SciPost Submission Page
Recipes for the Digital Quantum Simulation of Lattice Spin Systems
by Guido Burkard
This is not the latest submitted version.
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Guido Burkard |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2209.07918v1 (pdf) |
| Date submitted: | 2025-01-21 16:57 |
| Submitted by: | Burkard, Guido |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| 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 been fully explored yet.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2025-2-12 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2209.07918v1, delivered 2025-02-12, doi: 10.21468/SciPost.Report.10656
Strengths
The topic of digital quantum simulation is enhanced via the analysis of strategies for scaling up the simulated models via commuting terms which can be implemented in parallel, perhaps by means of native interactions which are named scaled gates here. Moreover, a novelty I find here is the time of the simulator analysis, which is interesting, especially in terms of the mentioned "scaled gates" which can reduce the implementation time of the simulator. This is also related to the analog blocks in digital-analog quantum simulations referred to in Ref. (8) in the submitted version, and perhaps this could be more explicitly mentioned, even though I think that the time analysis is rather new in this context, and possibly useful.
Weaknesses
Several typos throughout the paper should be corrected. A clearer mention of digital-analog quantum simulations as connected to the current concept in this paper of scaled gates should be mentioned (these are similar to the analog blocks in this paradigm).
Report
The topic of digital quantum simulation is enhanced via the analysis of strategies for scaling up the simulated models via commuting terms which can be implemented in parallel, perhaps by means of native interactions which are named scaled gates here. Moreover, a novelty I find here is the time of the simulator analysis, which is interesting, especially in terms of the mentioned "scaled gates" which can reduce the implementation time of the simulator. This is also related to the analog blocks in digital-analog quantum simulations referred to in Ref. (8) in the submitted version, and perhaps this could be more explicitly mentioned, even though I think that the time analysis is rather new in this context, and possibly useful.
Several typos throughout the paper should be corrected. A clearer mention of digital-analog quantum simulations as connected to the current concept in this paper of scaled gates should be mentioned (these are similar to the analog blocks in this paradigm).
Recommendation
Ask for minor revision