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Quantum reservoir neural network implementation on a Josephson mixer

Julien Dudas, Erwan Plouet, Frank Alice Mizrahi, Julie Grollier, Danijela Marković

Published Nov 3, 2022• 0 citations
OpenAlex

Abstract

Quantum reservoir computing is a promising approach to quantum neural networks capable of solving hard learning tasks on both classical and quantum input data. However, current approaches with qubits are limited by low connectivity. We propose an implementation for quantum reservoir that obtains a large number of densely connected neurons by using parametrically coupled quantum oscillators instead of physically coupled qubits. We analyse a specific hardware implementation based on superconducting circuits. Our results give the coupling and dissipation requirements in the system and show how they affect the performance of the quantum reservoir. Beyond quantum reservoir computation, the use of parametrically coupled bosonic modes holds promise for realizing large quantum neural network architectures.

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Quantum reservoir computing is a promising approach for quantum neural networks, capable of solving hard learning tasks on both classical and quantum input data. However, current approaches with qubits suffer from limited connectivity. We propose an implementation for quantum reservoir that obtains a large number of densely connected neurons by using parametrically coupled quantum oscillators instead of physically coupled qubits. We analyse a specific hardware implementation based on superconducting circuits: with just two coupled quantum oscillators, we create a quantum reservoir comprising up to 81 neurons. We obtain state-of-the-art accuracy of 99 % on benchmark tasks that otherwise require at least 24 classical oscillators to be solved. Our results give the coupling and dissipation requirements in the system and show how they affect the performance of the quantum reservoir. Beyond quantum reservoir computing, the use of parametrically coupled bosonic modes holds promise for realizing large quantum neural network architectures, with billions of neurons implemented with only 10 coupled quantum oscillators.

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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.

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Quantum neural networks promise to extend the power of machine learning into the quantum domain, with potential applications ranging from automatic recognition of quantum states to the control of quantum devices. However, their physical implementation and training remain challenging. In particular, the backpropagation algorithm that underpins the efficiency of classical neural networks cannot generally be applied to large quantum systems, as nonlinear quantum dynamics are not efficiently simulable. Instead, variational quantum circuits typically rely on parameter-shift rules or sampling-based gradient estimation. Here we propose a bosonic quantum neural network based on parametrically coupled Gaussian modes. Although the underlying quantum dynamics are linear, nonlinear output features are generated through Fock-basis measurements. Because Gaussian evolution can be efficiently simulated in the Heisenberg representation, the system admits gradient-based optimization by differentiating a classical model of the dynamics, while the forward evolution itself could be implemented on quantum hardware. This hybrid approach enables end-to-end training of physically meaningful parameters without requiring gradient extraction from the experimental device. Such architectures are naturally compatible with circuit quantum electrodynamics platforms featuring tunable parametric couplers, as well as integrated photonic systems with engineered $χ$(2) or $χ$(3) nonlinearities. Our results demonstrate that linear bosonic networks combined with nonlinear measurement provide a scalable and trainable route toward experimentally realizable quantum neural networks.

