{"paper":{"title":"Tight Bound for Estimating Expectation Values from a System of Linear Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Abhijeet Alase, Barry C. Sanders, Mohsen Bagherimehrab, Peter H{\\o}yer, Robert R. Nerem","submitted_at":"2021-11-20T00:10:51Z","abstract_excerpt":"The System of Linear Equations Problem (SLEP) is specified by a complex invertible matrix $A$, the condition number $\\kappa$ of $A$, a vector $b$, a Hermitian matrix $M$ and an accuracy $\\epsilon$, and the task is to estimate $x^\\dagger Mx$, where $x$ is the solution vector to the equation $Ax = b$. We aim to establish a lower bound on the complexity of the end-to-end quantum algorithms for SLEP with respect to $\\epsilon$, and devise a quantum algorithm that saturates this bound. To make lower bounds attainable, we consider query complexity in the setting in which a block encoding of $M$ is gi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.10485","kind":"arxiv","version":3},"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/2111.10485/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"}