventional neural network of similar architecture, but lacking the quantum physical reservoir computer layer. Remarkably, as the dataset size increases, the quantum physical reservoir computer outperforms the conventional neural network, requiring fewer training epochs and a smaller dataset to achieve comparable accuracy. Furthermore, we employ the quantum physical reservoir computing approach to model the dynamics of open quantum systems, focusing on atomic system ensembles interacting with a structured photonic reservoir associated with a photonic band-gap material. Our results reveal that the quantum reservoir computer provides equally powerful representations for quantum dynamical problems, maintaining effectiveness even under constraints of limited training data.
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.