{"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-amplitude-damping-for-solving","title":"Quantum amplitude damping for solving homogeneous linear differential equations: A noninterferometric algorithm","arxiv_id":"2111.05646","date":"2021-11-10","proceeding":null,"authors":["João H. Romeiro","Frederico Brito"],"abstract":"In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum hardware can conceptually enable such high-dimensional problems to be solved with a foreseeable number of qubits, whilst also yielding quantum advantage in terms of time complexity. Nevertheless, in order to bridge towards experimental realizations with several qubits and harvest such potential in a short-term basis, one must dispose of efficient quantum algorithms that are compatible with near-term projections of state-of-the-art hardware, in terms of both techniques and limitations. As the conception of such algorithms is no trivial task, insights on new heuristics are welcomed. This work proposes a novel approach by using the Quantum Amplitude Damping operation as a resource, in order to construct an efficient quantum algorithm for solving homogeneous LDEs. As the intended implementation involves performing Amplitude Damping exclusively via a simple equivalent quantum circuit, our algorithm shall be given by a gate-level quantum circuit (predominantly composed of elementary 2-qubit gates) and is particularly nonrestrictive in terms of connectivity within and between some of its main quantum registers. We show that such an open quantum system-inspired circuitry allows for constructing the real exponential terms in the solution in a non-interferometric way; we also provide a guideline for guaranteeing a lower bound on the probability of success for each realization, by exploring the decay properties of the underlying quantum operation.","url_abs":"https://arxiv.org/abs/2111.05646v2","url_pdf":"https://arxiv.org/pdf/2111.05646v2.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-amplitude-damping-for-solving","repo_url":"https://github.com/jhromeiro/Quantum-sim-AD","is_official":0,"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}