{"paper":{"title":"Quantum Fast-Forwarding Beyond Reversibility: The $\\alpha$-Perturbed $n$-Cycle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Asim Sharma, Avah Banerjee, Sooraj Sooman","submitted_at":"2026-06-25T04:17:26Z","abstract_excerpt":"Quantum fast-forwarding (QFF) is usually formulated for reversible Markov chains, where the projected quantum walk evolution is exactly governed by Chebyshev polynomials of a Hermitian discriminant matrix. We study whether this framework can be extended to nonreversible dynamics for an $\\alpha$-perturbed $n$-cycle Markov chain, which preserves circulant structure while introducing controlled irreversibility.\n  We show that the nonreversible case has a fundamental obstruction: for $\\alpha \\neq 0$, the eigenvalues of $P_\\alpha$ leave the interval $[-1,1]$, so $T_m(P_\\alpha)$ is not uniformly bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26584","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.26584/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"}