{"paper":{"title":"Quantum singular value decomposition of non-sparse low-rank matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Adrian Steffens, Patrick Rebentrost, Seth Lloyd","submitted_at":"2016-07-19T05:19:59Z","abstract_excerpt":"In this work, we present a method to exponentiate non-sparse indefinite low-rank matrices on a quantum computer. Given an operation for accessing the elements of the matrix, our method allows singular values and associated singular vectors to be found quantum mechanically in a time exponentially faster in the dimension of the matrix than known classical algorithms. The method extends to non-Hermitian and non-square matrices via embedding matrices. In the context of the generic singular value decomposition of a matrix, we discuss the Procrustes problem of finding a closest isometry to a given m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05404","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":""},"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"}