Reservoir computing is a neural network framework capable of nonlinear information processing. The ambiguous nature of the information processing unit provides a fascinating opportunity of employing physical systems as reservoirs. This has also spiked an interest in the research and development of quantum systems. As quantum computing still faces many problems such as scalability and the loss of coherence, quantum reservoir computing offers an alternative way of conducting intricate quantum tasks. These results are not limited to quantum tasks, as the evidence in quantum reservoir computing suggest a possible advantage over classical algorithms in classical nonlinear tasks. This work provides a comprehensive inspection of the theory behind quantum reservoir computing and an entanglement classification task conducted on the reservoir. This includes the review of tools for the measurement of entanglement, Gaussian and non-Gaussian nature of systems, machine learning and quantum computing. The theoretical review is accompanied by results of classical reservoir computing and a greater research on the capabilities of different quantum substrates used in quantum reservoir computing. The main part of this work is to build a working quantum reservoir computing system containing a fermionic reservoir. The task of the reservoir is to learn to classify quantum entanglement of two-mode bosonic inputs. The bosonic inputs used in this work are squeezed thermal states, photon added squeezed vacuum states, photon subtracted squeezed vacuum states and number states. This way Gaussian and non-Gaussian entanglement recognition is tested. Reservoirs of sizes 2, 3 and 4 modes are used and different connectivities inside the reservoir networks are studied. Even though the entanglement is assessed for different classes of states, the training is conducted with only squeezed thermal states
Reservoir computing is a neural network framework capable of nonlinear information processing. The ambiguous nature of the information processing unit provides a fascinating opportunity of employing physical systems as reservoirs. This has also spiked an interest in the research and development of quantum systems. As quantum computing still faces many problems such as scalability and the loss of coherence, quantum reservoir computing offers an alternative way of conducting intricate quantum tasks. These results are not limited to quantum tasks, as the evidence in quantum reservoir computing suggest a possible advantage over classical algorithms in classical nonlinear tasks. This work provides a comprehensive inspection of the theory behind quantum reservoir computing and an entanglement classification task conducted on the reservoir. This includes the review of tools for the measurement of entanglement, Gaussian and non-Gaussian nature of systems, machine learning and quantum computing. The theoretical review is accompanied by results of classical reservoir computing and a greater research on the capabilities of different quantum substrates used in quantum reservoir computing. The main part of this work is to build a working quantum reservoir computing system containing a fermionic reservoir. The task of the reservoir is to learn to classify quantum entanglement of two-mode bosonic inputs. The bosonic inputs used in this work are squeezed thermal states, photon added squeezed vacuum states, photon subtracted squeezed vacuum states and number states. This way Gaussian and non-Gaussian entanglement recognition is tested. Reservoirs of sizes 2, 3 and 4 modes are used and different connectivities inside the reservoir networks are studied. Even though the entanglement is assessed for different classes of states, the training is conducted with only squeezed thermal states
Quantum reservoir computing is an unconventional computing approach that exploits the quantumness of physical systems used as reservoirs to process information, combined with an easy training strategy. An overview is presented about a range of possibilities including quantum inputs, quantum physical substrates and quantum tasks. Recently, the framework of quantum reservoir computing has been proposed using Gaussian quantum states that can be realized e.g. in linear quantum optical systems. The universality and versatility of the system makes it particularly interesting for optical implementations. In particular, full potential of the proposed model can be reached even by encoding into quantum fluctuations, such as squeezed vacuum, instead of classical intense fields or thermal fluctuations. Some examples of the performance of this linear quantum reservoir in temporal tasks are reported.
The paradigm of reservoir computing exploits the nonlinear dynamics of a physical reservoir to perform complex time-series processing tasks such as speech recognition and forecasting. Unlike other machine-learning approaches, reservoir computing relaxes the need for optimization of intra-network parameters, and is thus particularly attractive for near-term hardware-efficient quantum implementations. However, the complete description of practical quantum reservoir computers requires accounting for their placement in a quantum measurement chain, and its conditional evolution under measurement. Consequently, training and inference has to be performed using finite samples from obtained measurement records. Here we describe a framework for reservoir computing with nonlinear quantum reservoirs under continuous heterodyne measurement. Using an efficient truncated-cumulants representation of the complete measurement chain enables us to sample stochastic measurement trajectories from reservoirs of several coupled nonlinear bosonic modes under strong excitation. This description also offers a mathematical basis to directly compare the computational capabilities of a given physical reservoir operated across classical and quantum regimes. Applying this framework to the classification of quantum states of systems that are part of the same measurement chain as the quantum reservoir computer, we assess and explain measurement-contingent advantages and disadvantages of reservoir processing in quantum regimes. Our results also identify the vicinity of bifurcation points as presenting optimal nonlinear processing regimes of an oscillator-based quantum reservoir. The considered models are directly realizable in modern circuit QED experiments, while the framework is applicable to more general quantum nonlinear reservoirs.
The concurrent rise of artificial intelligence and quantum information poses opportunity for creating interdisciplinary technologies like quantum neural networks. Quantum reservoir processing, introduced here, is a platform for quantum information processing developed on the principle of reservoir computing that is a form of artificial neural network. A quantum reservoir processor can perform qualitative tasks like recognizing quantum states that are entangled as well as quantitative tasks like estimating a non-linear function of an input quantum state (e.g. entropy, purity or logarithmic negativity). In this way experimental schemes that require measurements of multiple observables can be simplified to measurement of one observable on a trained quantum reservoir processor.
Quantum reservoir computing is a machine-learning framework that offers ease of training compared to other quantum neural networks, as it does not rely on gradient-based optimization. Learning is performed in a single step on the output features measured from the quantum system. Various implementations of quantum reservoir computing have been explored in simulations, with different measured features. Although simulations have shown that quantum reservoirs present advantages in performance compared to classical reservoirs, experimental implementations have remained scarce. This is due to the challenge of obtaining a large number of output features that are nonlinear transformations of the input data. In this work, we show that even with a circuit quantum electrodynamics system as simple as a single transmon coupled to a readout resonator, we can implement a proof-of-concept realization of quantum reservoir computing. We obtain a large number of nonlinear features from a single physical system by encoding the input data in the amplitude of a coherent drive and measuring the cavity state in the Fock basis. We demonstrate classification of two classical tasks with significantly smaller hardware resources and fewer measured features compared to classical neural networks. Our experimental results are supported by numerical simulations that show additional Kerr nonlinearity is beneficial to reservoir performance. Our work demonstrates a hardware-efficient quantum neural-network implementation that can be further scaled up and generalized to other quantum machine-learning models.
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.
Abstract Quantum reservoir computing aims at harnessing the rich dynamics of quantum systems for machine-learning purposes. It can be used for online time series processing while having a remarkably low training cost. Here, we establish the potential of continuous-variable Gaussian states of linear dynamical systems for quantum reservoir computing. We prove that Gaussian resources are enough for universal reservoir computing. We find that encoding the input into Gaussian states is both a source and a means to tune the nonlinearity of the overall input-output map. We further show that the full potential of the proposed model can be reached by encoding to quantum fluctuations, such as squeezed vacuum, instead of classical fields or thermal fluctuations. Our results introduce a research paradigm for reservoir computing harnessing quantum systems and engineered Gaussian quantum states.