arXiv subjects

Fernando M. de Paula Neto

Publications and source records attributed to Fernando M. de Paula Neto.

6 recordsLinked to original sources

arXiv2026

Fourier Analysis of Parametrized Interactive Quantum Classifiers

Interactive Quantum Classifiers (IQCs) constitute a family of quantum machine learning models inspired by open quantum systems, in which the interaction between a target qubit and an environment is described by a Hamiltonian. Previous works introduced alternative Hamiltonian parameterizations and showed empirically that they can improve classification performance, but the role of these parameters in the resulting classifier remains poorly understood. In this work, we derive a closed-form expression for the reduced quantum channel generated by a parametrized IQC with a single target qubit. The analytical solution explicitly reveals how the Hamiltonian parameters control the constant, sine, and cosine components of the classifier output, establishing a Fourier interpretation of the induced feature map. This analysis motivates a generalized family of Hamiltonian encodings, including matrix-parameterized environmental Hamiltonians whose Fourier components depend on linear combinations of input features, thereby enabling non-separable Fourier structures. Numerical experiments on synthetic and real-world datasets show that the proposed models can improve classification performance on several nonlinear benchmarks. The generalized matrix encoding achieves the strongest aggregate performance in the evaluated benchmark, while a simpler four-parameter extension often attains comparable performance with substantially fewer trainable parameters. We additionally characterize the generated state ensembles using the standard fidelity-based expressibility measure, finding that global expressibility does not directly predict classification performance. Our results provide an analytical characterization of parametrized Hamiltonians in Interactive Quantum Classifiers and establish Fourier analysis as a useful framework for understanding and designing open-system-inspired quantum learning models.

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arXiv2026

Quantum-classical hybrid models based on error correction for time series forecasting

Time series forecasting largely benefits from combining the strengths of different models, especially using a scheme where a model corrects another model by capturing supplementary patterns from forecasting errors. Concurrently, quantum models are providing a means to augment the classical capacity, including in time series forecasting, by acting alongside classical models in hybrid architectures. In this work, we propose the first forecasting system based on error correction that jointly uses quantum and classical models. Here, quantum models first extract patterns by exploring quantum phenomena, and classical models capture the remaining patterns from the quantum errors. Compared to classical single models and classical-classical hybrid models based on error correction, the complementary capacity that emerges from this quantum-classical system provided the best results in most of the addressed problems. Therefore, this work paves the way to introduce quantum models in established hybridization schemes for time series forecasting.

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arXiv2025

Regression of Functions by Quantum Neural Networks Circuits

The performance of quantum neural network models depends strongly on architectural decisions, including circuit depth, placement of parametrized operations, and data-encoding strategies. Selecting an effective architecture is challenging and closely related to the classical difficulty of choosing suitable neural-network topologies, which is computationally hard. This work investigates automated quantum-circuit construction for regression tasks and introduces a genetic-algorithm framework that discovers Reduced Regressor QNN architectures. The approach explores depth, parametrized gate configurations, and flexible data re-uploading patterns, formulating the construction of quantum regressors as an optimization process. The discovered circuits are evaluated against seventeen classical regression models on twenty-two nonlinear benchmark functions and four analytical functions. Although classical methods often achieve comparable results, they typically require far more parameters, whereas the evolved quantum models remain compact while providing competitive performance. We further analyze dataset complexity using twelve structural descriptors and show, across five increasingly challenging meta-learning scenarios, that these measures can reliably predict which quantum architecture will perform best. The results demonstrate perfect or near-perfect predictive accuracy in several scenarios, indicating that complexity metrics offer powerful and compact representations of dataset structure and can effectively guide automated model selection. Overall, this study provides a principled basis for meta-learning-driven quantum architecture design and advances the understanding of how quantum models behave in regression settings--a topic that has received limited exploration in prior work. These findings pave the way for more systematic and theoretically grounded approaches to quantum regression.

