ArticleNPJ quantum information2024
Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies.
Article in NPJ quantum information, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- Does provable absence of barren plateaus imply classical simulability?Nature communications · 2025Review
- Characterizing barren plateaus in quantum ansätze with the adjoint representation.Nature communications · 2024Article
- A Lie algebraic theory of barren plateaus for deep parameterized quantum circuits.Nature communications · 2024Article
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Abstract
Much is understood about 1-dimensional spin chains in terms of entanglement properties, physical phases, and integrability. However, the Lie algebraic properties of the Hamiltonians describing these systems remain largely unexplored. In this work, we provide a classification of all Lie algebras generated by the terms of 2-local spin chain Hamiltonians, or so-called dynamical Lie algebras, on 1-dimensional linear and circular lattice structures. We find 17 unique dynamical Lie algebras. Our classification includes some well-known models such as the transverse-field Ising model and the Heisenberg chain, and we also find more exotic classes of Hamiltonians that appear new. In addition to the closed and open spin chains, we consider systems with a fully connected topology, which may be relevant for quantum machine learning approaches. We discuss the practical implications of our work in the context of variational quantum computing, quantum control and the spin chain literature.
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