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Quantum many-body simulations with PauliStrings.jl
by Nicolas Loizeau, J. Clayton Peacock, Dries Sels
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Submission summary
| Authors (as registered SciPost users): | Nicolas Loizeau |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202410_00034v2 (pdf) |
| Code repository: | https://github.com/nicolasloizeau/PauliStrings.jl |
| Code version: | v1.5.0 |
| Code license: | MIT |
| Date accepted: | 2025-03-10 |
| Date submitted: | 2025-01-27 18:51 |
| Submitted by: | Loizeau, Nicolas |
| Submitted to: | SciPost Physics Codebases |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We present the Julia package PauliStrings.jl for quantum many-body simulations, which performs fast operations on the Pauli group by encoding Pauli strings in binary. All of the Pauli string algebra is encoded into low-level logic operations on integers, and is made efficient by various truncation methods which allow for systematic extrapolation of the results. We illustrate the effectiveness of our package by (i) performing Heisenberg time evolution through direct numerical integration and (ii) by constructing a Liouvillian Krylov space. We benchmark the results against tensor network methods, and we find our package performs favorably. In addition, we show that this representation allows for easy encoding of any geometry. We present results for chaotic and integrable spin systems in 1D as well as some examples in 2D. Currently, the main limitations are the inefficiency of representing non-trivial pure states (or other low-rank operators), as well as the need to introduce dissipation to probe long-time dynamics.
List of changes
- Equations (6,7,10,11) in section 2 have been corrected
- Algorithms 1 and 2 have been rewritten more clearly
- The second paragraph of 'Tensor networks' has been updated to clarify the notions of MPS and MPO
- A few references have been added
- infinite temperature inner product - > Frobenius inner product
- Add the sentence : "Note that Algorithm 2 can easily be adapted to higher dimensions by iterating over the necessary shifts corresponding to each dimension."
Published as SciPost Phys. Codebases 54 (2025) , SciPost Phys. Codebases 54-r1.5 (2025)
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All my previous remarks have been addressed in a satisfactory manner.
I would only suggest to speak of rank-3 (or rank-4) instead of 3-dimensional (or 4-dimensional) tensors in the "Tensor networks" section.
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