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Recipes for the Digital Quantum Simulation of Lattice Spin Systems
by Guido Burkard
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Submission summary
| Authors (as registered SciPost users): | Guido Burkard |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2209.07918v2 (pdf) |
| Date accepted: | 2025-02-25 |
| Date submitted: | 2025-02-21 18:46 |
| Submitted by: | Burkard, Guido |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We describe methods to construct digital quantum simulation algorithms for quantum spin systems on a regular lattice with local interactions. In addition to tools such as the Trotter-Suzuki expansion and graph coloring, we also discuss the efficiency gained by parallel execution of an extensive number of commuting terms. We provide resource estimates and quantum circuit elements for the most important cases and classes of spin systems. As resource estimates we indicate the total number of gates N and simulation time T, expressed in terms of the number n of spin 1/2 lattice sites (qubits), target accuracy ϵ, and simulated time t. We provide circuit constructions that realize the simulation time T(1)∝nt2/ϵ and T(2q)∝t1+ηnη/ϵη for arbitrarily small η=1/2q for the first-order and higher-order Trotter expansions. We also discuss the potential impact of scaled gates, which have not yet been fully explored.
Author comments upon resubmission
I'd like to thank the anonymous referee for their reading of the paper and for the helpful comments.
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I have strengthened the link between scaled gates and the concept of digital-analog quantum simulation of Ref. [8] at several places in the text.
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Also, I have corrected an embarrassingly large number of typos (thanks for the hint)
I hope that with these changes, the paper can be accepted for SciPost Core.
List of changes
- Added the text: "The concept of scaled gates is also related to the analog blocks in digital-analog quantum simulations [8]."
towards the end of the third paragraph of the Introduction.
- Added the text: "(see also the concept of digital-analog simulation [8])"
in the discussion of scaled gates in Section III, bottom of page 3.
- Added the text: ", similar to the analog blocks in digital-analog simulation [8]."
in the Section V, 3rd paragraph (bottom of page 4).
- Corrected several typos throughout the manuscript.
The reference occurring in these changes is:
[8] L. Lamata, A. Parra-Rodriguez, M. Sanz, and E. Solano, Digital-analog quantum simulations with superconducting circuits,
Advances in Physics: X 3, 1457981 (2018), https://doi.org/10.1080/23746149.2018.1457981
Published as SciPost Phys. Core 8, 030 (2025)