Physical reservoir computing offers an energy-efficient alternative to conventional neural networks, where the material-specific intrinsic memory capacity in a physical system plays an indispensable role. Substituting temporal memory with spatial degrees of freedom, we demonstrate that the memory capacity can be created extrinsically in systems with no intrinsic memory by exploiting the computational space-time tradeoff. Our approach utilizes multidimensional input nodes to function as a spatial memory axis, thereby replacing the dependency on intrinsic history-dependent dynamics in the reservoir. Our scheme is validated in a multi-terminal quantum dot system, whose discrete energy levels provide strong nonlinearity and complexity crucial for reservoir computing, while its short relaxation time leaves no room for intrinsic memory. Numerically, the quantum dot reservoir with a tunable extrinsic memory shows high performance on both chaotic future prediction and nonlinear transformation tasks. Furthermore, from the analysis of quantum state trajectory acquired from task operations, the geometric understanding of the extrinsic memory capacity, nonlinearity, and complexity is provided and their correlations are systematically investigated.
Physical reservoir computing offers an energy-efficient alternative to conventional neural networks, where the material-specific intrinsic memory capacity in a physical system plays an indispensable role. Substituting temporal memory with spatial degrees of freedom, we demonstrate that the memory capacity can be created extrinsically in systems with no intrinsic memory by exploiting the computational space-time tradeoff. Our approach utilizes multidimensional input nodes to function as a spatial memory axis, thereby replacing the dependency on intrinsic history-dependent dynamics in the reservoir. Our scheme is validated in a multi-terminal quantum dot system, whose discrete energy levels provide strong nonlinearity and complexity crucial for reservoir computing, while its short relaxation time leaves no room for intrinsic memory. Numerically, the quantum dot reservoir with a tunable extrinsic memory shows high performance on both chaotic future prediction and nonlinear transformation tasks. Furthermore, from the analysis of quantum state trajectory acquired from task operations, the geometric understanding of the extrinsic memory capacity, nonlinearity, and complexity is provided and their correlations are systematically investigated.
We investigate quantum reservoir computing (QRC) using a hybrid qubit-boson system described by the Jaynes-Cummings (JC) Hamiltonian and its dispersive limit (DJC). These models provide high-dimensional Hilbert spaces and intrinsic nonlinear dynamics, making them powerful substrates for temporal information processing. We systematically benchmark both reservoirs through linear and nonlinear memory tasks, demonstrating that they exhibit an unusual superior nonlinear over linear memory capacity. We further test their predictive performance on the Mackey-Glass time series, a widely used benchmark for chaotic dynamics, and show comparable forecasting ability. We also investigate how memory and prediction accuracy vary with reservoir parameters and show the role of higher-order bosonic observables and time multiplexing in enhancing expressivity, even in minimal spin-boson configurations. Our results establish JC- and DJC-based reservoirs as versatile platforms for time-series processing and as elementary units that overcome the setting of equivalent qubit pairs and offer pathways toward tunable, high-performance quantum machine learning architectures.
We propose a scheme that can enhance the performance and reduce the computational cost of quantum reservoir computing. Quantum reservoir computing is a computing approach which aims at utilizing the complexity and high dimensionality of small quantum systems, together with the fast trainability of reservoir computing, in order to solve complex tasks. The suitability of quantum reservoir computing for solving temporal tasks is hindered by the collapse of the quantum system when measurements are made. This leads to the erasure of the memory of the reservoir. Hence, for every output, the entire input signal is needed to reinitialize the reservoir, leading to quadratic time complexity. Another critical issue for the hardware implementation of quantum reservoir computing is the need for an experimentally accessible means of tuning the nonlinearity of the quantum reservoir. We present an approach which addresses both of these issues. We propose artificially restricting the memory of the quantum reservoir by only using a small number inputs to reinitialize the reservoir after measurements are performed. This strongly influences the nonlinearity of the reservoir response due to the influence of the initial reservoir state, while also substantially reducing the number of quantum operations needed to perform time-series prediction tasks due to the linear rather than quadratic time complexity. The reinitialization length therefore provides an experimental accessible means of tuning the nonlinearity of the response of the reservoir, which can lead to significant task-specific performance improvement. We numerically study the linear and quadratic algorithms for a fully connected transverse Ising model and a quantum processor model. Published by the American Physical Society 2024
The intersection of quantum information processing and machine learning has recently at-tracted considerable interest within the physics and artificial intelligence communities. From a physical perspective, quantum computing offers fundamentally new modes of information processing, enabled by superposition, interference, and entanglement, which can lead to ad-vantages in computational speed and resource efficiency over classical approaches. These developments have motivated the exploration of machine learning paradigms that lever-age quantum dynamics as a computational resource. In parallel, reservoir computing—a non–von Neumann and neuromorphic computing framework—has gained attention due to its reliance on high-dimensional dynamical systems, in-memory computation, and low en-ergy consumption. Quantum reservoir computing extends this paradigm by exploiting the intrinsic dynamics of quantum many-body systems, such as spin networks, to process tem-poral information. Despite growing interest in quantum reservoir architectures, the role of genuinely quantum resources, in particular entanglement, in determining their information-processing capabilities remains incompletely understood. In this thesis, we study a distributed spin-network reservoir in which two independent time series are injected into separate qubits. Using short-term memory capacity as an opera-tional measure, we analyze how information introduced at distinct sites propagates through the network and how different entanglement structures contribute to storing and combining past inputs. Focusing on bilinear memory tasks, which require reconstructing the product of the two inputs at various delays, we probe temporal memory. Due to the computational cost associated with simulating open quantum many-body dynamics, the present study focuses on a minimal spin-network architecture consisting of four qubits, with two qubits serving as input nodes that receive independent time series. Even for such moderate system sizes, the numerical integration of the open-system dynamics are computationally demanding. Nevertheless, this minimal setting already captures the essential mechanisms of distributed information processing in quantum reservoirs. By computing the logarithmic negativity across different bipartitions of the reservoir, we investigate how memory performance relates to the underlying entanglement structure. We find that the short-term memory capacity is maximized at relatively weak coupling strengths, where entanglement is present but remains moderate. Among the various bipar-titions, the entanglement between the two input qubits consistently plays the most promi-nent role in learning performance. In this optimal regime, the reservoir exhibits long-lived memory, while a characteristic reduction in performance at zero delay, observed across all frequencies, reflects the finite time required for information to propagate through the sys-tem. Taken together, these results indicate that effective learning in distributed quantum reservoir computing is enabled by moderate, well-structured entanglement, rather than by maximal correlations.
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.
Quantum reservoir computing is a promising paradigm for processing temporal data. So far, the primary focus has been on univariate time series. However, the most relevant and complex real-world data is multidimensional. In this paper, we establish an extensive framework for multivariate data processing in quantum reservoir computing. We propose and evaluate three multivariate encoding schemes and introduce the mixing capacity as a novel metric to evaluate the effectiveness with which a reservoir combines independent data streams. The computational performance of these proposed schemes is systematically assessed using this metric, as well as on the chaotic Lorenz-63 system prediction task, for two quantum reservoirs based on discrete and continuous-variable quantum systems. Furthermore, we relate the computational performance on these tasks to the underlying quantum properties of the reservoir. Our findings reveal that the optimal encoding method is highly dependent on the reservoir system and the specific task, underlining the importance of a task-specific input design. Moreover, we observe that peak computational performance coincides with the presence of non-classical effects, which indicates that quantum resources play a role in processing multivariate data.
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.