arXiv:2411.19112•Nov 28, 2024•0 citations
Quantum reservoir computing is a promising approach to quantum neural networks capable of solving hard learning tasks on both classical and quantum input data. However, current approaches with qubits are limited by low connectivity. We propose an implementation for quantum reservoir that obtains a large number of densely connected neurons by using parametrically coupled quantum oscillators instead of physically coupled qubits. We analyse a specific hardware implementation based on superconducting circuits. Our results give the coupling and dissipation requirements in the system and show how they affect the performance of the quantum reservoir. Beyond quantum reservoir computation, the use of parametrically coupled bosonic modes holds promise for realizing large quantum neural network architectures.
Quantum reservoir computing is a promising approach for quantum neural networks, capable of solving hard learning tasks on both classical and quantum input data. However, current approaches with qubits suffer from limited connectivity. We propose an implementation for quantum reservoir that obtains a large number of densely connected neurons by using parametrically coupled quantum oscillators instead of physically coupled qubits. We analyse a specific hardware implementation based on superconducting circuits: with just two coupled quantum oscillators, we create a quantum reservoir comprising up to 81 neurons. We obtain state-of-the-art accuracy of 99 % on benchmark tasks that otherwise require at least 24 classical oscillators to be solved. Our results give the coupling and dissipation requirements in the system and show how they affect the performance of the quantum reservoir. Beyond quantum reservoir computing, the use of parametrically coupled bosonic modes holds promise for realizing large quantum neural network architectures, with billions of neurons implemented with only 10 coupled quantum oscillators.
Abstract Quantum reservoir computing is a promising approach for quantum neural networks, capable of solving hard learning tasks on both classical and quantum input data. However, current approaches with qubits suffer from limited connectivity. We propose an implementation for quantum reservoir that obtains a large number of densely connected neurons by using parametrically coupled quantum oscillators instead of physically coupled qubits. We analyze a specific hardware implementation based on superconducting circuits: with just two coupled quantum oscillators, we create a quantum reservoir comprising up to 81 neurons. We obtain state-of-the-art accuracy of 99% on benchmark tasks that otherwise require at least 24 classical oscillators to be solved. Our results give the coupling and dissipation requirements in the system and show how they affect the performance of the quantum reservoir. Beyond quantum reservoir computing, the use of parametrically coupled bosonic modes holds promise for realizing large quantum neural network architectures, with billions of neurons implemented with only 10 coupled quantum oscillators.
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.
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 neural networks promise to extend the power of machine learning into the quantum domain, with potential applications ranging from automatic recognition of quantum states to the control of quantum devices. However, their physical implementation and training remain challenging. In particular, the backpropagation algorithm that underpins the efficiency of classical neural networks cannot generally be applied to large quantum systems, as nonlinear quantum dynamics are not efficiently simulable. Instead, variational quantum circuits typically rely on parameter-shift rules or sampling-based gradient estimation. Here we propose a bosonic quantum neural network based on parametrically coupled Gaussian modes. Although the underlying quantum dynamics are linear, nonlinear output features are generated through Fock-basis measurements. Because Gaussian evolution can be efficiently simulated in the Heisenberg representation, the system admits gradient-based optimization by differentiating a classical model of the dynamics, while the forward evolution itself could be implemented on quantum hardware. This hybrid approach enables end-to-end training of physically meaningful parameters without requiring gradient extraction from the experimental device. Such architectures are naturally compatible with circuit quantum electrodynamics platforms featuring tunable parametric couplers, as well as integrated photonic systems with engineered χ(2) or χ(3) nonlinearities. Our results demonstrate that linear bosonic networks combined with nonlinear measurement provide a scalable and trainable route toward experimentally realizable quantum neural networks.
Quantum neural networks promise to extend the power of machine learning into the quantum domain, with potential applications ranging from automatic recognition of quantum states to the control of quantum devices. However, their physical implementation and training remain challenging. In particular, the backpropagation algorithm that underpins the efficiency of classical neural networks cannot generally be applied to large quantum systems, as nonlinear quantum dynamics are not efficiently simulable. Instead, variational quantum circuits typically rely on parameter-shift rules or sampling-based gradient estimation. Here we propose a bosonic quantum neural network based on parametrically coupled Gaussian modes. Although the underlying quantum dynamics are linear, nonlinear output features are generated through Fock-basis measurements. Because Gaussian evolution can be efficiently simulated in the Heisenberg representation, the system admits gradient-based optimization by differentiating a classical model of the dynamics, while the forward evolution itself could be implemented on quantum hardware. This hybrid approach enables end-to-end training of physically meaningful parameters without requiring gradient extraction from the experimental device. Such architectures are naturally compatible with circuit quantum electrodynamics platforms featuring tunable parametric couplers, as well as integrated photonic systems with engineered χχχ(2) or χχχ(3) nonlinearities. Our results demonstrate that linear bosonic networks combined with nonlinear measurement provide a scalable and trainable route toward experimentally realizable quantum neural networks.