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.
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) 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 Quantum computers require precise control over parameters and careful engineering of the underlying physical system. In contrast, neural networks have evolved to tolerate imprecision and inhomogeneity. Here, using a reservoir computing architecture we show how a random network of quantum nodes can be used as a robust hardware for quantum computing. It induces quantum operations by optimising only a single layer of quantum nodes, a key advantage over the traditional neural networks where many layers of neurons have to be optimised. We demonstrate how a single network can induce different quantum gates, including a universal gate set. Moreover, we show that sequences of multiple quantum gates in quantum circuits can be compressed with a single operation, greatly reducing the operation time and complexity. As the key resource is a random network of nodes, with no specific topology or structure, this architecture is a hardware friendly alternative paradigm for quantum computation.
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.
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.
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
Abstract Quantum reservoir networks combine the intelligence of neural networks with the potential of quantum computing in a single platform. This platform operates on the architecture of reservoir computing, which can function even with random connections between neural nodes. This is a major advantage for hardware implementation. Herein is described how reservoir computing is brought into the quantum domain to perform various tasks, including characterization of quantum states, quantum estimation, quantum state preparation, and quantum computing. It shows quantum enhancement in classical data processing, and creates the opportunity for quantum information processing within the robust paradigm of neural networks. It is friendly for implementation in a wide range of physical systems, including quantum dots, superconductors, trapped ions, cold atoms, and exciton‐polaritons.