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arXiv2025

A Quantum Genetic Algorithm Framework for the MaxCut Problem

The MaxCut problem is a fundamental problem in Combinatorial Optimization, with significant implications across diverse domains such as logistics, network design, and statistical physics. The algorithm represents innovative approaches that balance theoretical rigor with practical scalability. The proposed method introduces a Quantum Genetic Algorithm (QGA) using a Grover-based evolutionary framework and divide-and-conquer principles. By partitioning graphs into manageable subgraphs, optimizing each independently, and applying graph contraction to merge the solutions, the method exploits the inherent binary symmetry of MaxCut to ensure computational efficiency and robust approximation performance. Theoretical analysis establishes a foundation for the efficiency of the algorithm, while empirical evaluations provide quantitative evidence of its effectiveness. On complete graphs, the proposed method consistently achieves the true optimal MaxCut values, outperforming the Semidefinite Programming (SDP) approach, which provides up to 99.7\% of the optimal solution for larger graphs. On Erdős-Rényi random graphs, the QGA demonstrates competitive performance, achieving median solutions within 92-96\% of the SDP results. These results showcase the potential of the QGA framework to deliver competitive solutions, even under heuristic constraints, while demonstrating its promise for scalability as quantum hardware evolves.

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arXiv2023

Parametrized constant-depth quantum neuron

Quantum computing has been revolutionizing the development of algorithms. However, only noisy intermediate-scale quantum devices are available currently, which imposes several restrictions on the circuit implementation of quantum algorithms. In this paper, we propose a framework that builds quantum neurons based on kernel machines, where the quantum neurons differ from each other by their feature space mappings. Besides contemplating previous schemes, our generalized framework can instantiate quantum neurons with other feature mappings. We present here a neuron that applies a tensor-product feature mapping to an exponentially larger space. The proposed neuron is implemented by a circuit of constant depth with a linear number of elementary single-qubit gates. The existing neuron applies a phase-based feature mapping with an exponentially expensive circuit implementation, even using multi-qubit gates. Additionally, the proposed neuron has parameters that can change its activation function shape. Here, we show the activation function shape of each quantum neuron. It turns out that parametrization allows the proposed neuron to optimally fit underlying patterns that the existing neuron cannot fit, as demonstrated in the toy problems addressed here. The feasibility of those quantum neuron solutions is also contemplated in the demonstration through executions on a quantum simulator. Finally, we compare those kernel-based quantum neurons in the problem of handwritten digit recognition, where the performances of quantum neurons that implement classical activation functions are also contrasted here. The repeated evidence of the parametrization potential achieved in real-life problems allows concluding that this work provides a quantum neuron with improved discriminative abilities. As a consequence, the generalized framework of quantum neurons can contribute toward practical quantum advantage.

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arXiv2023

On Applying the Lackadaisical Quantum Walk Algorithm to Search for Multiple Solutions on Grids

Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than their classical counterparts. A quantum-walk-based algorithm standing out in the literature is the lackadaisical quantum walk. The lackadaisical quantum walk is an algorithm developed to search graph structures whose vertices have a self-loop of weight $l$. This paper addresses several issues related to applying the lackadaisical quantum walk to search for multiple solutions on grids successfully. Firstly, we show that only one of the two stopping conditions found in the literature is suitable for simulations. We also demonstrate that the final success probability depends on both the space density of solutions and the relative distance between solutions. Furthermore, this work generalizes the lackadaisical quantum walk to search for multiple solutions on grids of arbitrary dimensions. In addition, we propose an optimal adjustment of the self-loop weight $l$ for such $d$-dimensional grids. It turns out other fits of $l$ found in the literature are particular cases. Finally, we observe a two-to-one relation between the steps of the lackadaisical quantum walk and Grover's algorithm, which requires modifications in the stopping condition. In conclusion, this work deals with practical issues one should consider when applying the lackadaisical quantum walk, besides expanding the technique to a broader range of search problems.

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