{"paper":{"title":"Bounds on the dynamics of periodic quantum walks and emergence of the gapless and gapped Dirac equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"C. M. Chandrashekar, N. Pradeep Kumar, Radhakrishna Balu, Raymond Laflamme","submitted_at":"2017-11-16T04:26:34Z","abstract_excerpt":"We study the dynamics of discrete-time quantum walk using quantum coin operations, $\\hat{C}(\\theta_1)$ and $\\hat{C}(\\theta_2)$ in time-dependent periodic sequence. For the two-period quantum walk with the parameters $\\theta_1$ and $\\theta_2$ in the coin operations we show that the standard deviation [$\\sigma_{\\theta_1, \\theta_2} (t)$] is the same as the minimum of standard deviation obtained from one of the one-period quantum walks with coin operations $\\theta_1$ or $\\theta_2$, $\\sigma_{\\theta_1, \\theta_2}(t) = \\min \\{\\sigma_{\\theta_1}(t), \\sigma_{\\theta_2}(t) \\}$. Our numerical result is anal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05920","kind":"arxiv","version":2},"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"}