arXiv subjects

André J. Ferreira-Martins

Publications and source records attributed to André J. Ferreira-Martins.

4 recordsLinked to original sources

arXiv2026

Scalable Message-Passing Quantum Graph Neural Networks in the Weisfeiler-Leman Hierarchy

Graphs provide a natural language for relational data in chemistry, biology and optimisation. Graph neural networks (GNNs) have driven much of the recent progress in learning from such data through message passing, a single primitive that generalises convolution and attention. Quantum counterparts have been proposed, but with limited connection to message passing and few guarantees on performance or scalability. More broadly, the trainability of variational quantum circuits is a recognised bottleneck for their wide applicability, and pre-training has emerged as one way to address it. Yet for a quantum model to be useful, it must offer expressivity guarantees along with demonstrable scalability. Here we show how a quantum graph neural network can be built to perform message passing, to be permutation equivariant, and to sit at a chosen level of the Weisfeiler-Leman hierarchy, the standard measure of how finely a model can tell graphs apart. We show that, as for classical GNNs, the training can be done first on small graph instances, allowing for a pre-training that can mitigate usual training issues, and its output can be read out at a cost that stays low as the graph grows. We validate the framework in large-scale simulations of up to 56 qubits across three datasets, on synthetic graphs that ordinary message passing cannot separate, on molecular property prediction, and on the travelling salesperson problem. Our framework opens a path for near-term quantum algorithms with theoretical guarantees and practical scalability, bringing the principles of graph learning into quantum circuit design.

quant-ph↗

arXiv2026

Quantum optimization with exact geodesic transport

We introduce an architecture for variational quantum algorithms that can be efficiently trained via parameter updates along exact geodesics on the Riemannian state manifold. This features a parameter-optimal circuit ansatz which supersedes known quantum natural gradient methods by removing expensive estimations of the metric tensor and provably reducing gradient estimation costs by $62.5\%$. Moreover, the framework also naturally incorporates conjugate gradients as a built-in feature, giving an accelerated descent method with convergence guarantees that we dub exact geodesic transport with conjugate gradients. Numerical benchmarks against state-of-the-art variational methods for ground-state preparation of molecular Hamiltonians or $1$-dimensional spin chains (both with and without particle-number conservation) up to $n=16$ qubits show reductions of over one order of magnitude in the number of optimization steps, with global convergence even for degenerate cases and competitive quantum-resource scalings. In addition, we perform proof-of-principle demonstrations on IonQ's Forte quantum processor, showcasing deployment of pre-trained circuits for the $H_{3}^{+}$ molecule and experimental training for $H_{2}$. Our work enables quantum machine learning applications with shorter training runtime, with implications at the interface of quantum simulation, differential geometry, and optimal control theory.

quant-ph↗

arXiv2024

Improved Financial Forecasting via Quantum Machine Learning

Quantum algorithms have the potential to enhance machine learning across a variety of domains and applications. In this work, we show how quantum machine learning can be used to improve financial forecasting. First, we use classical and quantum Determinantal Point Processes to enhance Random Forest models for churn prediction, improving precision by almost 6%. Second, we design quantum neural network architectures with orthogonal and compound layers for credit risk assessment, which match classical performance with significantly fewer parameters. Our results demonstrate that leveraging quantum ideas can effectively enhance the performance of machine learning, both today as quantum-inspired classical ML solutions, and even more in the future, with the advent of better quantum hardware.

q-fin.ST↗

arXiv2023

Detecting quantum phase transitions in a frustrated spin chain via transfer learning of a quantum classifier algorithm

The classification of phases and the detection of phase transitions are central and challenging tasks in diverse fields. Within physics, it relies on the identification of order parameters and the analysis of singularities in the free energy and its derivatives. Here, we propose an alternative framework to identify quantum phase transitions. Using the axial next-nearest neighbor Ising (ANNNI) model as a benchmark, we show how machine learning can detect three phases (ferromagnetic, paramagnetic, and a cluster of the antiphase with the floating phase). Employing supervised learning, we demonstrate the feasibility of transfer learning. Specifically, a machine trained only with nearest-neighbor interactions can learn to identify a new type of phase occurring when next-nearest-neighbor interactions are introduced. We also compare the performance of common classical machine learning methods with a version of the quantum nearest neighbors (QNN) algorithm.

quant-ph↗