{"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/quantum-wave-simulation-with-sources-and-loss","title":"Quantum Wave Simulation with Sources and Loss Functions","arxiv_id":"2411.17630","date":"2024-11-26","proceeding":null,"authors":["Cyrill Bösch","Malte Schade","Giacomo Aloisi","Scott D. Keating","Andreas Fichtner"],"abstract":"We present a quantum algorithmic framework for simulating linear, anti-Hermitian (lossless) wave equations in heterogeneous, anisotropic, and time-independent media. This framework encompasses a broad class of wave equations, including the acoustic wave equation, Maxwell$'$s equations and the elastic wave equation. Our formulation is compatible with standard numerical discretization schemes and allows for the efficient implementation of multiple practically relevant time- and space-dependent sources. Furthermore, we demonstrate that subspace energies can be extracted and wave fields compared through an $l_2$ loss function, achieving optimal precision scaling with the number of samples taken. Additionally, we introduce techniques for incorporating boundary conditions and linear constraints that preserve the anti-Hermitian nature of the equations. Leveraging the Hamiltonian simulation algorithm, our framework achieves a quartic speed-up over classical solvers in 3D simulations, under conditions of sufficiently global measurements and compactly supported sources and initial conditions. This quartic speed-up is optimal for time-domain solutions, as the Hamiltonian of the discretized wave equations has local couplings. In summary, our framework provides a versatile approach for simulating wave equations on quantum computers, offering substantial speed-ups over state-of-the-art classical methods.","url_abs":"https://arxiv.org/abs/2411.17630v3","url_pdf":"https://arxiv.org/pdf/2411.17630v3.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":"quantum-wave-simulation-with-sources-and-loss","repo_url":"https://github.com/malteschade/Quantum-Wave-Simulation-with-Sources-and-Loss-Functions","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","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}