SciPost Submission Page
A numerical approach for calculating exact non-adiabatic terms in quantum dynamics
by Ewen D C Lawrence, Sebastian F J Schmid, Ieva Čepaitė, Peter Kirton, Callum W Duncan
Submission summary
| Authors (as registered SciPost users): | Peter Kirton · Ewen Lawrence |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2401.10985v2 (pdf) |
| Code repository: | https://github.com/ewenlawrence/mAGPy |
| Date submitted: | 2024-09-20 14:53 |
| Submitted by: | Lawrence, Ewen |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Understanding how non-adiabatic terms affect quantum dynamics is fundamental to improving various protocols for quantum technologies. We present a novel approach to computing the Adiabatic Gauge Potential (AGP), which gives information on the non-adiabatic terms that arise from time dependence in the Hamiltonian. Our approach uses commutators of the Hamiltonian to build up an appropriate basis of the AGP, which can be easily truncated to give an approximate form when the exact result is intractable. We use this approach to study the AGP obtained for the transverse field Ising model on a variety of graphs, showing how the different underlying graph structures can give rise to very different scaling for the number of terms required in the AGP.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
20 September 2024
Dear Editor, This letter accompanies the resubmission of our manuscript “A numerical approach for calcu- lating exact non-adiabatic terms in quantum dynamics” for publication in SciPost Physics. All of the referees were positive about the novelty and usefulness of our results. Their concerns lie with the lack of detail about the implementation of our method and the lack of source code availability for the reproduction of our results. With the revised version of our manuscript we have addressed these issues as detailed below as well as all of the other concerns raised by the referees.
We hope that with these responses, our manuscript is now suitable for publication. Yours Sincerely,
Ewen D C Lawrence, Sebastian FJ Schmid, Ieva ˇCepait˙e, Peter Kirton and Callum W Duncan
List of changes
Summary of major changes to the manuscript:
• A complete rewrite of section 3
– Included all necessary equations for using the method into the main text
– Moved the flow chart from the appendix to help clarify the steps in the OCE method
– Included a detailed example of finding the operator basis for a simple 2 site problem.
– Discussion on mathematical structures surrounding the dynamical Lie algebra e.g.
chaos and controlability.
• Updated Section 4.3 on the LMG model to more fully describe the result obtained.
• Supplied links to the source code used to produce all results in form of the mAGPy
package