SciPost Submission Page
Understanding and utilizing the inner bonds of process tensors
by Moritz Cygorek, Erik M. Gauger
Submission summary
| Authors (as registered SciPost users): | Moritz Cygorek |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2404.01287v2 (pdf) |
| Date submitted: | 2024-11-11 13:39 |
| Submitted by: | Cygorek, Moritz |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Process tensor matrix product operators (PT-MPOs) enable numerically exact simulations for an unprecedentedly broad range of open quantum systems. By representing environment influences in MPO form, they can be efficiently compressed using established algorithms. The dimensions of inner bonds of the compressed PT-MPO may be viewed as an indicator of the complexity of the environment. Here, we show that the inner bonds themselves, not only their dimensions, have a concrete physical meaning: They represent the subspace of the full environment Liouville space which hosts environment excitations that may influence the subsequent open quantum systems dynamics the most. This connection can be expressed in terms of lossy linear transformations, whose pseudoinverses facilitate the extraction of environment observables. We demonstrate this by extracting the environment spin of a central spin problem, the current through a quantum system coupled to two leads, the number of photons emitted from quantum emitters into a structured environment, and the distribution of the total absorbed energy in a driven non-Markovian quantum system into system, environment, and interaction energy terms. Numerical tests further indicate that different PT-MPO algorithms compress environments to similar subspaces. Thus, the physical interpretation of inner bonds of PT-MPOs both provides a conceptional understanding and it enables new practical applications.
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
We are grateful to the Referees for their constructive and positive, and supportive reports. We have addressed the few remaining questions in our response and through revisions to the the manuscript.
We would like to acknowledge that we have identified an error in our treatment of the example where currents into fermionic environments are extracted. The treatment in the first version of our manuscript was correct for an environment consisting of two-levels treated as spins, but did not enforce the proper fermionic canonical anticommutation relations. Our resubmission has been delayed by the theoretical derivation, implementation, and numerical testing of an approach that fixes this issue, both for the calculation of fermionic PT-MPOs as well as for the extraction of currents. We have revised to corresponding section in the manuscript and updated the figure. Note, however, that the final results differ only in minor details, our conclusions remain entirely unaltered, and only a single example was affected.
List of changes
1) In Sec. III.B, we now provide a more detailed discussion and rationale for the particular MPO compression strategy used throughout our article.
2) We have revised the example on the extraction of currents in Sec. IV.B to now fully account for fermionic anticommutation relations.
3) We have added and updated references.
Current status:
Reports on this Submission
Report
I am grateful to the authors for a detailed answer to my comment. I do not want to hold this very interesting manuscript and recommend its publication in its present form.
However, I would like to point out that the MPO-MPS compression can be done in a locally optimal and efficient way by the zipper method described in Section IV of https://arxiv.org/pdf/2310.08533. One can have both the efficiency of the present manuscript and the mixed canonical form warranting the locally optimal truncation.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)