arXiv subjects

Jordi Pérez-Guijarro

Publications and source records attributed to Jordi Pérez-Guijarro.

6 recordsLinked to original sources

arXiv2026

Analysis of the sample complexity for PAC-learning functions defined over quantum states

A fundamental question in PAC learning is determining the number of labeled examples required to learn a concept class to a desired accuracy and confidence. In classical learning theory, this quantity is characterized by the VC-dimension, while several quantum generalizations have established analogous results when examples are provided in quantum superposition. In this work, we study a distinct quantum PAC-learning model in which concepts are functions acting on quantum states. We demonstrate that the VC-dimension, although still relevant, fails to fully capture the sample complexity of this model. To further characterize this setting, we develop a new lower bound on the required number of samples and establish an upper bound when the states in the domain are linearly independent. Remarkably, this upper bound has a form similar to the classical PAC-learning bound. We further examine a setting in which the learner receives more informative data and show that the limitations of the VC-dimension persist in this extended model.

quant-ph↗

arXiv2025

Limitations of Using Identical Distributions for Training and Testing When Learning Boolean Functions

When the distributions of the training and test data do not coincide, the problem of understanding generalization becomes considerably more complex, prompting a variety of questions. Prior work has shown that, for some fixed learning methods, there are scenarios where training on a distribution different from the test distribution improves generalization. However, these results do not account for the possibility of choosing, for each training distribution, the optimal learning algorithm, leaving open whether the observed benefits stem from the mismatch itself or from suboptimality of the learner. In this work, we address this question in full generality. That is, we study whether it is always optimal for the training distribution to be identical to the test distribution when the learner is allowed to be optimally adapted to the training distribution. Surprisingly, assuming the existence of one-way functions, we find that the answer is no. That is, matching distributions is not always the best scenario. Nonetheless, we also show that when certain regularities are imposed on the target functions, the standard conclusion is recovered in the case of the uniform distribution.

cs.LG↗

arXiv2025

Bounds in Sequential Unambiguous Discrimination of Multiple Pure Quantum States

Sequential methods for quantum hypothesis testing offer significant advantages over fixed-length approaches, which rely on a predefined number of state copies. Despite their potential, these methods remain underexplored for unambiguous discrimination. In this work, we derive performance bounds for such methods when applied to the discrimination of a set of pure states. The performance is evaluated based on the expected number of copies required. We establish a lower bound applicable to any sequential method and an upper bound on the optimal sequential method. The upper bound is derived using a novel and simple non-adaptive method. Importantly, the gap between these bounds is minimal, scaling logarithmically with the number of distinct states.

quant-ph↗

arXiv2025

On classical advice, sampling advice and complexity assumptions for learning separations

In this paper, we study the relationship between advice in the form of a training set and classical advice. We do this by analyzing the class $\mathsf{BPP/samp}$ and certain variants of it. Specifically, our main result demonstrates that $\mathsf{BPP/samp}$ is a proper subset of the class $\mathsf{P/poly}$, which implies that advice in the form of a training set is strictly weaker than classical advice. This result remains valid when considering quantum advice and a quantum generalization of the training set. Finally, leveraging the insights from our proofs, we identify both sufficient and necessary complexity-theoretic assumptions for the existence of concept classes that exhibit a quantum learning speed-up. We consider both the worst-case setting, where accurate results are required for all inputs, and the average-case setting.

quant-ph↗

arXiv2024

Extension of Clifford Data Regression Methods for Quantum Error Mitigation

To address the challenge posed by noise in real quantum devices, quantum error mitigation techniques play a crucial role. These techniques are resource-efficient, making them suitable for implementation in noisy intermediate-scale quantum devices, unlike the more resource-intensive quantum error correction codes. A notable example of such a technique is Clifford Data Regression, which employs a supervised learning approach. This work investigates two variants of this technique, both of which introduce a non-trivial set of gates into the original circuit. The first variant uses multiple copies of the original circuit, while the second adds a layer of single-qubit rotations. Different characteristics of these methods are analyzed theoretically, such as their complexity, or the scaling of the error with various parameters. Additionally, the performance of these methods is evaluated through numerical experiments, demonstrating a reduction in root mean square error.

quant-ph↗

arXiv2023

Relation between quantum advantage in supervised learning and quantum computational advantage

The widespread use of machine learning has raised the question of quantum supremacy for supervised learning as compared to quantum computational advantage. In fact, a recent work shows that computational and learning advantage are, in general, not equivalent, i.e., the additional information provided by a training set can reduce the hardness of some problems. This paper investigates under which conditions they are found to be equivalent or, at least, highly related. The existence of efficient algorithms to generate training sets emerges as the cornerstone of such conditions. These results are applied to prove that there is a quantum speed-up for some learning tasks based on the prime factorization problem, assuming the classical intractability of this problem.

quant-ph↗