arXiv subjects

João T. Dias

Publications and source records attributed to João T. Dias.

4 recordsLinked to original sources

arXiv2026

Training-Free Certified Bounds for Quantum Regression: A Scalable Framework

We present a training-free, certified error bound for quantum regression derived directly from Pauli expectation values. Generalizing the heuristic of minimum accuracy from classification to regression, we evaluate axis-aligned predictors within the Pauli feature space. We formally prove that the optimal axis-aligned predictor constitutes a rigorous upper bound on the minimum training Mean Squared Error (MSE) attainable by any linear or kernel-based regressor defined on the same quantum feature map. Since computing this exact bound requires an intractable scan of the full Pauli basis, we introduce a Monte Carlo framework to efficiently estimate it using a tractable subset of measurement axes. We further provide non-asymptotic statistical guarantees to certify performance within a practical measurement budget. This method enables rapid comparison of quantum feature maps and early diagnosis of expressivity, allowing for the informed selection of architectures before deploying higher-complexity models.

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arXiv2025

Certified Lower Bounds and Efficient Estimation of Minimum Accuracy in Quantum Kernel Methods

The minimum accuracy heuristic evaluates quantum feature maps without requiring full quantum support vector machine (QSVM) training. However, the original formulation is computationally expensive, restricted to balanced datasets, and lacks theoretical backing. This work generalizes the metric to arbitrary binary datasets and formally proves it constitutes a certified lower bound on the optimal empirical accuracy of any linear classifier in the same feature space. Furthermore, we introduce Monte Carlo strategies to efficiently estimate this bound using a random subset of Pauli directions, accompanied by rigorous probabilistic guarantees. These contributions establish minimum accuracy as a scalable, theoretically sound tool for pre-screening feature maps on near-term quantum devices.

quant-ph↗

arXiv2025

New Algorithm for Structured OFDM Channel Estimation using Subgroup Duality

This paper presents a group-theoretic framework for structured channel estimation in Orthogonal Frequency Division Multiplexing (OFDM). By modeling subcarriers as the cyclic group \(\mathbb{Z}_N\), we show that nulling a subgroup \(H \subseteq \mathbb{Z}_N\) constrains the channel impulse response to its annihilator \(H^\perp\) in the dual domain. A low-complexity estimator is proposed that detects such structure by evaluating energy concentration across candidate annihilators. Simulations demonstrate consistent gains in mean squared error, bit error rate, and throughput compared with least-squares and linear minimum mean square error baselines, achieving competitive performance with substantially lower complexity and preserved interpretability.

eess.SP↗

arXiv2023

Implementation and Performance Analysis of a Low Resolution OFDM System Prototype With Low Cost Hardware

The present work focus on the implementation and analyze of performance of a low-resolution OFDM system prototype with low-cost hardware. A software defined radio (SDR) system was chosen in this implementation due to its various advantages over a traditional radio system. Among the options of SDR devices available, the use of universal software radio peripherals (USRP) was avoided due to its high cost, despite its popularity in this field of research. Alternatively, a combination of two low-cost SDRs, "Hackrf One" and "RTL- SDR Blog V3" with the GNU Radio, a popular, free and open source radio software, were used. Thus, it was possible to emulate the behavior of a low resolution ADC in the receiver, characterize its performance and estimate its energy savings. This allowed us to determine the feasibility of building a component with the analog-to-digital conversion function with few bits of resolution. We conclude that the performance of an ADC with at least 5 bits of resolution is pretty reasonable and that this reduction in the number of bits, in comparison to 8-bit ADC, represents a fairly expressive energy saving.

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