Information-Theoretic Constraints on Variational Quantum Optimization: Efficiency Transitions and the Dynamical Lie Algebra
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915687987937280 |
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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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14701 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| 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 |