{"paper":{"title":"RFOX (Rotated-Field Oscillatory eXchange) quantum algorithm: Towards Parameter-Free Quantum Optimizers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The RFOX algorithm maintains an essentially flat spectral gap independent of interpolation parameter and disorder strength.","cross_cats":["math.OC"],"primary_cat":"quant-ph","authors_text":"Brian Garc\\'ia Sarmina, Guo-Hua Sun, Shi-Hai Dong","submitted_at":"2026-04-02T22:44:10Z","abstract_excerpt":"We introduce RFOX (Rotated-Field Oscillatory eXchange), a parameter-free quantum algorithm for combinatorial optimization that combines an almost constant non-stoquastic $XX$ catalyst with a weak harmonic $ZX$ counter-diabatic term. Using the Floquet-Magnus expansion, we derive an effective Hamiltonian whose leading-order $\\mathcal{O}(\\delta/\\omega)$ corrections yield local $Y$ fields, field-modulated 2-body terms, and poly-local 3-body topological interactions driven by graph connectivity. This structure ensures a nearly flat instantaneous spectral gap, preventing the unpredictable gap collap"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The instantaneous spectral gap remains essentially flat, independent of both the interpolation parameter and the disorder strength, modulated only by a δ parameter.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the Floquet-Magnus expansion at high drive frequency accurately captures the effective Hamiltonian such that the derived corrections preserve gap flatness for the full range of disorder strengths and system sizes.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"RFOX keeps the instantaneous spectral gap flat across interpolation and disorder by using a constant XX catalyst plus derived ZX counter-diabatic drive, yielding faster ground-state convergence on small RFIM instances.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The RFOX algorithm maintains an essentially flat spectral gap independent of interpolation parameter and disorder strength.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5793e65f0325aebdfc1dfebb615319c2f93c890500e20a7314ccac319925d1ba"},"source":{"id":"2604.02569","kind":"arxiv","version":3},"verdict":{"id":"8f1ae61d-6ee7-4581-94db-c9cff91e58cb","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T20:18:15.293563Z","strongest_claim":"The instantaneous spectral gap remains essentially flat, independent of both the interpolation parameter and the disorder strength, modulated only by a δ parameter.","one_line_summary":"RFOX keeps the instantaneous spectral gap flat across interpolation and disorder by using a constant XX catalyst plus derived ZX counter-diabatic drive, yielding faster ground-state convergence on small RFIM instances.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the Floquet-Magnus expansion at high drive frequency accurately captures the effective Hamiltonian such that the derived corrections preserve gap flatness for the full range of disorder strengths and system sizes.","pith_extraction_headline":"The RFOX algorithm maintains an essentially flat spectral gap independent of interpolation parameter and disorder strength."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.02569/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":2,"snapshot_sha256":"5d30f41f22127c9a04c731b1e0b0a54731cdb610732140aa464dc3013f406a44"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}