The quantum extreme reservoir computation (QERC) is a versatile quantum neural network model that combines the concepts of extreme machine learning with quantum reservoir computation. Key to QERC is the generation of a complex quantum reservoir (feature space) that does not need to be optimized for different problem instances. Originally, a periodically driven system Hamiltonian dynamics was employed as the quantum feature map. In this work we capture how the quantum feature map is generated as the number of time-steps of the dynamics increases by a method to characterize unitary matrices in the form of weighted networks. Furthermore, to identify the key properties of the feature map that has sufficiently grown, we evaluate it with various weighted network models that could be used for the quantum reservoir in image classification situations. At last, we show how a simple Hamiltonian model based on a disordered discrete time crystal with its simple implementation route provides nearly optimal performance while removing the necessity of programming of the quantum processor gate by gate.
The quantum extreme reservoir computation (QERC) is a versatile quantum neural network model that combines the concepts of extreme machine learning with quantum reservoir computation. Key to QERC is the generation of a complex quantum reservoir (feature space) that does not need to be optimized for different problem instances. Originally, a periodically driven system Hamiltonian dynamics was employed as the quantum feature map. In this work we capture how the quantum feature map is generated as the number of time-steps of the dynamics increases by a method to characterize unitary matrices in the form of weighted networks. Furthermore, to identify the key properties of the feature map that has sufficiently grown, we evaluate it with various weighted network models that could be used for the quantum reservoir in image classification situations. At last, we show how a simple Hamiltonian model based on a disordered discrete time crystal with its simple implementation route provides nearly optimal performance while removing the necessity of programming of the quantum processor gate by gate.
It is well known in quantum machine learning that the form of the feature map has a significant effect on the operation and performance of those tasks being undertaken. It is essential to investigate how to generate an effective feature map within the limitations of the number of qubits and quantum gates to apply in noisy intermediate-scale quantum devices. In this paper, we explore how the qubit connectivity impacts the performance of quantum extreme reservoir computation (QERC) for image classification using the Hamiltonian. We find that networks of qubits with simple connectivity generate an effective feature map, whereas a network with high connectivity does not since the Hamiltonian on it yields a unitary map with a periodic property. The existence of the periodicity can be fully determined by the underlying connectivity and the overall symmetry of the Hamiltonian. However, the symmetries in the Hamiltonians can contribute to a better generalization for QERC. We further find that it is possible to design QERC to give this high generalization property while maintaining high accuracy. Our work suggests that Hamiltonian dynamics with simple connectivity or symmetry can be exploited as a computational resource in quantum machine learning.
It is well known in quantum machine learning that the form of the feature map has a significant effect on the operation and performance of those tasks being undertaken. It is essential to investigate how to generate an effective feature map within the limitations of the number of qubits and quantum gates to apply in noisy intermediate-scale quantum devices. In this paper, we explore how the qubit connectivity impacts the performance of quantum extreme reservoir computation (QERC) for image classification using the XY Hamiltonian. We find that networks of qubits with simple connectivity generate an effective feature map, whereas a network with high connectivity does not since the XY Hamiltonian on it yields a unitary map with a periodic property. The existence of the periodicity can be fully determined by the underlying connectivity and the overall symmetry of the Hamiltonian. However, the symmetries in the XY Hamiltonians can contribute to a better generalization for QERC. We further find that it is possible to design QERC to give this high generalization property while maintaining high accuracy. Our work suggests that Hamiltonian dynamics with simple connectivity or symmetry can be exploited as a computational resource in quantum machine learning.
