Accelerating computation with quantum resources is limited by the challenges of high-fidelity control of quantum systems. Reservoir computing presents an attractive alternative, as precise control and full calibration of system dynamics are not required. Instead, complex internal trajectories in a large state space are leveraged as a computational resource. Quantum systems offer a unique venue for reservoir computing, given the presence of interactions unavailable in classical systems and a potentially exponentially-larger computational space. With a reservoir comprised of a single $d$-dimensional quantum system, we demonstrate clear performance improvement with Hilbert space dimension at two benchmark tasks and advantage over the physically analogous classical reservoir. Quantum reservoirs as realized by current-era quantum hardware offer immediate practical implementation and a promising outlook for increased performance in larger systems.
Accelerating computation with quantum resources is limited by the challenges of high-fidelity control of quantum systems. Reservoir computing presents an attractive alternative, as precise control and full calibration of system dynamics are not required. Instead, complex internal trajectories in a large state space are leveraged as a computational resource. Quantum systems offer a unique venue for reservoir computing, given the presence of interactions unavailable in classical systems and a potentially exponentially-larger computational space. With a reservoir comprised of a single d-dimensional quantum system, we demonstrate clear performance improvement with Hilbert space dimension at two benchmark tasks and advantage over the physically analogous classical reservoir. Quantum reservoirs as realized by current-era quantum hardware offer immediate practical implementation and a promising outlook for increased performance in larger systems.
Accelerating computational tasks with quantum resources is a widely-pursued goal that is presently limited by the challenges associated with high-fidelity control of many-body quantum systems. The paradigm of reservoir computing presents an attractive alternative, especially in the noisy intermediate-scale quantum era, since control over the internal system state and knowledge of its dynamics are not required. Instead, complex, unsupervised internal trajectories through a large state space are leveraged as a computational resource. Quantum systems offer a unique venue for reservoir computing, given the presence of interactions unavailable in analogous classical systems, and the potential for a computational space that grows exponentially with physical system size. Here, we consider a reservoir comprised of a single qudit (d-dimensional quantum system). We demonstrate a robust performance advantage compared to an analogous classical system accompanied by a clear improvement with Hilbert space dimension for two benchmark tasks: signal processing and short-term memory capacity. Qudit reservoirs are directly realized by current-era quantum hardware, offering immediate practical implementation, and a promising outlook for increased performance in larger systems.
Quantum reservoir computing (QRC) uses the dynamics of a fixed or weakly tuned quantum system to transform temporal and sequential inputs into measured features, while training is typically confined to a classical readout. This separation reduces reliance on repeated quantum parameter updates and avoids the barren plateaus associated with variational circuit training. Its computational power is often attributed to the exponentially large Hilbert space of the quantum system. However, the memory, nonlinearity, and expressivity that determine what a reservoir can actually compute depend jointly on the input encoding, quantum evolution, observables, measurement, and readout, not on Hilbert space dimension alone. On hardware, these capabilities are further constrained by finite sampling, hardware noise, measurement backaction, and the cost of estimating observables, so a large state space alone does not guarantee useful computation. In this survey, we develop a common system model that connects these components and use it to organize QRC foundations, computational properties, reservoir architectures, operating protocols, and physical implementations. We examine spin, photonic, superconducting, bosonic, neutral atom, and other analog platforms, together with applications, software and high performance computing support, benchmarking, and reproducibility. The analysis distinguishes hardware demonstrations from simulations and identifies the assumptions and resources that govern comparisons across implementations. Current results do not establish a broad quantum advantage over well matched classical reservoirs. We therefore specify the resource accounting, benchmark standards, and theoretical criteria needed to evaluate claims of quantum advantage.
Abstract Combining the benefits of quantum computing and artificial neural networks, quantum reservoir computing shows potential for handling complex tasks due to its access to the Hilbert space in exponential dimensions. In this study, the quantum Fourier transform algorithm is implemented utilizing quantum reservoir computing, demonstrating its unique advantages. For the random interactions within the reservoirs, quantum reservoir computing avoids the cost of precise control of the physical system. The proposed model only requires to optimize a linear readout layer, thus significantly reducing the computational cost required for training. The accuracy of the implementation is numerically demonstrated and the model is integrated into quantum circuits to correctly execute the quantum phase estimation algorithm. Additionally, the impacts of different reservoir structures and dissipation intensities within the reservoir, and the results indicate the robustness of the model are discussed.
Quantum Reservoir Computing (QRC) offers potential advantages over classical reservoir computing, including inherent processing of quantum inputs and a vast Hilbert space for state exploration. Yet, the relation between the performance of reservoirs based on complex and many-body quantum systems and non-classical state features is not established. Through an extensive analysis of QRC based on a transverse-field Ising model we show how different quantum effects, such as quantum coherence and correlations, contribute to improving the performance in temporal tasks, as measured by the Information Processing Capacity. Additionally, we critically assess the impact of finite measurement resources and noise on the reservoir’s dynamics in different regimes, quantifying the limited ability to exploit quantum effects for increasing damping and noise strengths. Our results reveal a monotonic relationship between reservoir performance and coherence, along with the importance of quantum effects in the ergodic regime. Quantum Reservoir Computing leverages the quantum properties of physical systems for solving temporal tasks. This study shows the importance of quantum effects, such as coherence and superposition, in the reservoir’s performance for different dynamical regimes, while considering the impact of finite measurements and noisy environments.
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 is an emerging field in machine learning with quantum systems. While classical reservoir computing has proven to be a capable concept for enabling machine learning on real, complex dynamical systems with many degrees of freedom, the advantage of its quantum analog has yet to be fully explored. Here, we establish a link between quantum properties of a quantum reservoir, namely, entanglement and its occupied phase-space dimension, and its linear short-term memory performance. We find that a high degree of entanglement in the reservoir is a prerequisite for a more complex reservoir dynamics, which is key to unlocking the exponential phase space and higher short-term memory capacity. We quantify these relations and discuss the effect of dephasing in the performance of physical quantum reservoirs.