arXiv subjects

Pablo Rodriguez-Grasa

Publications and source records attributed to Pablo Rodriguez-Grasa.

9 recordsLinked to original sources

arXiv2026

Quantum Hamiltonian Evolution for Coherent Quantum Learning

We introduce Coherent Quantum Learning (CQL), a training framework for quantum learning models in which the model parameters are quantum degrees of freedom evolved under a Hamiltonian that encodes the loss function. Current quantum machine learning retains classical optimization: parameters are updated by a classical outer loop using gradient estimates from measurements, and quantum coherence has no role in the training dynamics, just as in any classical treatment of the same problem. In the quantum case, a parameter register initialized in superposition evolves unitarily, and probability amplitude concentrates near low-loss configurations through interference, without gradient computation or classical feedback. We give an explicit construction using block encodings and Hamiltonian simulation, applicable to arbitrary parameterized circuits. Numerical experiments on binary classification and interferometric phase estimation confirm that the evolved distribution peaks at the optimal parameters, matching gradient-based performance. The construction is compatible in principle with fault-tolerant implementations and extends to batched training via sequential Hamiltonian evolution.

quant-ph↗

arXiv2026

Qutrit-Based Neural Quantum Kernels for Classification Tasks

Neural quantum kernels (NQKs) construct quantum kernels by pretraining a quantum neural network (QNN) and subsequently reusing the trained circuit as a task-adapted embedding. Extending this framework to qudits, with local unitaries in $\mathrm{SU}(d)$, provides a natural route to richer data embeddings through the increased local degrees of freedom and a direct interface for multiclass classification via intrinsically multi-level quantum systems. In this work, focusing on qutrits ($d=3$), we extend NQKs to the qudit setting and perform a systematic study of key design choices, including the number of encoded features, the number of qutrits, the kernel construction (1-to-$n$ and $n$-to-$n$), and the parameterization of $\mathrm{SU}(3)$ unitaries. Across binary and three-class tasks on four benchmark datasets, qutrit NQKs improve over the corresponding QNN baselines in nearly all settings considered and can benefit from scaling both the feature budget and the system size, although the magnitude of these gains may saturate, is dataset-dependent, and depends on the chosen parameterization. In particular, an ablation over $\mathrm{SU}(3)$ parameterizations shows that the unitary representation can substantially impact both optimization behaviour and classifier performance. These findings highlight the potential of qudit-based quantum models not only as a straightforward generalization of qubit-based architectures, but also as a promising means to better exploit complex data structures in quantum machine learning.

quant-ph↗

arXiv2026

A PAC-Bayesian approach to generalization for quantum models

Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These capacity-based uniform bounds are often too loose and entirely insensitive to the actual training and learning process. Previous theoretical guarantees have failed to provide non-uniform, data-dependent bounds that reflect the specific properties of the learned solution rather than the worst-case behavior of the entire hypothesis class. To address this limitation, we derive the first PAC-Bayesian generalization bounds for a broad class of quantum models by analyzing layered circuits composed of general quantum channels, which include dissipative operations such as mid-circuit measurements and feedforward. Through a channel perturbation analysis, we establish non-uniform bounds that depend on the norms of learned parameter matrices; we extend these results to symmetry-constrained equivariant quantum models; and we validate our theoretical framework with numerical experiments. This work provides actionable model design insights and establishes a foundational tool for a more nuanced understanding of generalization in quantum machine learning.

quant-ph↗

arXiv2025

Pulsed learning for quantum data re-uploading models

While Quantum Machine Learning (QML) holds great potential, its practical realization on Noisy Intermediate-Scale Quantum (NISQ) hardware has been hindered by the limitations of variational quantum circuits (VQCs). Recent evidence suggests that VQCs suffer from severe trainability and noise-related issues, leading to growing skepticism about their long-term viability. However, the possibility of implementing learning models directly at the pulse-control level remains comparatively unexplored and could offer a promising alternative. In this work, we formulate a pulse-based variant of data re-uploading, embedding trainable parameters directly into the native system's dynamics. We benchmark our approach on a simulated superconducting transmon processor with realistic noise profiles. The pulse-based model consistently outperforms its gate-based counterpart, exhibiting higher test accuracy and improved generalization under equivalent noise conditions. Moreover, by systematically increasing noise strength, we show that pulse-level implementations retain higher fidelity for longer, demonstrating enhanced resilience to decoherence and control errors. These results suggest that pulse-native architectures, though less explored, may offer a viable and hardware-aligned path forward for practical QML in the NISQ era.

