2024/06/18 by Igor Ermakov, Tim Byrnes, Ermakov, Igor +3 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Physical sciences #Holomorphic and Operator Theory #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2406.13026
openalex publication_date 2024/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a framework to determine the upper bound to the complexity of a computing a given observable with respect to a Hamiltonian. By considering the Heisenberg evolution of the observable, we show that each Hamiltonian defines an equivalence relation, causing the operator space to be partitioned into equivalence classes. Any operator within a specific class never leaves its equivalence class during the evolution. We provide a method to determine the dimension of the equivalence classes and evaluate it for various models, such as the XY chain and Kitaev model on trees. Our findings reveal that the complexity of operator evolution in the XY model grows from the edge to the bulk, which is physically manifested as suppressed relaxation of qubits near the boundary. Our methods are used to reveal several new cases of simulable quantum dynamics, including a XY-ZZ model which cannot be reduced to free fermions.