{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/destructive-error-interference-in-product","title":"Destructive Error Interference in Product-Formula Lattice Simulation","arxiv_id":"1912.11047","date":"2019-12-23","proceeding":null,"authors":["Minh C. Tran","Su-Kuan Chu","Yuan Su","Andrew M. Childs","Alexey V. Gorshkov"],"abstract":"Quantum computers can efficiently simulate the dynamics of quantum systems. In this paper, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product formula algorithm. We show that the errors from different Trotterization steps in the algorithm can interfere destructively, yielding a much smaller error than previously estimated. In particular, we prove that the total error in simulating a nearest-neighbor interacting system of $n$ sites for time $t$ using the first-order product formula with $r$ time slices is $O({nt}/{r}+{nt^3}/{r^2})$ when $nt^2/r$ is less than a small constant. Given an error tolerance $\\epsilon$, the error bound yields an estimate of $\\max\\{O({n^2t}/{\\epsilon}),O({n^2 t^{3/2}}/{\\epsilon^{1/2}})\\}$ for the total gate count of the simulation. The estimate is tighter than previous bounds and matches the empirical performance observed in Childs et al. [PNAS 115, 9456-9461 (2018)]. We also provide numerical evidence for potential improvements and conjecture an even tighter estimate for the gate count.","url_abs":"http://arxiv.org/abs/1912.11047v1","url_pdf":"http://arxiv.org/pdf/1912.11047v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"destructive-error-interference-in-product","repo_url":"https://github.com/jue-xu/interference-trotter-error","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}