{"paper":{"title":"Enhancing the Harrow-Hassidim-Lloyd (HHL) algorithm in systems with large condition numbers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.chem-ph","quant-ph"],"primary_cat":"physics.atom-ph","authors_text":"Akshaya Jayashankar, K. Sugisaki, Nishanth Baskaran, Peniel Bertrand Tsemo, Sayan Chakraborty, V. S. Prasannaa","submitted_at":"2024-07-31T14:41:30Z","abstract_excerpt":"Although the Harrow-Hassidim-Lloyd (HHL) algorithm offers an exponential speedup in system size for treating linear equations of the form $A\\vec{x}=\\vec{b}$ on quantum computers when compared to their traditional counterparts, it faces a challenge related to the condition number ($\\mathcal{\\kappa}$) scaling of the $A$ matrix. In this work, we address the issue by introducing the post-selection-improved HHL (Psi-HHL) framework that operates on a simple yet effective premise: subtracting mixed and wrong signals to extract correct signals while providing the benefit of optimal scaling in the cond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.21641","kind":"arxiv","version":4},"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/2407.21641/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"}