quant-ph↗

arXiv2025

Neutrino Telescope Event Classification on Quantum Computers

Quantum computers represent a new computational paradigm with steadily improving hardware capabilities. In this article, we present the first study exploring how current quantum computers can be used to classify different neutrino event types observed in neutrino telescopes. We investigate two quantum machine learning approaches, Neural Projected Quantum Kernels (NPQKs) and Quantum Convolutional Neural Networks (QCNNs), and find that both achieve classification performance comparable to classical machine learning methods across a wide energy range. By introducing a moment-of-inertia-based encoding scheme and a novel preprocessing approach, we enable efficient and scalable learning with large neutrino astronomy datasets. Tested on both simulators and the IBM Strasbourg quantum processor, the NPQK achieves a testing accuracy near 80%, with robust results above 1 TeV and close agreement between simulation and hardware performance. A simulated QCNN achieves a ~70% accuracy over the same energy range. These results underscore the promise of quantum machine learning for neutrino astronomy, paving the way for future advances as quantum hardware matures.

hep-ex↗

arXiv2024

Satellite image classification with neural quantum kernels

Achieving practical applications of quantum machine learning for real-world scenarios remains challenging despite significant theoretical progress. This paper proposes a novel approach for classifying satellite images, a task of particular relevance to the earth observation (EO) industry, using quantum machine learning techniques. Specifically, we focus on classifying images that contain solar panels, addressing a complex real-world classification problem. Our approach begins with classical pre-processing to reduce the dimensionality of the satellite image dataset. We then apply neural quantum kernels (NQKs)-quantum kernels derived from trained quantum neural networks (QNNs)-for classification. We evaluate several strategies within this framework, demonstrating results that are competitive with the best classical methods. Key findings include the robustness of or results and their scalability, with successful performance achieved up to 8 qubits.

quant-ph↗

arXiv2024

Neural quantum kernels: training quantum kernels with quantum neural networks

Quantum and classical machine learning have been naturally connected through kernel methods, which have also served as proof-of-concept for quantum advantage. Quantum embeddings encode classical data into quantum feature states, enabling the construction of embedding quantum kernels (EQKs) by measuring vector similarities and projected quantum kernels (PQKs) through projections of these states. However, in both approaches, the model is influenced by the choice of the embedding. In this work, we propose using the training of a quantum neural network (QNN) to construct neural quantum kernels: both neural EQKs and neural PQKs, which are problem-inspired kernels. Unlike previous methods in the literature, our approach requires the kernel matrix to be constructed only once. We present several strategies for constructing neural quantum kernels and propose a scalable method to train an $n$-qubit data re-uploading quantum neural network (QNN). We provide numerical evidence of the performance of these models under noisy conditions. Additionally, we demonstrate how neural quantum kernels can alleviate exponential concentration and enhance generalization capabilities compared to problem-agnostic kernels, positioning them as a scalable and robust solution for quantum machine learning applications.

quant-ph↗

arXiv2023

Quantum approximated cloning-assisted density matrix exponentiation

Classical information loading is an essential task for many processing quantum algorithms, constituting a cornerstone in the field of quantum machine learning. In particular, the embedding techniques based on Hamiltonian simulation techniques enable the loading of matrices into quantum computers. A representative example of these methods is the Lloyd-Mohseni-Rebentrost protocol, which efficiently implements matrix exponentiation when multiple copies of a quantum state are available. However, this is a quite ideal set up, and in a realistic scenario, the copies are limited and the non-cloning theorem prevents from producing more exact copies in order to increase the accuracy of the protocol. Here, we propose a method to circumvent this limitation by introducing imperfect quantum copies, which significantly improve the performance of the LMR when the eigenvectors are known.

quant-ph↗

arXiv2023

Efficient quantum amplitude encoding of polynomial functions

Loading functions into quantum computers represents an essential step in several quantum algorithms, such as quantum partial differential equation solvers. Therefore, the inefficiency of this process leads to a major bottleneck for the application of these algorithms. Here, we present and compare two efficient methods for the amplitude encoding of real polynomial functions on $n$ qubits. This case holds special relevance, as any continuous function on a closed interval can be uniformly approximated with arbitrary precision by a polynomial function. The first approach relies on the matrix product state representation. We study and benchmark the approximations of the target state when the bond dimension is assumed to be small. The second algorithm combines two subroutines. Initially we encode the linear function into the quantum registers with a shallow sequence of multi-controlled gates that loads the linear function's Hadamard-Walsh series, exploring how truncating the Hadamard-Walsh series of the linear function affects the final fidelity. Applying the inverse discrete Hadamard-Walsh transform transforms the series coefficients into an amplitude encoding of the linear function. Then, we use this construction as a building block to achieve a block encoding of the amplitudes corresponding to the linear function on $k_0$ qubits and apply the quantum singular value transformation that implements a polynomial transformation to the block encoding of the amplitudes. This unitary together with the Amplitude Amplification algorithm will enable us to prepare the quantum state that encodes the polynomial function on $k_0$ qubits. Finally we pad $n-k_0$ qubits to generate an approximated encoding of the polynomial on $n$ qubits, analyzing the error depending on $k_0$. In this regard, our methodology proposes a method to improve the state-of-the-art complexity by introducing controllable errors.

quant-ph↗