{"paper":{"title":"Improved stochastic trace estimation using mutually unbiased bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.NA","quant-ph"],"primary_cat":"cs.NA","authors_text":"J. F. Fitzsimons, J. K. Fitzsimons, M. A. Osborne, S. J. Roberts","submitted_at":"2016-07-30T13:06:05Z","abstract_excerpt":"We examine the problem of estimating the trace of a matrix $A$ when given access to an oracle which computes $x^\\dagger A x$ for an input vector $x$. We make use of the basis vectors from a set of mutually unbiased bases, widely studied in the field of quantum information processing, in the selection of probing vectors $x$. This approach offers a new state of the art single shot sampling variance while requiring only $O(\\log(n))$ random bits to generate each vector. This significantly improves on traditional methods such as Hutchinson's and Gaussian estimators in terms of the number of random "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00117","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"}