Today's quantum processors composed of fifty or more qubits have allowed us to enter a computational era where the output results are not easily simulatable on the world's biggest supercomputers. What we have not seen yet, however, is whether or not the complexity achievable with such quantum processors would ever be useful for any practical applications. In the quantum neural network approach, there has been an expectation that the Hilbert space can serve as a computational resource by providing a large feature space; however, it is not understood, nor illustrated in what way the Hilbert space provides that computational power. In this work we introduce a resource-efficient quantum neural network model with a focus on the role of the feature space the quantum processors can give. Then we apply it for classification tasks, showing a quantum advantage in terms of the physical resources needed to realize the neural network. To facilitate the Hilbert space as a large feature space, we utilize scale-free networks that can be generated in a discrete-time crystal model. The virtue of this approach is in both its theoretical simplicity and its practical applicability: our quantum neural network model is simple enough to identify the role of the Hilbert space as the feature space, and, furthermore, can be implemented with current technology. Our model does not require optimization of the quantum processor, and hence once the quantum processor has been set, it can be used for other different classification problems without any changes in the quantum processor itself.
Quantum machine learning (QML) is expected to offer new opportunities to process high-dimensional data efficiently by exploiting the exponentially large state space of quantum systems. In this work, we apply quantum extreme reservoir computing (QERC) to the classification of microstructure images of polymer alloys generated using self-consistent field theory (SCFT). While previous QML efforts have primarily focused on benchmark datasets such as MNIST, our work demonstrates the applicability of QERC to engineering data with direct materials relevance. Through numerical experiments, we examine the influence of key computational parameters-including the number of qubits, sampling cost (the number of measurement shots), and reservoir configuration-on classification performance. The resulting phase classifications are depicted as phase diagrams that illustrate the phase transitions in polymer morphology, establishing an understandable connection between quantum model outputs and material behavior. These results illustrate QERC performance on realistic materials datasets and suggest practical guidelines for quantum encoder design and model generalization. This work establishes a foundation for integrating quantum learning techniques into materials informatics.
Quantum Extreme Reservoir Computing (QERC) has been proposed for machine learning on near-term quantum processors. We audit static and temporal QERC against matched, equally tuned classical baselines, following a protocol committed to version control before test-set evaluation. We reproduce the canonical MNIST baseline (N = 10, D = 1024) with test accuracy 0.9688 (published: 0.970). On compact MNIST (N = 6, n_train = 1000), the disordered quantum reservoir exceeds tuned random Fourier features (C-RFF, within the specified search grid) by +3.87 pp (95% CI [+2.69, +5.12]) and shows no significant difference from tuned tanh features (-0.38 pp, 95% CI [-1.07, +0.58]), while parameter-free cosine encoding, raw PCA features and a trained SVM reach higher mean accuracy. The C-RFF gap depends on its selected scale sitting at the lower grid boundary (on an exploratory extended grid it shrinks to +0.33 pp, 95% CI [-0.62, +1.48]), and on MNIST at N = 10 tuned tanh features are significantly more accurate than the reservoir (delta = -0.94 pp, 95% CI [-1.36, -0.45]). In the canonical regime on MNIST, C-RFF is 0.83 pp more accurate than R-CAN-ZZ: the pre-specified superiority hypothesis for R-CAN-ZZ is not supported, although the difference lies within a +/-1 pp equivalence margin. Static QERC has no delayed memory under an independent-input, reset-per-sample protocol; in the temporal density-matrix formulation and hyperparameter grids studied, a matched echo state network has higher memory capacity (8.457 vs 3.352) and lower NARMA10 error (0.304 vs 0.790) at D = 21.
Interest in quantum machine learning is growing due to its potential to offer more efficient solutions for problems that are difficult to tackle with classical methods. In this context, the research work presented here focuses on the use of quantum machine-learning techniques for image-classification tasks. We exploit a quantum extreme learning machine by taking advantage of its rich feature map provided by the quantum reservoir substrate. We systematically analyze different phases of the quantum extreme learning machine process, from dataset preparation to final image classification. In particular, we test different encodings, together with principal component analysis and the use of autoencoders, and we examine the dynamics of the model through the use of different Hamiltonians for the quantum reservoir. Our results show that the introduction of a quantum reservoir systematically improves the accuracy of the classifier. In addition, our findings indicate that variations in encoding methods can significantly influence performance and that Hamiltonians with distinct structures exhibit the same discrimination rate, depending on how their eigenstates are related to the encoding and measurement basis.