arXiv subjects

Leandro Morais

Publications and source records attributed to Leandro Morais.

4 recordsLinked to original sources

arXiv2026

A Representation-Theoretic Framework for Characterizing Barren Plateaus

The scalability of variational quantum algorithms is fundamentally limited by the barren plateau effect, where the cost-function variance vanishes with system size, rendering optimization impractical. Recent Lie-algebraic approaches for deep parameterized have enabled a unified analytical understanding of this challenge but require either the initial state or the measurement observable to belong to the dynamical Lie algebra generated by the circuit. Here, we introduce a representation-theoretic framework under $2$-design hypothesis showing that variational quantum landscapes admit a natural decomposition into irreducible representation channels. This yields exact expressions and analytical bounds for the cost-function variance applicable to arbitrary initial states and observables, with previous Lie-algebraic results emerging as a special case. We illustrate the framework by analyzing the energy landscape of the one-dimensional ANNNI model for several circuit architectures, revealing trainability regimes inaccessible to existing methods. Our results establish a general representation-theoretic framework for analyzing variational quantum landscapes, substantially extending the analytical theory of barren plateaus.

quant-ph↗

arXiv2025

Lie groups for quantum complexity and barren plateau theory

Advances in quantum computing over the last two decades have required sophisticated mathematical frameworks to deepen the understanding of quantum algorithms. In this review, we introduce the theory of Lie groups and their algebras to analyze two fundamental problems in quantum computing as done in some recent works. Firstly, we describe the geometric formulation of quantum computational complexity, given by the length of the shortest path on the $SU(2^n)$ manifold with respect to a right-invariant Finsler metric. Secondly, we deal with the barren plateau phenomenon in Variational Quantum Algorithms (VQAs), where we use the Dynamical Lie Algebra (DLA) to identify algebraic sources of untrainability

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arXiv2025

A variational quantum algorithm for entanglement quantification

Quantum entanglement is a foundational resource in quantum information science, underpinning applications across physics. However, detecting and quantifying entanglement remains a significant challenge. In this article, we introduce a variational quantum algorithm inspired by Uhlmann's theorem to quantify the Bures entanglement of general quantum states, a method that naturally extends to other quantum resources, including genuine multipartite entanglement, quantum discord, quantum coherence, and total correlations, while also enabling reconstruction of the closest free states. The algorithm requires a polynomial number of ancillary qubits and circuit depth relative to the system size, dimensionality, and free state cardinality, making it scalable for practical implementations. Thus, it provides a versatile framework for quantifying quantum resources, demonstrated here through several applications.

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arXiv2025

Distinguishing Ordered Phases using Machine Learning and Classical Shadows

Classifying phase transitions is a fundamental and complex challenge in condensed matter physics. This work proposes a framework for identifying quantum phase transitions by combining classical shadows with unsupervised machine learning. We use the axial next-nearest neighbor Ising model as our benchmark and extend the analysis to the Kitaev-Heisenberg model on a two-leg ladder. Even with few qubits, we can effectively distinguish between the different phases of the Hamiltonian models. {Furthermore, by relying on a restricted set of local observables, such as pairwise correlations and plaquette operators, the sample complexity of the classical shadows protocol scales logarithmically with the number of measured features. This makes our approach a scalable and efficient tool for studying phase transitions in larger many-body systems where classical verification becomes intractable.

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