2024/12/29 by Sarah Chehade, Chehade, Sarah, Andrea Delgado +5
Computer Science · Mathematics · #15A16(Primary) #17C65 #17C90 #46H70(Secondary) #81P45 #81R15 #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2412.20604
openalex publication_date 2024/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In quantum computing, Trotter estimates are critical for enabling efficient simulation of quantum systems and quantum dynamics, help implement complex quantum algorithms, and provide a systematic way to control approximate errors. In this paper, we extend the analysis of Trotter-Suzuki approximations, including third and higher orders, to Jordan-Banach algebras. We solve an open problem in our earlier paper on the existence of second-order Trotter formula error estimation in Jordan-Banach algebras. To illustrate our work, we apply our formula to simulate Trotter-factorized spins, and show improvements in the approximations. Our approach demonstrates the adaptability of Trotter product formulas and estimates to non-associative settings, which offers new insights into the applications of Jordan algebra theory to operator dynamics.