Information-Theoretic Constraints on Variational Quantum Optimization: Efficiency Transitions and the Dynamical Lie Algebra

Fuente: arXiv
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Autor principal: Tan, Jun Liang
Formato: Preprint
Publicado: 2025
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author Tan, Jun Liang
author_facet Tan, Jun Liang
contents Variational quantum algorithms are leading candidates for near-term advantage, yet their scalability is fundamentally limited by the ``Barren Plateau'' phenomenon. While traditionally attributed to geometric concentration of measure, I propose an information-theoretic origin: a bandwidth bottleneck in the optimization feedback loop. By modeling the optimizer as a coherent Maxwell's Demon, I derive a thermodynamic constitutive relation, $ΔE \leq ηI(S:A)$, where work extraction is strictly bounded by the mutual information established via entanglement. I demonstrate that systems with polynomial Dynamical Lie Algebra (DLA) dimension exhibit ``Information Superconductivity'' (sustained $η> 0$), whereas systems with exponential DLA dimension undergo an efficiency collapse when the rate of information scrambling exceeds the ancilla's channel capacity. These results reframe quantum trainability as a thermodynamic phase transition governed by the stability of information flow.
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id arxiv_https___arxiv_org_abs_2512_14701
institution arXiv
publishDate 2025
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spellingShingle Information-Theoretic Constraints on Variational Quantum Optimization: Efficiency Transitions and the Dynamical Lie Algebra
Tan, Jun Liang
Quantum Physics
Emerging Technologies
81P68, 82B26, 68Q12
F.1.1; F.2.2; J.2
Variational quantum algorithms are leading candidates for near-term advantage, yet their scalability is fundamentally limited by the ``Barren Plateau'' phenomenon. While traditionally attributed to geometric concentration of measure, I propose an information-theoretic origin: a bandwidth bottleneck in the optimization feedback loop. By modeling the optimizer as a coherent Maxwell's Demon, I derive a thermodynamic constitutive relation, $ΔE \leq ηI(S:A)$, where work extraction is strictly bounded by the mutual information established via entanglement. I demonstrate that systems with polynomial Dynamical Lie Algebra (DLA) dimension exhibit ``Information Superconductivity'' (sustained $η> 0$), whereas systems with exponential DLA dimension undergo an efficiency collapse when the rate of information scrambling exceeds the ancilla's channel capacity. These results reframe quantum trainability as a thermodynamic phase transition governed by the stability of information flow.
title Information-Theoretic Constraints on Variational Quantum Optimization: Efficiency Transitions and the Dynamical Lie Algebra
topic Quantum Physics
Emerging Technologies
81P68, 82B26, 68Q12
F.1.1; F.2.2; J.2
url https://arxiv.org/abs/2512.14701