Details
| Original language | English |
|---|---|
| Article number | L040201 |
| Journal | Physical Review A |
| Volume | 107 |
| Issue number | 4 |
| Publication status | Published - 6 Apr 2023 |
Abstract
The Trotter product formula is a key instrument in numerical simulations of quantum systems. However, computers cannot deal with continuous degrees of freedom, such as the position of particles in molecules, or the amplitude of electromagnetic fields. It is therefore necessary to discretize these variables to make them amenable to digital simulations. Here, we give sufficient conditions to conclude the validity of this approximate discretized physics. Essentially, it depends on the state-dependent Trotter error, for which we establish explicit bounds that are also of independent interest.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
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In: Physical Review A, Vol. 107, No. 4, L040201, 06.04.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - State-dependent Trotter limits and their approximations
AU - Burgarth, Daniel
AU - Galke, Niklas
AU - Hahn, Alexander
AU - Van Luijk, Lauritz
N1 - Funding Information: Acknowledgments. D.B. thanks P. Facchi and D. Berry for interesting discussions. A.H. would like to thank C. Kargı for a helpful exchange on the numerical simulations. L.v.L. thanks R. F. Werner for helpful discussions and suggestions. D.B. acknowledges funding by the Australian Research Council (Projects No. FT190100106, No. DP210101367, and No. CE170100009). N.G. was supported by MCIN with funding from European Union NextGenerationEU (PRTR-C17.I1) and by the Generalitat de Catalunya. A.H. was supported by the Sydney Quantum Academy. L.v.L. acknowledges support by the Quantum Valley Lower Saxony.
PY - 2023/4/6
Y1 - 2023/4/6
N2 - The Trotter product formula is a key instrument in numerical simulations of quantum systems. However, computers cannot deal with continuous degrees of freedom, such as the position of particles in molecules, or the amplitude of electromagnetic fields. It is therefore necessary to discretize these variables to make them amenable to digital simulations. Here, we give sufficient conditions to conclude the validity of this approximate discretized physics. Essentially, it depends on the state-dependent Trotter error, for which we establish explicit bounds that are also of independent interest.
AB - The Trotter product formula is a key instrument in numerical simulations of quantum systems. However, computers cannot deal with continuous degrees of freedom, such as the position of particles in molecules, or the amplitude of electromagnetic fields. It is therefore necessary to discretize these variables to make them amenable to digital simulations. Here, we give sufficient conditions to conclude the validity of this approximate discretized physics. Essentially, it depends on the state-dependent Trotter error, for which we establish explicit bounds that are also of independent interest.
UR - http://www.scopus.com/inward/record.url?scp=85152948774&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2209.14787
DO - 10.48550/arXiv.2209.14787
M3 - Article
AN - SCOPUS:85152948774
VL - 107
JO - Physical Review A
JF - Physical Review A
SN - 2469-9926
IS - 4
M1 - L040201
ER -