Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 430-449 |
| Number of pages | 20 |
| Journal | Linear Algebra and Its Applications |
| Volume | 730 |
| DOIs | |
| State | Published - Feb 1 2026 |
Funding
This manuscript has been partially authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).The authors would like to thank the referee for the very careful reading of our manuscript, and for his or her numerous comments and suggestions, which greatly enhanced the quality and readability of the paper. S. C. is supported by the DOE Advanced Scientific Computing Research (ASCR) Accelerated Research in Quantum Computing (ARQC) Program under field work proposal 3ERKJ354. A.D. is supported by DOE Office of Nuclear Physics (NP) through the “Quantum learning for accelerated nuclear science” (QLASS) project under FWP ERKBP91. This work was initiated during Z.W.'s visit to Oak Ridge National Laboratory in Summer 2024, supported by the DOE Office of High Energy Physics (HEP) under grant ERKAP89. Z.W. extends his gratitude to Oak Ridge National Laboratory for their warm hospitality and generous support during the visit. S. C. is supported by the DOE Advanced Scientific Computing Research (ASCR) Accelerated Research in Quantum Computing (ARQC) Program under field work proposal 3ERKJ354 . A.D. is supported by DOE Office of Nuclear Physics (NP) through the “Quantum learning for accelerated nuclear science” (QLASS) project under FWP ERKBP91 . This work was initiated during Z.W.'s visit to Oak Ridge National Laboratory in Summer 2024, supported by the DOE Office of High Energy Physics (HEP) under grant ERKAP89 . Z.W. extends his gratitude to Oak Ridge National Laboratory for their warm hospitality and generous support during the visit. This manuscript has been partially authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( http://energy.gov/downloads/doe-public-access-plan ).
Keywords
- Error estimate
- Higher order approximation
- Jordan-Banach algebra
- Trotter product formula