The paper develops a theoretical framework for quantum extreme learning machines (QELMs) using the Pauli transfer matrix (PTM) formalism. It shows how encoding, reservoir dynamics, and measurement observables jointly determine the nonlinear information processing capacity of a QELM, and provides interpretable diagnostics that can guide model design. The authors apply their analysis to forecasting nonlinear dynamical systems, demonstrating that a trained QELM’s readout closely reproduces the underlying flow map at leading orders.
arXiv:2608. 19306v1 Announce Type: cross Abstract: Given a set of input states, we consider the task of predicting the expectation value of a Pauli observable at the output of an unknown quantum evolution, using only a limited number of measurements.
The paper introduces task‑resolved Fisher spectroscopy for quantum reservoir computing, defining orthonormal score coordinates from prediction targets that reweight labeled histories to produce an affine family of reservoir states and measurement outcomes. It establishes a Fisher‑information hierarchy linking state quantum Fisher information, measurement record Fisher information, and moment matrices up to many‑body order, providing a quadratic form that equals the stationary capacity of the optimal linear readout. The method requires only stationary labeled records and measured outcomes, enabling predictions of held‑out capacities, necessary feature order, and measurement‑budget dependence, and demonstrates how optimizing local measurement axes can recover hidden task information in a five‑spin open reservoir.
arXiv:2607. 22516v1 Announce Type: cross Abstract: A central design principle in modern machine learning and artificial intelligence is to align a model's inductive bias with the structure of its input data.
arXiv:2607. 07978v1 Announce Type: cross Abstract: Quantum reservoir computing uses a fixed quantum circuit as a feature generator and trains only a simple linear readout on top of it.
arXiv:2606. 31536v1 Announce Type: new Abstract: As Quantum Machine Learning (QML) transitions toward practical implementation, the field faces a critical architectural bottleneck that challenges the fundamental assumptions of classical statistical learning theory.
The paper derives a closed‑form expression for the reduced quantum channel of a single‑qubit Interactive Quantum Classifier (IQC), revealing that Hamiltonian parameters directly control the constant, sine, and cosine components of the classifier output. This Fourier interpretation motivates a generalized family of Hamiltonian encodings, including matrix‑parameterized environmental Hamiltonians that produce non‑separable Fourier structures. Numerical experiments on synthetic and real‑world datasets demonstrate that these generalized encodings improve classification performance on several nonlinear benchmarks, with a simpler four‑parameter extension achieving comparable results with fewer trainable parameters.
arXiv:2607. 21688v1 Announce Type: cross Abstract: Machine-learning surrogates of physical systems face a paradox: explainable models facing the challenge of expressivity to capture complex nonlinear flows, whereas expressive deep surrogates match high-fidelity simulations only through massive parameterisations that turn the learned dynamics into a black box.
arXiv:2609.00372v1 Announce Type: cross Abstract: With quantum sensors, simulators and networks emerging, a future of quantum technology may produce quantum states as data---that is, coherently rathe...
arXiv:2607. 05000v1 Announce Type: cross Abstract: Canonical quantization provides a systematic procedure for constructing quantum models from classical Hamiltonians.
arXiv:2607. 16281v1 Announce Type: cross Abstract: The analysis of highly non-linear stochastic data within non-equilibrium dynamical systems requires computational frameworks capable of detecting latent phase transitions before systemic structural breakdowns occur.
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.
Quantum Neural Networks (QNNs) are a promising framework for quantum machine learning on near-term quantum devices, but their security risks remain insufficiently understood. Studies have shown that QNNs are vulnerable to backdoor attacks, yet existing quantum backdoors mostly rely on a fixed trigger shared by all poisoned inputs.