Quantum Reservoir Computing

Modeling the response of driven many-body quantum systems from input--output data is difficult: the dynamics are nonlinear, history dependent, and expensive to simulate as system size grows. A paradigmatic case is High-Harmonic Generation~(HHG), where a strong field drives a medium to emit radiation that is highly sensitive to the drive and encodes long-range temporal correlations. We introduce a dissipative quantum reservoir computing~(DQRC) framework that builds a digital twin of such a system, learning its input--output map directly from data while the reservoir---itself a small open quantum system---stays fixed and only a classical readout is trained. We show that a minimal single-qubit reservoir reproduces the HHG response of a substantially larger Ising spin chain, and on a representative benchmark matches and on several metrics surpasses previously reported temporal convolutional and Kolmogorov--Arnold-network models, while using a simpler, physically realizable system. A single fixed reservoir further generalizes across a broad range of drives, indicating that it learns a shared physical response structure rather than memorizing trajectories. These results establish dissipative quantum reservoirs as compact, physically grounded digital twins for nonlinear, memory-dependent quantum dynamics. Code is available at https://github.com/AI-and-Quantum-Computing/DQuRC.

Quantum reservoir computing (QRC) uses quantum dynamics to represent input histories for prediction through a trained classical readout. Discrete time crystals (DTCs) exhibit robust subharmonic responses under periodic driving, and previous work has used their dynamics to construct DTC-QRC. Here we construct a DTC-based reservoir architecture to predict molecular properties from structural and dynamical observations. Coherent Floquet evolution processes local molecular graph events and surface-hopping frames, while controlled reset regulates the contribution of earlier inputs. Measurements at the end of each input sequence yield a feature vector of fixed dimension. Trained classical decoders use this vector for inhibitor-activity and blood--brain-barrier permeability classification and electronic-gap forecasting, while the reservoir parameters remain fixed during training. With matched input lengths and output widths, DTC-QRC outperforms echo-state networks on long-prefix graph classification and the studied ethene gap forecasting tasks. Dephasing lowers performance in both applications, consistent with a role for coherent propagation. Experiments on the Quafu superconducting quantum cloud platform show that pair observables retain task information under device noise. The architecture provides a common framework for molecular screening and time-resolved property prediction using quantum reservoir computing.

Universal approximation in reservoir computing is typically associated with a class of reservoirs. We show that universality can be associated with a single reservoir, considering a minimal setup of a single atom in front of a mirror. In its linear-transducer limit, our reservoir is a universal approximator of fading-memory maps under an operating class of checkable conditions, with a rate constant measured at the operating point. A given reservoir can reach arbitrary accuracy by changing measurement settings. The proof gives an explicit recipe: for a target accuracy, it specifies the required physical resources and resonator modes. Enlarging the number of accessible modes increases the matchable kernel span without reducing capability. Beyond the linear limit, the atom's saturation replaces high-order polynomial readouts, and the device operates on real-world tasks alongside classical baselines. Our results highlight an example of universality with a minimal quantum setup.

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.

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.

This paper presents a unified quantum-classical hybrid framework for multi-horizon time-series forecasting, introducing two model variants Quantum Reservoir Forecaster (QRC-F) and Variational Quantum Forecaster (VQF-F). The proposed framework investigates the complexity-fidelity trade-off of quantum forecasting under near-term NISQ hardware constraints. Continuous time-series signals are transformed into binary representations through uniform quantization and encoded into quantum states using angle encoding with parameterized RY rotation gates. Cross-channel entanglement layers capture dependencies among multiple variables. QRC-F utilizes a fixed random unitary quantum reservoir for stable, gradient-free temporal feature extraction, whereas VQF-F employs a trainable variational quantum circuit optimized through the parameter-shift rule to learn temporal and inter-variable patterns from Pauli expectation values. Both models replace computationally expensive quadratic self-attention with efficient linear transformations, reducing parameter complexity. A shared MIMO-based multi-horizon prediction head simultaneously generates forecasts across multiple horizons, avoiding error accumulation in recursive forecasting. Experimental evaluations on benchmark datasets, including ETTh1, ETTh2, ETTm1, ETTm2, Weather, electricity, and exchange-rate, demonstrate that VQF-F achieves superior training stability and parameter efficiency, while QRC-F provides enhanced robustness and circuit fidelity under quantum noise. The results establish a practical quantum-native forecasting framework with strong potential for deployment on near-term NISQ devices.

Can a small quantum computer forecast a changing signal better than an ordinary classical method? Many studies say yes, but the classical methods they compare against are often left in a basic, untuned state while the quantum model is carefully optimised. We ask what happens when the classical competitor is given exactly the same care: the same size and the same amount of tuning effort. We study two popular reasons a quantum reservoir is thought to help, using exact simulations of small quantum systems (up to eleven qubits) on prediction tasks. In both cases the quantum advantage disappears once the comparison is fair. In the first, extra quantum measurements add nothing that a simple classical formula of the same size does not already provide. In the second, a feedback loop genuinely helps the quantum model, turning a useless setup into a working predictor, yet a well-tuned classical network still predicts slightly more accurately, and the gap is statistically reliable. Our point is not that quantum reservoirs can never win, but that two of their commonly cited advantages do not hold up against fair classical competitors at this scale. We provide these matched comparisons as a simple, reusable checklist for honest benchmarking. All results are fully reproducible from fixed random seeds.

