{"paper":{"title":"Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Davide Orsucci, Rolando D. Somma, Yigit Subasi","submitted_at":"2018-05-26T22:34:02Z","abstract_excerpt":"We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state $\\vert x \\rangle$ that is proportional to the solution of the system of linear equations $A \\vec{x}=\\vec{b}$. The time complexities of our algorithms are $O(\\kappa^2 \\log(\\kappa)/\\epsilon)$ and $O(\\kappa \\log(\\kappa)/\\epsilon)$, where $\\kappa$ is the condition number of $A$ and $\\epsilon$ is the precision. Both algorithms are constructed using families of Hamiltonians that are linear combinations of products of $A$, the projector onto the initial state"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10549","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}