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Quantum 2.0 Conference and Exhibition

Computing with two quantum reservoirs connected via optimized two-qubit nonselective measurements

Stephen Vintskevich, Dmitry Grigoriev

Published Jan 1, 2022• 0 citations
Publisher

Abstract

We propose a novel approach to link multipartite quantum systems - quantum reservoirs into a network to implement quantum reservoir computing. We present the machine learning-based heuristics to optimize performance and information transfer between systems.
DOI
10.1364/quantum.2022.qw2a.48

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Computing with two quantum reservoirs connected via optimized two-qubit nonselective measurements

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Currently, quantum reservoir computing is one of the most promising and experimentally accessible techniques for hybrid, quantum-classical machine learning. However, its applications are limited due to practical restrictions on the size of quantum systems and the influence of noise. Here we propose a novel approach to connect two quantum reservoirs in a network to overcome these issues and enhance their computing performance. To transfer information between quantum reservoirs, we perform optimized two-qubit non-selective measurements. We suggest a general heuristic optimization strategy based on tensor network language and matrix representation of two-qubit quantum channels specified for quantum reservoir computing. In addition, we introduce a single qubit purification channel and its optimization for further enhancement of quantum reservoir computing. We also demonstrate that the optimized channels applied to a seven-qubit network can efficiently transfer information between its parts with the resulting performance comparable to a network up to twenty-five qubits connected via a classical information link.
Abstract Currently, quantum reservoir computing is one of the most promising and experimentally accessible techniques for hybrid, quantum-classical machine learning. However, its applications are limited due to practical restrictions on the size of quantum systems and the influence of noise. Here we propose a novel approach to connect two quantum reservoirs in a network to overcome these issues and enhance their computing performance. To transfer information between quantum reservoirs, we perform optimized two-qubit non-selective measurements. We suggest a general heuristic optimization strategy based on tensor network language and matrix representation of two-qubit quantum channels specified for quantum reservoir computing. In addition, we introduce a single qubit purification channel and its optimization for further enhancement of quantum reservoir computing. We also demonstrate that the optimized channels applied to a seven-qubit network can efficiently transfer information between its parts with the resulting performance comparable to a network up to twenty-five qubits connected via a classical information link.
Efficient quantum state measurement is important for maximizing the extracted information from a quantum system.For multiqubit quantum processors, in particular, the development of a scalable architecture for rapid and high-fidelity readout remains a critical unresolved problem.Here we propose reservoir computing as a resource-efficient solution to quantum measurement of superconducting multiqubit systems.We consider a small network of Josephson parametric oscillators, which can be implemented with minimal device overhead and in the same platform as the measured quantum system.We theoretically analyze the operation of such a device as a reservoir computer to classify stochastic timedependent signals subject to quantum statistical features.We apply this reservoir computer to the task of multinomial classification of measurement trajectories from joint multiqubit readout.For a 2-qubit dispersive measurement under realistic conditions we demonstrate a classification fidelity reliably exceeding that of an optimal linear filter using only 2-5 reservoir nodes, while simultaneously requiring far less calibration data-as little as a few shots per state.We understand this remarkable performance through an analysis of the network dynamics and develop an intuitive picture of reservoir processing generally.Finally, we demonstrate how to operate this device to perform 2-qubit state tomography and continuous parity monitoring with equal effectiveness and ease of calibration.This reservoir processor avoids computationally intensive training common to other machine learning frameworks and can be implemented as an integrated cryogenic superconducting device for low-latency processing of quantum signals on the computational edge.
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 has emerged as a promising paradigm within the field of quantum machine learning, harnessing the inherent properties of quantum systems to optimise and enhance information processing capabilities. Here, we explore the potential of quantum-inspired machine learning methodologies by leveraging the complex dynamics of quantum reservoirs to address computationally challenging tasks with enhanced efficiency and accuracy. To this end, we employ an open quantum system model comprising two-level atomic ensembles coupled to Lorentzian photonic cavities to construct a quantum physical reservoir computer layer for a recurrent neural network. We evaluate the effectiveness of this approach by applying it to a standard machine learning image-recognition problem and benchmarking its performance against a conventional neural network of similar architecture, but lacking the quantum physical reservoir computer layer. Remarkably, as the dataset size increases, the quantum physical reservoir computer outperforms the conventional neural network, requiring fewer training epochs and a smaller dataset to achieve comparable accuracy. Furthermore, we employ the quantum physical reservoir computing approach to model the dynamics of open quantum systems, focusing on atomic system ensembles interacting with a structured photonic reservoir associated with a photonic band-gap material. Our results reveal that the quantum reservoir computer provides equally powerful representations for quantum dynamical problems, maintaining effectiveness even under constraints of limited training data.
Quantum reservoir computing employs fixed quantum dynamics as a feature map for machine learning. Integrating multiple quantum reservoirs, however, raises a key question: how few inter-module connections are sufficient to match the performance of a single reservoir? To address this, we explicitly separate intra-module dynamics from inter-module couplings and systematically examine different connectivity schemes. We find that even a small number of well-placed connections between two modules can match single-reservoir accuracy, with simple one-to-one connections proving highly effective. Performance generally improves with increasing inter-module entanglement, and these correlations persist for both ZZZZZZ-coupled and random modular reservoirs. Extensions to three modules and evaluations across multiple datasets (MNIST, Fashion-MNIST, CIFAR-10) suggest that the modular architecture can be applied to diverse reservoir types and image-classification datasets. These results motivate modular quantum reservoir designs that align naturally with realistic hardware, such as two-dimensional quantum-chip layouts or networks of small integrated quantum systems.