Parts | Days | Selection | Search | Updates | Downloads | Help
QI: Fachverband Quanteninformation
QI 22: Quantum Simulation I
QI 22.3: Talk
Thursday, March 21, 2024, 10:15–10:30, HFT-FT 101
Strong error bounds for Trotter & Strang Splittings and their implications to Quantum Chemistry — •Daniel Burgarth1, Paolo Facchi2, Alexander Hahn3, Mattias Johnsson4, and Kazuya Yuasa4 — 1FAU Erlangen-Nürnberg — 2University of Bari — 3Macqaurie University — 4Waseda University
Efficient error estimates for the Trotter product formula are central in quantum computing, mathematical physics and numerical simulations (strang-splitting and split-step algorithms). However, the dependency of the Trotter error on the actual input state is not properly understood and not much is known for the important case of unbounded operators. Here, we develop such a general theory of error estimation for the Trotter product formula and higher-order product formulas with an explicit dependency on the input state. These bounds have two crucial advantages over the operator norm estimates in the literature: First, previous bounds are too pessimistic as they quantify the worst-case scenario. Second, previous bounds become trivial for unbounded operators. Therefore, they cannot be applied to a wide class of Trotter scenarios, including atomic and molecular Hamiltonians considered in chemistry simulations. By providing state-dependent bounds, we overcome both problems and are able to treat errors in chemistry simulations from an analytical perspective.
Keywords: Quantum Simulation; Trotter; Strang Splitting; Error Bounds