{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3OAHU66XLLVHDK3SXCJJ2Z3LGT","short_pith_number":"pith:3OAHU66X","schema_version":"1.0","canonical_sha256":"db807a7bd75aea71ab72b8929d676b34d4f02fd63f9a72a050c4076cb84b90fb","source":{"kind":"arxiv","id":"1606.02136","version":3},"attestation_state":"computed","paper":{"title":"Oscillatory Localization of Quantum Walks Analyzed by Classical Electric Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Andris Ambainis, Jevg\\=enijs Vihrovs, Kri\\v{s}j\\=anis Pr\\=usis, Thomas G. Wong","submitted_at":"2016-06-07T13:44:39Z","abstract_excerpt":"We examine an unexplored quantum phenomenon we call oscillatory localization, where a discrete-time quantum walk with Grover's diffusion coin jumps back and forth between two vertices. We then connect it to the power dissipation of a related electric network. Namely, we show that there are only two kinds of oscillating states, called uniform states and flip states, and that the projection of an arbitrary state onto a flip state is bounded by the power dissipation of an electric circuit. By applying this framework to states along a single edge of a graph, we show that low effective resistance i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.02136","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T13:44:39Z","cross_cats_sorted":[],"title_canon_sha256":"a65514411a256ebace1705c3a33bed476b9b8511d513c8d05ee6b7e92f2c8aef","abstract_canon_sha256":"bd08dd64561491ad97681ab4549186864418670466624a10ecc9422f71c1edd3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:36.254257Z","signature_b64":"xgst3TbyzBLN1NfJMWhAH1YCG9zKtK9hMtG7sth7IAR0YyKGezmWO8kYtFR9YZco40pQIQM5ydNGtGgRuERYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db807a7bd75aea71ab72b8929d676b34d4f02fd63f9a72a050c4076cb84b90fb","last_reissued_at":"2026-05-18T00:54:36.253582Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:36.253582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Oscillatory Localization of Quantum Walks Analyzed by Classical Electric Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Andris Ambainis, Jevg\\=enijs Vihrovs, Kri\\v{s}j\\=anis Pr\\=usis, Thomas G. Wong","submitted_at":"2016-06-07T13:44:39Z","abstract_excerpt":"We examine an unexplored quantum phenomenon we call oscillatory localization, where a discrete-time quantum walk with Grover's diffusion coin jumps back and forth between two vertices. We then connect it to the power dissipation of a related electric network. Namely, we show that there are only two kinds of oscillating states, called uniform states and flip states, and that the projection of an arbitrary state onto a flip state is bounded by the power dissipation of an electric circuit. By applying this framework to states along a single edge of a graph, we show that low effective resistance i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02136","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.02136","created_at":"2026-05-18T00:54:36.253679+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.02136v3","created_at":"2026-05-18T00:54:36.253679+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02136","created_at":"2026-05-18T00:54:36.253679+00:00"},{"alias_kind":"pith_short_12","alias_value":"3OAHU66XLLVH","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"3OAHU66XLLVHDK3S","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"3OAHU66X","created_at":"2026-05-18T12:29:55.572404+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT","json":"https://pith.science/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT.json","graph_json":"https://pith.science/api/pith-number/3OAHU66XLLVHDK3SXCJJ2Z3LGT/graph.json","events_json":"https://pith.science/api/pith-number/3OAHU66XLLVHDK3SXCJJ2Z3LGT/events.json","paper":"https://pith.science/paper/3OAHU66X"},"agent_actions":{"view_html":"https://pith.science/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT","download_json":"https://pith.science/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT.json","view_paper":"https://pith.science/paper/3OAHU66X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.02136&json=true","fetch_graph":"https://pith.science/api/pith-number/3OAHU66XLLVHDK3SXCJJ2Z3LGT/graph.json","fetch_events":"https://pith.science/api/pith-number/3OAHU66XLLVHDK3SXCJJ2Z3LGT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT/action/storage_attestation","attest_author":"https://pith.science/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT/action/author_attestation","sign_citation":"https://pith.science/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT/action/citation_signature","submit_replication":"https://pith.science/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT/action/replication_record"}},"created_at":"2026-05-18T00:54:36.253679+00:00","updated_at":"2026-05-18T00:54:36.253679+00:00"}