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arXiv:2609.29570

Task-Resolved Fisher Spectroscopy for Quantum Reservoir Computing

Yang Peng

quant-phcs.LGSubmitted Aug 26, 2026• Announced Aug 28, 2026• 0 citations
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Abstract

Quantum reservoir computing (QRC) uses fixed quantum dynamics to encode a time series and trains only a classical readout, but a benchmark capacity alone does not reveal whether task information is lost in the reservoir, the measurement, feature compression, or finite sampling. We introduce \emph{task-resolved Fisher spectroscopy}, in which prediction targets define orthonormal score coordinates on the stationary distribution of input histories. Reweighting labeled histories along these scores generates an exactly affine family of reservoir states and measurement outcomes. In the same coordinates, we obtain a many-body Fisher-information hierarchy relating the state quantum Fisher information, the Fisher information of the complete measurement record, and moment matrices retained through many-body order $r$. The quadratic form of each moment matrix is exactly the stationary capacity of the optimal linear readout, while a finite-measurement extension predicts the approach from one-shot records to ideal expectation-value features. The measurement-level quantities require only stationary labeled records and measured outcome strings, not an input model or quantum-state tomography. In a five-spin open reservoir, interactions route fourth-order temporal information into higher-body correlations, so low-order compression can incur orders-of-magnitude sampling overhead even when a conventional parity target remains accessible. For correlated inputs and outputs, record-defined task scores predict held-out capacities, the required feature order, and measurement-budget dependence; optimizing the local measurement axis recovers otherwise hidden task information. The framework connects benchmark performance to experimentally actionable diagnoses of reservoir encoding, measurement choice, classical representation, and shot allocation.

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18 pages, 11 figures

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Quantum reservoir computing (QRC) uses fixed quantum dynamics to encode a time series and trains only a classical readout, but a benchmark capacity alone does not reveal whether task information is lost in the reservoir, the measurement, feature compression, or finite sampling. We introduce \emph{task-resolved Fisher spectroscopy}, in which prediction targets define orthonormal score coordinates on the stationary distribution of input histories. Reweighting labeled histories along these scores generates an exactly affine family of reservoir states and measurement outcomes. In the same coordinates, we obtain a many-body Fisher-information hierarchy relating the state quantum Fisher information, the Fisher information of the complete measurement record, and moment matrices retained through many-body order rrr. The quadratic form of each moment matrix is exactly the stationary capacity of the optimal linear readout, while a finite-measurement extension predicts the approach from one-shot records to ideal expectation-value features. The measurement-level quantities require only stationary labeled records and measured outcome strings, not an input model or quantum-state tomography. In a five-spin open reservoir, interactions route fourth-order temporal information into higher-body correlations, so low-order compression can incur orders-of-magnitude sampling overhead even when a conventional parity target remains accessible. For correlated inputs and outputs, record-defined task scores predict held-out capacities, the required feature order, and measurement-budget dependence; optimizing the local measurement axis recovers otherwise hidden task information. The framework connects benchmark performance to experimentally actionable diagnoses of reservoir encoding, measurement choice, classical representation, and shot allocation.
Quantum reservoir computing processes temporal information through driven many-body dynamics, but its performance is ultimately limited by how accurately past inputs can be extracted from finite measurements. Here we formulate this limitation as a local multiparameter estimation problem and introduce a delay-space quantum Fisher information matrix to quantify the distinguishability of information stored at different delays. This perspective identifies Fisher-orthogonal memory as a measurement-efficient design principle: different delays should perturb the reservoir state along mutually Fisher-orthogonal directions. We first analyze the single-qubit limit using the Gill--Massar bound, revealing an optimal write-store-routing trade-off. Guided by this structure, we construct solvable multi-qubit reservoirs based on Clifford routing orbits and Singer-cycle Pauli algebra. The resulting dynamics yield diagonal delay-space QFIMs with analytically programmable fading profiles. Under finite-shot local Pauli readout, these reservoirs retain sharp memory windows that are absent in a validation-selected Ising baseline. Their product-task behavior is governed by second-order responses inherited from the same Pauli-routing algebra. Our results provide an analytically controlled route toward measurement-efficient quantum reservoir computing.
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The performance of a quantum reservoir computer in temporal processing tasks depends on how its driven quantum substrate retains information about past inputs, distributes it across physical degrees of freedom, and loses it through environmental dissipation and measurement feedback. We formulate these processes using a classical-quantum state obtained by restricting a reservoir process tensor to classical input encoding and single-time readout. Conditional subsystem Holevo quantities describe information about selected input histories and bound its accessibility to measurements on subsystems of the reservoir. In a six-qubit all-to-all transverse-field Ising reservoir, we find that the total stored information changes relatively little across Hamiltonian parameters, while its spatial distribution and temporal decay vary strongly. Effective diagnostics of these two behaviours identify different regions of high information-processing capacity for linear and higher-degree temporal tasks. Measurement-induced dephasing can improve noiseless task performance when it increases forgetting rates without strongly reducing information delocalisation. The framework separates storage from subsystem accessibility and provides a common description of information flow in driven quantum learning systems.
Reservoir computing (RC) is an effective method for predicting chaotic systems by using a high-dimensional dynamic reservoir with fixed internal weights, while keeping the learning phase linear, which simplifies training and reduces computational complexity compared to fully trained recurrent neural networks (RNNs). Quantum reservoir computing (QRC) uses the exponential growth of Hilbert spaces in quantum systems, allowing for greater information processing, memory capacity, and computational power. However, the original QRC proposal requires coherent injection of inputs multiple times, complicating practical implementation. We present a hybrid quantum-classical approach that implements memory through classical post-processing of quantum measurements. This approach avoids the need for multiple coherent input injections and is evaluated on benchmark tasks, including the chaotic Mackey-Glass time series prediction. We tested our model on two physical platforms: a fully connected Ising model and a Rydberg atom array. The optimized model demonstrates promising predictive capabilities, achieving a higher number of steps compared to previously reported approaches.
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.