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arXiv:2006.04821 · Communications Physics

Gaussian states of continuous-variable quantum systems provide universal and versatile reservoir computing

Johannes Nokkala, Rodrigo Martínez‐Peña, Gian Luca Giorgi, Valentina Parigi, Miguel C. Soriano, Roberta Zambrini

Published Mar 22, 2021• 94 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s42005-021-00556-w

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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.
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.
Reservoir computing is a powerful machine learning paradigm for online time series processing. It has reached state-of-the-art performance in tasks such as chaotic time series prediction and continuous speech recognition thanks to its unique combination of high computational power and low training cost which sets it aside from alternatives such as traditionally trained recurrent neural networks, and furthermore is amenable to implementations in dedicated hardware, potentially leading to extremely compact and efficient reservoir computers. Recently the use of random quantum systems has been proposed, leveraging the complexity of quantum dynamics for classical time series processing. Extracting the output from a quantum system without disturbing its state too much is problematic however, and can be expected to become a bottleneck in such approaches. Here we propose a reservoir computing inspired approach to online processing of time series consisting of quantum information, sidestepping the measurement problem. We illustrate its power by generalizing two paradigmatic benchmark tasks from classical reservoir computing to quantum information and introducing a task without a classical analogue where a random system is trained to both create and distribute entanglement between systems that never directly interact. Finally, we discuss partial generalizations where only the input or only the output time series is quantum.
Abstract The natural dynamics of complex networks can be harnessed for information processing purposes. A paradigmatic example are artificial neural networks used for machine learning. In this context, quantum reservoir computing (QRC) constitutes a natural extension of the use of classical recurrent neural networks using quantum resources for temporal information processing. Here, we explore the fundamental properties of QRC systems based on qubits and continuous variables. We provide analytical results that illustrate how nonlinearity enters the input–output map in these QRC implementations. We find that the input encoding through state initialization can serve to control the type of nonlinearity as well as the dependence on the history of the input sequences to be processed.
Abstract Quantum reservoir computing (QRC) is a machine learning paradigm in which a quantum system is used to perform information processing. A prospective approach to its physical realization is a photonic platform in which continuous variable quantum information methods are applied. The simplest continuous variable quantum states are Gaussian states, which can be efficiently simulated classically. As such, they provide a benchmark for the level of performance that non-Gaussian states should surpass in order to give a quantum advantage. In this article we propose two methods to increase the information processing capacity of QRC with Gaussian states compared to previous QRC schemes. We consider better utilization of the measurement distribution by sampling its cumulative distribution function. We show it provides memory in areas that conventional approaches are lacking, as well as improving the overall processing capacity of the reservoir. We also consider storing past measurement results in classical memory, and show that it improves the memory capacity and can be used to mitigate the effects of statistical noise due to finite measurement ensemble.
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 (QRC) leverages the nonlinearity and correlations of quantum systems to enhance machine learning tasks. We explore continuous-variable (CV) photonic platforms for QRC using frequency- and pulse-multiplexed squeezed states generated via nonlinear waveguides, enabling scalable, room-temperature architectures without single-photon sources or detectors. We introduce a novel, measurement-based QRC protocol that uses a neural network of cluster states and local operations, in which input data are encoded through measurement via quantum teleportation. In this design, measurements enable input injection, information processing, and continuous monitoring for time-series tasks. The architecture’s power and versatility are demonstrated through benchmark tasks, showing that the protocol exhibits internal memory and is suitable for both static and temporal information processing without hardware modifications. Additionally, we report a proof-of-principle experimental realization of QRC based on pump-phase encoding and electronic feedback, demonstrating temporal data processing capabilities.