{"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/a-quantum-algorithm-for-solving-linear","title":"A Quantum Algorithm for Solving Linear Differential Equations: Theory and Experiment","arxiv_id":"1807.04553","date":"2018-07-12","proceeding":null,"authors":["Tao Xin","Shijie Wei","Jianlian Cui","Junxiang Xiao","Iñigo Arrazola","Lucas Lamata","Xiangyu Kong","Dawei Lu","Enrique Solano","Guilu Long"],"abstract":"We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\\times N$ matrix $\\mathcal{M}$, an $N$-dimensional vector $\\textbf{\\emph{b}}$, and an initial vector $\\textbf{\\emph{x}}(0)$, obtain a target vector $\\textbf{\\emph{x}}(t)$ as a function of time $t$ according to the constraint $d\\textbf{\\emph{x}}(t)/dt=\\mathcal{M}\\textbf{\\emph{x}}(t)+\\textbf{\\emph{b}}$. We show that our algorithm exhibits an exponential speedup over its classical counterpart in certain circumstances. In addition, we demonstrate our quantum algorithm for a $4\\times4$ linear differential equation using a 4-qubit nuclear magnetic resonance quantum information processor. Our algorithm provides a key technique for solving many important problems which rely on the solutions to linear differential equations.","url_abs":"https://arxiv.org/abs/1807.04553v1","url_pdf":"https://arxiv.org/pdf/1807.04553v1.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":"a-quantum-algorithm-for-solving-linear","repo_url":"https://github.com/Dot145/QLinearDiffEqs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"a-quantum-algorithm-for-solving-linear","repo_url":"https://github.com/QuantumBFS/QuDiffEq.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}