Large-scale quantum reservoir learning with an analog quantum computer

TL;DR

This work tackles the scalability and trainability bottlenecks of quantum machine learning by proposing a gradient-free quantum reservoir computing (QRC) framework implemented on a neutral-atom analog quantum computer. The approach co-designs data encodings with the Rydberg Hamiltonian dynamics, yielding embeddings from measurements that train with simple linear models, while assessing uncertainty through shot and data resampling. Key contributions include experimental demonstration of learning up to 108 qubits, validation of a universal parameter regime where performance is robust to hyperparameters, and evidence of comparative quantum kernel advantage via kernel-geometry analyses on both real and synthetic data. The results underscore the potential of quantum reservoir embeddings to access classically intractable quantum correlations for practical ML tasks, with implications for future hardware platforms and hybrid quantum-classical learning paradigms.

Abstract

Quantum machine learning has gained considerable attention as quantum technology advances, presenting a promising approach for efficiently learning complex data patterns. Despite this promise, most contemporary quantum methods require significant resources for variational parameter optimization and face issues with vanishing gradients, leading to experiments that are either limited in scale or lack potential for quantum advantage. To address this, we develop a general-purpose, gradient-free, and scalable quantum reservoir learning algorithm that harnesses the quantum dynamics of neutral-atom analog quantum computers to process data. We experimentally implement the algorithm, achieving competitive performance across various categories of machine learning tasks, including binary and multi-class classification, as well as timeseries prediction. Effective and improving learning is observed with increasing system sizes of up to 108 qubits, demonstrating the largest quantum machine learning experiment to date. We further observe comparative quantum kernel advantage in learning tasks by constructing synthetic datasets based on the geometric differences between generated quantum and classical data kernels. Our findings demonstrate the potential of utilizing classically intractable quantum correlations for effective machine learning. We expect these results to stimulate further extensions to different quantum hardware and machine learning paradigms, including early fault-tolerant hardware and generative machine learning tasks.

Figures (11)

• Figure 1: Overview of the quantum reservoir computing (QRC) algorithm with neutral atoms. The QRC algorithm pipeline contains three steps -- classical preprocessing (left), quantum reservoir (center), and classical postprocessing and prediction (right). In the preprocessing step, data features are brought into a form readily encoded to the neutral-atom analog quantum computer. They may require optional dimensional reduction for high-dimensional data (such as images, top) or feature engineering and selection (such as data windowing for timeseries, bottom). The encoding of the data features proceeds by three methods, i.e, encoding into the time profile of the global detuning pulse, the interaction strengths by atom position modulation, and the local pattern of the detuning pulse. The quantum system serving as the reservoir is then evolved over varying time periods and probed through repeated projective measurements. In the third step, the measurement outputs are processed classically to provide expectation values of local observables that form a set of QRC embeddings. The embeddings are subsequently used as inputs to a simple and fast classical training step, for which we typically employ linear support vector machines or regression. The trained models are tested and used for inference by processing additional data through the QRC pipeline and evaluating classical outputs based on obtained embeddings.
• Figure 2: Timeseries prediction with QRC and encoding performance comparison. (a) The pipeline for global pulse encoding timeseries prediction with QRC. The dataset chosen is a part of the Santa Fe laser timeseries Weigend1993-bg, with feature vectors constructed by sliding windows and the task set to one-step prediction. The profile of the window feature is encoded into the piecewise linear global detuning pulse. The select local observables obtained by probing the quantum evolution are shown for exact simulation and experiment, with the vertical axis corresponding to different embedding components and the horizontal to the timeseries steps. (b) An example of test outcomes predicted by local pulse encoded QRC with 12 qubits, compared to the equivalent finite-sampled simulation (110 shots per datapoint) and the true outcomes. (c) Comparison of the normalized mean-square error (NMSE, lower is better) for three different QRC encodings in finite-sampled simulation and experiment.
• Figure 3: Image classification with QRC and qubit number scaling. (a) The MNIST Deng2012 images of handwritten digits are downsampled to feature vectors that are encoded into the modulation of the nearest neighbor Rydberg interaction strengths via the position encoding. The quantum reservoir consists of parallel, well-separated neutral-atom chains evolving under the Rydberg Hamiltonian. The equivalent classical spin reservoir (CRC), where the vector spins precess in the external and neighbor magnetic field, is simulated for comparison. (b) The test classification accuracy of several classical machine learning methods and QRC on the 3/8-MNIST binary classification tasks. (c) The test accuracy of QRC simulation and experiment as a function of the number of shots drawn per datapoint, $N_s$, for the 10-class MNIST classification task. (d) The QRC performance scaling with the number of qubits was probed on the tomato disease task, with three classes selected from the plant village dataset hughes2016tomato. The data features, the pixel values of the downscaled images of different sizes, were encoded in the vertical interaction strengths of a 2D atom array. An example experimental image of the position-encoded atom array is shown, together with one measurement shot after the quantum reservoir dynamics. (e) The test accuracy as a function of the qubit number, $N_q$, or the equivalent feature dimension, for the QRC performed on the experiment, linear SVM, and 4-layer feedforward neural network.
• Figure 4: Comparative quantum kernel advantage with QRC. (a) The test classification accuracy of the QRC and CRC methods on the original 3/8 binary MNIST classification and the synthetic task constructed with kernel geometry. (b) Test accuracy difference between QRC and CRC on the synthetic 3/8-binary task as a function of the number of measurements drawn per datapoint for simulation, experiment with synthetic data constructed from experimental data, and experiment with synthetic data constructed from simulation.
• Figure 5: Proof of concept neutral-atom QRC implementation in numerical simulations. The 10-class MNIST handwritten digit classification dataset was used to gauge QRC performance in numerical simulations. The image data was downsampled with principal component analysis (PCA) and encoding through local pulse and position encodings to a linear neutral-atom chain. (a) Test classification accuracy of the local pulse encoded QRC and several classical models as a function of PCA encoding dimension (or equivalently, qubit number, $N_q$). Comparison between QRC that uses both single- and two-site- local operator expectation values and single-site-only approach is also presented. (b) The test accuracy of the position-encoded QRC and several classical methods as the function of the PCA encoding dimension. (c) The scaling of local pulse encoded QRC with the number of shots drawn per datapoint ($N_s$) for several system sizes. (d) Test accuracy of local pulse encoded QRC as a function of qubit number for several $N_s$.