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.
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.
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.
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.
Quantum reservoir computing (QRC) uses fixed quantum dynamics as a high-dimensional temporal feature map and trains only a lightweight classical readout. QRC is attractive for near-term quantum machine learning, but its performance depends strongly on architecture choices such as input encoding, reservoir depth, entanglement topology, measurement features, state-reset policy, feature construction, and readout regularization. We introduce \method, a simulator-based benchmark that formulates QRC design as constrained black-box architecture search and evaluates whether large language models can act as proposal controllers for this search problem. The benchmark compares five policies under identical evaluation budgets: random search, evolutionary search, Bayesian/TPE optimization, a feedback-based LLM agent, and \hybrid, which combines LLM proposals with memory, mutation, crossover, duplicate avoidance, and exploration. On NARMA10, Mackey-Glass forecasting, and temporal parity, \hybrid{} is the most consistent policy: it ranks first on NARMA10 and temporal parity and second on Mackey-Glass, narrowly behind evolutionary search. Under a 25-evaluation budget and three seeds, \hybrid{} improves over random search on all tasks, including a 23.6\% relative reduction in Mackey-Glass error. The results do not show that LLMs are universal QRC optimizers; rather, they show that generative models can be useful high-level controllers when embedded inside validated, reproducible hybrid search loops.
Reservoir computing promises a fast method for handling large amounts of temporal data. This hinges on constructing a good reservoir--a dynamical system capable of transforming inputs into a high-dimensional representation while remembering properties of earlier data. In this work, we introduce a reservoir based on recurrent quantum feature maps where a fixed quantum circuit is reused to encode both current inputs and a classical feedback signal derived from previous outputs. We evaluate the model on the Mackey-Glass time-series prediction task using our recently introduced CP feature map, and find that it achieves lower mean squared error than standard classical baselines, including echo state networks and multilayer perceptrons, while maintaining compact circuit depth and qubit requirements. We further analyze memory capacity and show that the model effectively retains temporal information, consistent with its forecasting accuracy. Finally, we study the impact of realistic noise and find that performance is robust to several noise channels but remains sensitive to two-qubit gate errors, identifying a key limitation for near-term implementations.
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.
Quantum reservoir computing (QRC) uses the dynamics of a fixed or weakly tuned quantum system to transform temporal and sequential inputs into measured features, while training is typically confined to a classical readout. This separation reduces reliance on repeated quantum parameter updates and avoids the barren plateaus associated with variational circuit training. Its computational power is often attributed to the exponentially large Hilbert space of the quantum system. However, the memory, nonlinearity, and expressivity that determine what a reservoir can actually compute depend jointly on the input encoding, quantum evolution, observables, measurement, and readout, not on Hilbert space dimension alone. On hardware, these capabilities are further constrained by finite sampling, hardware noise, measurement backaction, and the cost of estimating observables, so a large state space alone does not guarantee useful computation. In this survey, we develop a common system model that connects these components and use it to organize QRC foundations, computational properties, reservoir architectures, operating protocols, and physical implementations. We examine spin, photonic, superconducting, bosonic, neutral atom, and other analog platforms, together with applications, software and high performance computing support, benchmarking, and reproducibility. The analysis distinguishes hardware demonstrations from simulations and identifies the assumptions and resources that govern comparisons across implementations. Current results do not establish a broad quantum advantage over well matched classical reservoirs. We therefore specify the resource accounting, benchmark standards, and theoretical criteria needed to evaluate claims of quantum advantage.