Quantum 2025 – wissenschaftliches Programm
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MON: Monday Contributed Sessions
MON 2: Quantum Control
MON 2.4: Vortrag
Montag, 8. September 2025, 15:00–15:15, ZHG002
Lower bounds for the Trotter error — •Alexander Hahn1, Paul Hartung2, Daniel Burgarth2,1, Paolo Facchi3,4, and Kazuya Yuasa5 — 1Center for Engineered Quantum Systems, Macquarie University, 2109 NSW, Australia — 2Department Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany — 3Dipartimento di Fisica, Università di Bari, I-70126 Bari, Italy — 4Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari, Italy — 5Department of Physics, Waseda University, Tokyo 169-8555, Japan
In analog and digital simulations of practically relevant quantum systems, the target dynamics can only be implemented approximately. The Trotter product formula is the most common approximation scheme as it is a generic method which allows tuning accuracy. The Trotter simulation precision will always be inexact for noncommuting operators, but it is currently unknown what the minimum possible error is. This is an important quantity because upper bounds for the Trotter error are known to often be vast overestimates. Here we present explicit lower bounds on the error, in norm and on states, allowing to derive minimum resource requirements. Numerical comparison with the true error shows that our bounds offer accurate and tight estimates.
Based on Phys. Rev. A 111, 022417
https://doi.org/10.1103/PhysRevA.111.022417
Keywords: Quantum Simulation; Quantum Computing; Trotter Product Formula; Lower Bounds; Complexity