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.
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 processors require rapid and high-fidelity simultaneous measurements of many qubits. While superconducting qubits are among the leading modalities toward a useful quantum processor, their readout remains a bottleneck. Traditional approaches to processing measurement data often struggle to account for crosstalk present in frequency-multiplexed readout, the preferred method to reduce the resource overhead. Recent approaches to address this challenge use neural networks to improve the state-discrimination fidelity. However, they are computationally expensive to train and evaluate, resulting in increased latency and poor scalability as the number of qubits increases. We present an alternative machine learning approach based on next-generation reservoir computing that constructs polynomial features from the measurement signals and maps them to the corresponding qubit states. This method is highly parallelizable, avoids the costly nonlinear activation functions common in neural networks, and supports real-time training, enabling fast evaluation, adaptability, and scalability. Despite its lower computational complexity, our reservoir approach is able to maintain high qubit-state-discrimination fidelity. Relative to traditional methods, our approach achieves error reductions of up to 50% and 11% on single- and five-qubit datasets, respectively, and delivers up to 2.5x crosstalk reduction on the five-qubit dataset. Compared with recent machine-learning methods, evaluating our model requires 100x fewer multiplications for single-qubit and 2.5x fewer for five-qubit models. This work demonstrates that reservoir computing can enhance qubit-state discrimination while maintaining scalability for future quantum processors.
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.
Quantum reservoir computing (QRC) has been proposed as a paradigm for performing machine learning with quantum processors where the training takes place in the classical domain, avoiding the issue of barren plateaus in parameterized-circuit quantum neural networks. It is natural to consider using a quantum processor based on microwave superconducting circuits to classify microwave signals that are analog—continuous in time. However, while there have been theoretical proposals of analog QRC, to date QRC has been implemented using the circuit model—imposing a discretization of the incoming signal in time. In this paper we show how a quantum superconducting circuit comprising an oscillator coupled to a qubit can be used as an analog quantum reservoir for a variety of classification tasks, achieving high accuracy on all of them. Our work demonstrates processing of ultra-low-power microwave signals within our superconducting circuit, a step towards achieving a quantum sensing-computational advantage on impinging microwave signals. Quantum reservoir computing might in principle give advantages in solving signal classification tasks, but current implementations usually incur in the digitalization bottleneck. Here, the authors demonstrate an implementation dealing directly with the analogue MW signals.
Reservoir computing leverages rich, non-linear dynamics to process temporal data. Quantum variants promise enhanced expressivity from high-dimensional Hilbert spaces, yet their practical applicability is hindered by hardware noise and concentration effects that can erase input-output distinguishability at large system sizes. In this work, we present and experimentally demonstrate a Quantum Extreme Learning Machine (QELM) tailored to state-of-the-art superconducting platforms, employing up to 124 qubits and circuits with more than 5,000 two-qubit gates on IBM Quantum computers. We introduce a practical multi-objective hyperparameter tuning strategy that jointly monitors observable variability, capacity, and task performance to identify noise-robust operating points. In addition, we develop a local eigentask analysis that enables computationally efficient feature selection and effective information retrieval. We report evidence of a regime of optimality that is identifiable at small scales and transferable across tasks and larger systems, and we achieve performances competitive with leading classical baselines on representative benchmarks for time-series forecasting and satellite image classification. Together, our results establish a viable and robust framework for large-scale, pre-fault-tolerant quantum machine learning and provide a foundation for extending reservoir-based methods to more expressive architectures and real-world scenarios.
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.
Quantum amplifiers are intrinsically nonlinear systems whose performance limits are set by quantum mechanics. In quantum measurement, amplifier operation is conventionally optimized in the linear regime by maximizing signal-to-noise ratio, an objective that is well-suited to parameter estimation but is typically insufficient for more general tasks such as arbitrary quantum state discrimination. Here we show that single-shot quantum state classification can benefit from operating a quantum amplifier outside the linear regime, when the measurement chain is optimized end-to-end for a task-specific cost function. We analyze a realistic superconducting readout architecture that includes state preparation, cryogenic nonlinear amplification, and room-temperature detection with finite noise. By introducing performance metrics tailored to state discrimination, we identify operating regimes in which nonlinear amplification provides a measurable advantage and clarify the trade-offs that ultimately limit classification fidelity. Building on these results, we propose a qubit readout architecture without cavity displacement that exploits nonlinear amplification to enhance single-shot state discrimination performance. Our results establish the practical value of nonlinear quantum amplifiers for quantum state discrimination and lay the foundation for a broader program to develop a general, end-to-end framework for resource-constrained optimization of nonlinear amplification in quantum information processing tasks.