{"paper":{"title":"A Quantum Algorithm for Solving Linear Differential Equations: Theory and Experiment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dawei Lu, Enrique Solano, Guilu Long, I\\~nigo Arrazola, Jianlian Cui, Junxiang Xiao, Lucas Lamata, ShiJie Wei, Tao Xin, Xiangyu Kong","submitted_at":"2018-07-12T11:49:59Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04553","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1807.04553/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}