State-dependent Trotter Limits and their approximations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911785083207680 |
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| author | Burgarth, Daniel Galke, Niklas Hahn, Alexander van Luijk, Lauritz |
| author_facet | Burgarth, Daniel Galke, Niklas Hahn, Alexander van Luijk, Lauritz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_14787 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | State-dependent Trotter Limits and their approximations Burgarth, Daniel Galke, Niklas Hahn, Alexander van Luijk, Lauritz Quantum Physics Mathematical Physics 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. |
| title | State-dependent Trotter Limits and their approximations |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2209.14787 |