{"paper":{"title":"Quantum algorithm for the nonlinear Schr\\\"odinger equation via the Lax-pair scattering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Chenjia Zhu, Yousheng Zhang, Yue Yang, Zhaoyuan Meng","submitted_at":"2026-06-28T08:46:47Z","abstract_excerpt":"The nonlinear Schr\\\"odinger equation (NLSE) governs a broad class of wave phenomena, including deep-water waves, quantum turbulence, and solitons. The multiscale spatiotemporal coupling inherent in these systems imposes severe computational bottlenecks on classical high-fidelity numerical simulations. While quantum computing offers the potential for exponential speedup, its unitary dynamics pose a fundamental challenge to solve the NLSE. We propose a quantum framework based on the Lax-pair scattering for solving the 1D NLSE. Specifically, the physical field is first mapped into the spectral sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29276","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/2606.29276/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"}