Quantum reservoir computing uses a fixed quantum circuit as a feature generator and trains only a simple linear readout on top of it. This makes it cheap to train and free of the optimisation problems that affect many quantum machine-learning models. A natural worry is that the very large feature space the circuit produces might inflate apparent performance without adding anything real. This paper provides two things. First, it gives a complete, reproducible recipe for one such reservoir applied to forecasting chaotic systems, including how data is fed in, how the circuit is built, and how the readout is trained. Second, it gives a way to tell whether the reservoir's high dimension is actually doing useful work. We grow the size of the prediction problem and the size of the quantum reservoir together, so that extra capacity cannot be the explanation for any improvement, and we track a single stability number that measures how well behaved the readout fit is. On two chaotic test systems, a spatiotemporal chain and a shallow-water fluid model, the quantum reservoir keeps a flat, stable error as both sizes grow, while a matched classical reservoir does not. We report where the classical baseline is in fact stronger, so the comparison is honest. The result is a clean specification plus a diagnostic that other groups can apply to any reservoir whose features have a known scale.

Short-term load forecasting is essential for reliable energy management, but practical deployment on edge devices requires models that remain accurate under limited memory, finite measurement budgets, and hardware noise. This work proposes a hardware-efficient Quantum Reservoir Computing (QRC) framework for energy load forecasting, where a fixed quantum reservoir transforms temporal input windows into high-dimensional features and only a classical Elastic Net readout is trained. To reduce deployment cost, the trained readout is compressed using post-training fixed-point quantization at bit widths from 8 to 2 bits. The framework is evaluated on the Tetouan and Spain energy load datasets under exact statevector simulation, 512-shot finite sampling, and realistic hardware-noise models from IBM FakeTorino and IBM FakeMarrakesh. Results show that 6-bit readout precision preserves full-precision forecasting performance while reducing readout memory by 81.2%. Below this point, degradation becomes dataset dependent, with Tetouan showing stronger sensitivity and Spain degrading more gradually. Hardware-noise validation further shows that the trained readout transfers to noisy reservoir states without retraining. These findings support quantized QRC as a resource-aware forecasting approach for near-term quantum time-series applications.

In the field of quantum reservoir computing (QRC), many different computational models and architectures have been proposed. From these models, we identify feedback-based models -- which use a feedback mechanism to re-embed classical measurements from the QRC -- and recurrent models -- which use a multi-register approach with memory and readout qubits -- as the two major competing architectures that have been discussed and validated on hardware. In this paper, we advance upon the recurrent architectures, which employ a two register approach to endow the QRC with a fading memory. While these approaches have been validated on hardware and have demonstrated great real-world performance on noisy-intermediate-scale-quantum (NISQ) quantum processing units (QPUs), the exact mechanism through which the memory capacity arises is not completely understood or fully controllable. With this, we augment the recurrent approaches and present a hardware-realizable mechanism, which we call a tunable partial-SWAP, that allows for the direct control of the rate of memory dissipation from a QRN implemented on a gate-based QPU. The theory behind this mechanism is discussed in terms of a controlled amplitude-damping channel and validation experiments using a randomized short-term memory capacity (STMC) recall benchmark and the NARMA-5 dataset are conducted using simulation and IBM QPUs, respectively.

We introduce a hybrid quantum-classical pipeline, based on neutral-atom reservoir computing, for medical image classification, focusing on the binary classification task of polyp detection. To deal effectively with the high dimensionality, we integrate a guided auto-encoder. This pipeline learns compact and discriminative representations of image data that are also well-suited for quantum reservoir computing. A key challenge in such systems is the non-differentiable nature of quantum measurements, which creates a 'gradient barrier' for standard training. We overcome this barrier by incorporating a differentiable surrogate model that emulates the quantum layer, enabling end-to-end backpropagation through the entire system. This guided training process is jointly optimized for classification accuracy and for faithful image recovery from the auto-encoder. The learned latent representations are encoded as pulse detuning parameters within a Rydberg Hamiltonian, and quantum embeddings are subsequently obtained through expectation values. These embeddings are then passed to a linear classifier. Our simulations show that this method outperforms some traditional approaches that use PCA or unguided autoencoders. We also conduct ablation studies to assess the impact of various quantum and training parameters, demonstrating the robustness and flexibility of our proposed pipeline for real-world medical imaging applications, even in the current NISQ era.

Scrambling quantum systems have attracted attention as effective substrates for temporal information processing. Here we consider a quantum reservoir processing framework that captures a broad range of physical computing models with quantum systems. We examine the scalability and memory retention of the model with scrambling reservoirs modelled by high-order unitary designs in both noiseless and noisy settings. In the former regime, we show that measurement readouts become exponentially concentrated with increasing reservoir size, yet strikingly do not worsen with the reservoir iterations. Thus, while repeatedly reusing a small scrambling reservoir with quantum data might be viable, scaling up the problem size deteriorates generalization unless one can afford an exponential shot overhead. In contrast, the memory of early inputs and initial states decays exponentially in both reservoir size and reservoir iterations. In the noisy regime, we also prove that memory decays exponentially in time for local noisy channels. These results required us to introduce new proof techniques for bounding concentration in temporal quantum models. Beyond this extreme scrambling regime, we numerically demonstrate that exponential concentration can still exist even with a physical reservoir such as an Ising model whenever the reservoir operates in a quantum-chaotic phase. In contrast, physical reservoirs in a many-body localized phase and at the edge of chaos appear to not suffer from such phenomena