{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:B5UH3YOJFO4LXMB36VF2D3NFIV","short_pith_number":"pith:B5UH3YOJ","schema_version":"1.0","canonical_sha256":"0f687de1c92bb8bbb03bf54ba1eda54572a081e7499fc7e7189166cc7d367503","source":{"kind":"arxiv","id":"1203.3950","version":2},"attestation_state":"computed","paper":{"title":"Search on a Fractal Lattice using a Quantum Random Walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Apoorva Patel, K. S. Raghunathan","submitted_at":"2012-03-18T14:01:11Z","abstract_excerpt":"The spatial search problem on regular lattice structures in integer number of dimensions $d\\geq2$ has been studied extensively, using both coined and coinless quantum walks. The relativistic Dirac operator has been a crucial ingredient in these studies. Here we investigate the spatial search problem on fractals of non-integer dimensions. Although the Dirac operator cannot be defined on a fractal, we construct the quantum walk on a fractal using the flip-flop operator that incorporates a Klein-Gordon mode. We find that the scaling behavior of the spatial search is determined by the spectral (an"},"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":"1203.3950","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-03-18T14:01:11Z","cross_cats_sorted":[],"title_canon_sha256":"20267f320caf25c625cfa7c33c79ee9da689ab1ec1b7d88f6f1994bbb8493318","abstract_canon_sha256":"58dee0e4ec74d230e5e9180a9ac7386f1d228b19df9916fbc4582ca5f9ea6037"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:06.355741Z","signature_b64":"Xw/+D7v7NqkEjX2fg1TfOmAljO3W5DTIKeujOgsq4KPJhNTgnR5AjpP1Anyh8ATdGGa9vH2XjTao+4RIt3WBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f687de1c92bb8bbb03bf54ba1eda54572a081e7499fc7e7189166cc7d367503","last_reissued_at":"2026-05-18T01:58:06.355217Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:06.355217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Search on a Fractal Lattice using a Quantum Random Walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Apoorva Patel, K. S. Raghunathan","submitted_at":"2012-03-18T14:01:11Z","abstract_excerpt":"The spatial search problem on regular lattice structures in integer number of dimensions $d\\geq2$ has been studied extensively, using both coined and coinless quantum walks. The relativistic Dirac operator has been a crucial ingredient in these studies. Here we investigate the spatial search problem on fractals of non-integer dimensions. Although the Dirac operator cannot be defined on a fractal, we construct the quantum walk on a fractal using the flip-flop operator that incorporates a Klein-Gordon mode. We find that the scaling behavior of the spatial search is determined by the spectral (an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3950","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1203.3950","created_at":"2026-05-18T01:58:06.355296+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.3950v2","created_at":"2026-05-18T01:58:06.355296+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3950","created_at":"2026-05-18T01:58:06.355296+00:00"},{"alias_kind":"pith_short_12","alias_value":"B5UH3YOJFO4L","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"B5UH3YOJFO4LXMB3","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"B5UH3YOJ","created_at":"2026-05-18T12:26:58.693483+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/B5UH3YOJFO4LXMB36VF2D3NFIV","json":"https://pith.science/pith/B5UH3YOJFO4LXMB36VF2D3NFIV.json","graph_json":"https://pith.science/api/pith-number/B5UH3YOJFO4LXMB36VF2D3NFIV/graph.json","events_json":"https://pith.science/api/pith-number/B5UH3YOJFO4LXMB36VF2D3NFIV/events.json","paper":"https://pith.science/paper/B5UH3YOJ"},"agent_actions":{"view_html":"https://pith.science/pith/B5UH3YOJFO4LXMB36VF2D3NFIV","download_json":"https://pith.science/pith/B5UH3YOJFO4LXMB36VF2D3NFIV.json","view_paper":"https://pith.science/paper/B5UH3YOJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.3950&json=true","fetch_graph":"https://pith.science/api/pith-number/B5UH3YOJFO4LXMB36VF2D3NFIV/graph.json","fetch_events":"https://pith.science/api/pith-number/B5UH3YOJFO4LXMB36VF2D3NFIV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B5UH3YOJFO4LXMB36VF2D3NFIV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B5UH3YOJFO4LXMB36VF2D3NFIV/action/storage_attestation","attest_author":"https://pith.science/pith/B5UH3YOJFO4LXMB36VF2D3NFIV/action/author_attestation","sign_citation":"https://pith.science/pith/B5UH3YOJFO4LXMB36VF2D3NFIV/action/citation_signature","submit_replication":"https://pith.science/pith/B5UH3YOJFO4LXMB36VF2D3NFIV/action/replication_record"}},"created_at":"2026-05-18T01:58:06.355296+00:00","updated_at":"2026-05-18T01:58:06.355296+00:00"}