{"paper":{"title":"Undecidability of Hitting Times in Computably Described Quantum Dynamics: A No-Go Theorem for Universal Time Selection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"No algorithm exists that can output the hitting time for every computable quantum state and unitary evolution.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Katsufumi Matsuura","submitted_at":"2025-12-11T08:17:18Z","abstract_excerpt":"We study the Unitary Hitting Time Problem (UHTP) in quantum dynamics. Given computably described pure states |a>, |b> and a time-dependent unitary U(t), define the hitting time as the infimum of t > 0 such that the fidelity between U(t)|a> and |b> reaches a fixed threshold (with infinity if the threshold is never reached). We prove that there is no total algorithm that outputs this hitting time for all inputs; equivalently, the total UHTP is undecidable via a reduction from the halting problem. Operationally, we show a no-go theorem: for any fixed accuracy parameters, there is no universal fin"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that there is no total algorithm that outputs this hitting time for all inputs; equivalently, the total UHTP is undecidable via a reduction from the halting problem. Operationally, we show a no-go theorem: for any fixed accuracy parameters, there is no universal finite-resource protocol that, for all computably described inputs, correctly outputs the hitting time while obeying uniform finite upper bounds on observation time and on dissipation/work.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The proofs assume systems capable of embedding universal computation via reversible computation into unitary dynamics and a fixed-target beacon construction with continuous-time lifting via piecewise-constant Hamiltonians.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The Unitary Hitting Time Problem is undecidable by reduction from the halting problem, with an operational no-go for any universal finite-time protocol.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"No algorithm exists that can output the hitting time for every computable quantum state and unitary evolution.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"53b64b3886bba4f49a31f46597d9b44488100f14d7be1e091236ced6f7b30bda"},"source":{"id":"2512.11006","kind":"arxiv","version":3},"verdict":{"id":"2351cb52-200b-4bd9-be57-3f944d338c07","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T23:36:34.934396Z","strongest_claim":"We prove that there is no total algorithm that outputs this hitting time for all inputs; equivalently, the total UHTP is undecidable via a reduction from the halting problem. Operationally, we show a no-go theorem: for any fixed accuracy parameters, there is no universal finite-resource protocol that, for all computably described inputs, correctly outputs the hitting time while obeying uniform finite upper bounds on observation time and on dissipation/work.","one_line_summary":"The Unitary Hitting Time Problem is undecidable by reduction from the halting problem, with an operational no-go for any universal finite-time protocol.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The proofs assume systems capable of embedding universal computation via reversible computation into unitary dynamics and a fixed-target beacon construction with continuous-time lifting via piecewise-constant Hamiltonians.","pith_extraction_headline":"No algorithm exists that can output the hitting time for every computable quantum state and unitary evolution."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.11006/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":"fdf99f67c4884a2192f67224435081234a9e057c89a2cc90a56bc528030651c5"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}